Module 3

Module 3—Electrical Phenomena

 

Module Introduction

 

In Module 3 you will explore electrical phenomena and the behaviour of electrical charges. You will see how an understanding of electricity was built up over time through experimentation. You will explore the similarities between electrical phenomena and gravity, and see how the equations for working with both are similar. You will also learn how to describe electrical phenomena and transmission using electric field theory.

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Module 3—Electrical Phenomena

 

Big Picture

 

Have you ever spent a summer’s day hiking in the mountains? If you have, you know it’s important to keep an eye on cloud formations so you can anticipate stormy weather. Anticipating bad weather is about more than keeping dry—late afternoon thunderstorms can be a real hazard in open areas at high elevations.

 

Even when precautions are taken, storm clouds can suddenly blow in from behind a nearby ridge, giving only minutes’ warning that a storm is approaching. In these circumstances, hikers are urged to avoid ridges and trees and to wait in as low a location as possible for the storm to pass. As the storm clouds pass overhead, if the hikers notice that their skin starts to tingle, their hair stands on end, and/or the ends of metal gear starts to hum and spark, then lightning may be about to strike. This is an example of static electricity. You will learn more about this in this module.

 

As you are working in Module 3, keep the following questions in mind:

• How is it that thunderclouds, kilometers overhead, can produce such dramatic effects on the ground below?

• What is physically transferred between the cloud and the ground when lightning strikes?
  
  

• How can the energy transfer in events like this be described?

Module Assessment

 

Each lesson has a teacher-marked assignment, based on work completed in the lesson. In addition, you will be graded on your contributions to the Discuss section of each lesson.

 

You will also be asked to complete Self-Check or Try This questions, which you should place in your Physics 30 course folder. These are not formally assessed but are a valuable way to practise the concepts and skills of the lesson. These activities can provide you with reflective feedback on your understanding of the lesson work.

 

You will be marked for your lesson work on the following items:

• Module 3: Lesson 1 Assignment

• Module 3: Lesson 2 Assignment

• Module 3: Lesson 3 Assignment

• Module 3: Lesson 4 Assignment

• Module 3: Lesson 5 Assignment
• Module 3: Lesson 6 Assignment

At the end of the module you will complete a module assessment that consists of two Diploma Exam-style written-response questions. The first question will assess your knowledge of charge-to-mass ratios and the second question will assess your knowledge of electromagnetic induction.  See the Module Assessment page for more information.

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Module 3—Electrical Phenomena

 

In This Module

 

Lesson 1—Electrostatics

 

In this lesson, you will explore static electricity, conductors, insulators, charge conservation, and the three methods of transferring charge.

 

You will investigate the following essential questions:

• Can the concepts that explain large-scale phenomena like lightning be explored using small-scale equipment like a Van de Graaff generator?

• How can these concepts explain what happens to charges within a cloud during a lightning strike?

Lesson 2—Investigating Coulomb’s Law

 

If charges can interact and exert forces on one another over great distances, how can the interaction of these charges be described? If the law of universal gravitation describes the force of attraction of one mass on another mass, then which law explains the force that acts on one charge due to another charge?

 

In this lesson you will explore the work of Charles Coulomb and learn how the results of his torsion balance experiments led to an equation describing the electrostatic force between two objects, now known as Coulomb’s law.

 

You will investigate the following essential questions:

• What is Coulomb’s law, and how was this law determined using the results of experiments?
  
  
• Can Coulomb’s law predict the effect of electrostatic force if the distance of separation increases by a known amount? What does the answer to this question suggest about lightning safety?

Lesson 3—Applying Coulomb’s Law

 

In this lesson you will apply Coulomb’s law to the exploration of both large-scale and extremely small-scale phenomena.

 

You will investigate the following essential questions:

• How much charge is transferred in a lightning strike, and how is this amount of charge measured?
  
  
• How can Coulomb’s law be applied to predict the net force acting on one point charge due to the presence of other point charges? How does this sort of analysis relate to the symmetry found in crystals?

Lesson 4—Electric Fields

 

In this lesson you will study electric fields and how to describe and analyze their effects.

 

You will investigate the following essential questions:

• What is an electric field, and how can an electric field be described and analyzed?
  
  
• What exactly is St. Elmo’s fire, and why does it occur at the end of tall pointed surfaces like lightning rods and ships’ masts?

Lesson 5—Electric Potential Energy

 

In this lesson you will study electric fields and how they lead to electric potential energy. You will learn that there are similarities with gravitational potential energy.

 

You will investigate the following essential questions:

• What is electric potential energy? How is it similar to gravitational potential energy?
  
  
• What is voltage? How is voltage calculated?

Lesson 6—The Motion of Charges in Uniform Electric Fields

 

In this lesson you will study the motion of charged particles in electric fields. You will compare this to motion in other fields you have previously studied.

 

You will investigate the following essential questions:

• How do charged particles move in a uniform electric field? How is this motion similar to a mass moving in a gravitational field?
  
  
• Is it possible to predict the velocity, acceleration, and displacement of charged particles moving in electric fields?

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Module 3—Electrical Phenomena

 

Lesson 1—Electrostatics

Get Focused

 

This photograph shows a young woman at a lookout platform in a mountain park. Her brother was so surprised to see her hair standing on end that he took this photograph. Moments after the photograph was taken, lightning struck the platform, seriously injuring the woman and others on the platform.

 

What caused the woman’s hair to stand on end? How was this an indicator that lightning was about to strike? Is there a safe way to observe and analyze related phenomena in the lab?

 

In this lesson you will focus on answering the following essential questions:

• Can the concepts that explain large-scale phenomena like lightning be explored using small-scale equipment like a Van de Graaff generator?

• How can these concepts explain what happens to charges within a cloud during a lightning strike?

Module 3 Lesson 1 Assignments

 

Your teacher-marked Module 3, Lesson 1 Assignment requires you to submit a response to the following questions:

• Assignment—A 1, A 2, A 3, and A 4
• Discuss—D 4

The other questions in this lesson are not marked by the teacher; however, you should still answer these questions. The Self-Check and Try This questions are placed in this lesson to help you review important information and build key concepts that may be applied in future lessons.

 

After a discussion with your teacher, you must decide what to do with the questions that are not part of your assignment. For example, you may decide to submit to your teacher the responses to Try This questions that are not marked. You should record the answers to all the questions in this lesson and place those answers in your course folder.

Required Materials and Equipment

For this lesson, you will need

• two spherical balloons (about 25 cm in diameter)
• 2 m of thread
• something made from wool (e.g., a piece of cloth, wool sweater, sock, tuque, or blanket)

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Module 3—Electrical Phenomena

 

Explore

 

The effect observed in this photo is due to static electricity, as was the case in the photo of the woman in Get Focused. In this case it is produced by the machine the girl is touching—a Van de Graaff generator. It’s a powerful tool for studying static electricity. It can safely illustrate many of the key concepts that are involved in more complicated phenomena like lightning. You’re going to learn more about the nature of the electrical transmission that occurs in a lightning strike, starting with a Van de Graaff generator.

Try This: Charging Objects Using a Van de Graaff Generator

 

Think about charging objects using a Van de Graaff generator as you answer these questions:

 

TR 1. What do you already know about static electricity?

 

TR 2. How would you explain a person’s hair standing on end when he or she touches a Van de Graaff generator?

 

In this activity you will have a chance to apply what you know as you explore a number of intriguing demonstrations.

 

Your initial explanations of these ideas will mark your starting point as you begin this module. Even if you aren’t sure, go ahead and hypothesize as you determine what’s going on.

Lab Choice

 

This activity can be done in two ways. If you have access to a supervised science lab equipped with the materials and equipment listed on page 511 of your textbook, use Method A. If you do not have access to these facilities, use Method B. Both methods will require you to refer to page 511 in your textbook.

 

Method A: Using a Supervised Science Lab

 

Follow the instructions described in the “QuickLab” on page 511 of your textbook.

 

Method B: Without a Supervised Science Lab

 

Open the Charging Objects Using a Van de Graaff Generator multimedia object. This multimedia object follows the instructions outlined in the “QuickLab” on page 511 of your textbook, so you’ll need your textbook too.

 

Module 3: Lesson 1 Assignment

 

Remember to submit the answer to A 1 to your teacher as part of your assignment.

 

A 1. Record your observations and explanations for each of the following objects that interacted with the charged globe of the Van de Graaff generator:

1. animal fur
2. aluminum pie plates
3. confetti
4. soap bubbles

You will have a chance to revise some of your explanations by the end of this lesson.

 

Charging a Balloon

 

You can produce your own electrostatic effects using two balloons, about 2 m of thread, and a wool sweater.

 

Self-Check

 

SC 1. Inflate one of the balloons. Use about 1 m of thread to tie the balloon to a high point in a room away from any walls. A light fixture works well for this. Rub the balloon with the wool sweater; then bring the sweater close to the balloon but don’t let them touch. Record your observations.

 

SC 2. Inflate the second balloon and tie it to the same spot as the first balloon. Ensure that the centres of the balloons are at the same height above the floor. Rub each balloon vigorously with the wool sweater, and then observe what happens to each balloon. Record your observations.

 

SC 3. Apply Newton’s third law to the electrostatic forces that act on each balloon.

 

SC 4. Draw a free-body diagram to illustrate the forces acting on each balloon.

 

 

Read

 

Your experiences with the balloons are similar to electrostatic events that people have been observing for thousands of years. The basic properties of electricity were developed from these experiences. You can learn more about what other ancient peoples thought about lightning and electricity by reading page 510 and the top half of page 512 of your textbook.

 

Self-Check

 

You can check your understanding by answering these questions.

 

 

 

 

 

 

SC 5. Explain how the law of charges applies to the balloons shown in the preceding photographs.

 

SC 6. Recall your observations of the Van de Graaff generator lab earlier in this lesson. Provide one example of an object repelling and one example of an object attracting in the lab activity.

 

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Module 3—Electrical Phenomena

 

The Two Types of Charge

 

People developed an understanding of electricity gradually. Many of the earliest ideas came from everyday experiences. For example, if you scuff your feet while walking over a carpet, you can cause a charge to build up, which leads to a nasty shock when you touch a person or an object. Have you ever used these effects to give yourself or someone else a shock?

 

You’ll see from reading your textbook that observations from everyday experiences led to a series of experiments. These experiments established that there are, in fact, two types of electric charges.

 

Read

 

Read the information found on the bottom half of page 512 and the top half of page 513 of your textbook. It outlines the contributions of Benjamin Franklin and others to the study of electricity.

 

Self-Check

 

You can check your understanding by answering these questions:

 

SC 7. Identify the two types of electric charges.

 

SC 8. Refer to the “infoBIT” on page 513 of your textbook. Suggest a reason why doctors and nurses wear special slippers while working with patients receiving oxygen.

 

Conductors and Insulators

 

Today, electricity is essential to almost every daily activity. Whether it’s cooking, listening to music, or communicating with someone far away, electricity is likely involved. Cables, such as the ones shown in this photograph, are found in nearly every modern electrical device. The centre of the cable is made from copper while the outside is covered in a durable plastic coating. How does the arrangement of the electrons within a piece of copper make copper a good material for transferring electrical energy? How does the arrangement of the electrons within a piece of plastic make this material an ideal protective coating for the cable?

 

Read

 

To find out why electrical cables are built from these materials, read “The Modern Theory of Electrostatics” on pages 513 and 514 of your textbook.

 

Self-Check

You can check your understanding by answering these questions:

SC 9. Look around at your surroundings.

1. Identify two materials that are conductors. Describe the essential characteristic that makes these materials conductors.
   
   
2. Identify two materials that are insulators. Describe the essential characteristic that makes these materials insulators.

SC 10. Refer to subatomic structures to explain why electrical cables are often made with a core of copper wire surrounded by a protective plastic coating.

 

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Module 3—Electrical Phenomena

 

Detecting Charge

 

In the Big Picture for this module, hikers could tell that lightning was about to strike if their skin started to tingle, their hair stood on end, or the pointed tips of metal equipment started to spark or glow. These all acted as detectors of the huge amounts of charge in a thundercloud overhead.

 

A more sophisticated way to detect the presence of a charged object is to use an electroscope. The most common type of electroscope consists of two thin, metal "leaves" suspended from a metal rod in a container. The conducting metal rod is supported by an insulating rubber stopper to ensure that charges do not pass from the rod to the container.

 

 

 

Any excess charge on the electroscope can be removed by simply touching the knob with your finger. This is called grounding. Since the leaves are uncharged, they neither attract nor repel. Instead, the leaves hang loosely together.

 

If a negatively charged object is brought near the knob, the electrons on the knob are repelled, so they migrate to the leaves. Since both leaves are negatively charged, they repel one another and diverge. In the presence of a larger charge, the leaves separate even more.

 

Self-Check

 

You can check your understanding by answering these questions.

 

SC 11. Compare the electrical conductivity of the metal rod, leaves, and knob with the electrical conductivity of the rubber stopper.
 
SC 12. Sketch a diagram to show why the leaves of an electroscope diverge in the presence of a negative charge. Remember that only the outermost electrons are free to move in a conductor; therefore, the positive charges remain locked in the nucleus of each atom.

 

SC 13. Sketch a diagram or provide a written description to show why the leaves of an electroscope diverge in the presence of a positive charge.

 

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Module 3—Electrical Phenomenon

 

Three Methods of Transferring Charge

 

Method 1: Charging by Friction

 

When you rubbed the balloon with the wool sweater earlier in this activity, you were charging both of these objects by friction. When two objects are charged this way, one always develops a positive charge while the other develops a negative charge. Why is this always the case? The answer has to do with the law of conservation of charge.

 

Read

 

You can learn about the law of conservation of charge and charging by friction by reading “Methods of Charging Objects” beginning on page 517 and ending on page 519 of your textbook.

 

Self-Check

 

You can check your understanding by answering these questions:

 

SC 14. The balloon is made from a material that holds its electrons more tightly than wool.

1. If a balloon is rubbed with wool, state the resulting charge on the balloon and on the wool.
   
   
2. Explain why the process of rubbing the balloon with the wool does not generate additional electrons.
   
   
3. Explain why it is essential for the balloon to be an insulator in order for the excess charges on its surface to remain in place.

SC 15. Answer “Concept Check” question 1 on the bottom of page 518 of your textbook. As you answer this question, be sure to include the charge that ebonite acquires.

 

 

Three Methods of Transferring Charge

 

Method 2: Charging by Conduction

 

 

Watch and Listen

 

You can see how an electroscope can be charged by conduction by selecting the “Charge by Conduction” button in the linked animation.

Read

 

The law of conservation of charge is also used to explain what occurs when an object is charged by conduction. To find out more about this, read “Charging Objects by Conduction” on page 519 of your textbook.

 

Self-Check

 

You can check your understanding by answering these questions:

 

SC 16. Use the idea of conduction to explain what happens when you get a shock from a doorknob after acquiring excess electrons from scuffing your feet across a floor.

 

SC 17. Explain what occurs when a positively charged object is touched to the knob of a neutral electroscope.

 

 

Three Methods of Transferring Charge

 

Method 3: Charging by Induction

 

 

Watch and Listen

 

You can see how an electroscope can be charged by induction by selecting the “Charge by Induction” button in the linked animation.

Read

 

The most complex method of giving an object a charge is charging by induction. You can learn more about this procedure by reading “Charging Objects by Induction” on pages 520 and 521 of your textbook.

 

Self-Check

 

You can check your understanding by answering these questions:

 

SC 18. Define induction.

 

SC 19. The link Induction with a Negative Source shows a negative source charging an electroscope by induction. Write a concise description or illustrate with labels to explain what is occurring during each step of this process.

 

SC 20. Take one of your balloons and rub it vigorously with the wool sweater once again. Place the balloon high against a smooth, dry wall. See if the balloon will stick. If it does not, try recharging the balloon with the wool.

Concisely explain why the balloon can remain stuck to the wall and why this effect is able to last for many minutes.

 

SC 21. Sketch a series of diagrams to show how a positive source could charge an electroscope by induction. Write a concise description or illustrate with labels to explain what is occurring during each step of this process.

 

 

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Module 3—Electrical Phenomena

 

Reflect and Connect

 

Retrieve the chart of your explanations of what happened using the Van de Graaff generator at the beginning of the lesson. Now that you have explored the three methods of transferring charge, you may need to reconsider your previous explanations.

 

Before you revise your chart, you need a little background information about the charge on the top of a Van de Graaff generator.

 

The globe of the Van de Graaff generator becomes negatively charged as excess electrons are transferred from a connection to the ground. This is done as a fast-moving belt rushes by metal combs at the top and bottom of the machine. Since the globe of the Van de Graaff generator is a conductor, the excess electrons redistribute themselves evenly over the surface of the globe. These excess electrons cannot return to the base because the rubber belt and the plastic column supporting the globe are insulators.

 

It takes work to force electrons to move from the ground connection at the base to the globe at the top. This is why input energy must be supplied by the motor of the generator to rotate the rubber belt on its two pulleys. You’ll learn more about the energy required to do work on moving charges in later lessons.

 

Module 3: Lesson 1 Assignment

 

Remember to submit the answers to A 2 and A 3 to your teacher as part of your Module 3: Lesson 1 Assignment.

 

A 2. As you saw in the opening activity for this lesson, objects were placed on the globe of the Van de Graaff generator.

 

In each case, electrons were transferred from the negatively charged globe of the Van de Graaff generator to each of these objects. The result was that individual objects became negatively charged.

 

Use what you have learned in this lesson to explain the behaviour of each of these objects after the Van de Graaff generator was turned on. Submit your revised explanations for each of the following demonstrations to your teacher:

1. animal fur
2. aluminum pie plates
3. confetti

A 3. Place your explanations from A 2 alongside the explanations you developed in A 1 at the beginning of this lesson. Contrast the two sets of explanations to identify the most significant improvements that you have made to your explanations. Remember to add the answers to this question to your course folder.

 

Try This: Explaining the Behaviour of the Soap Bubbles

 

Now that you have improved upon your explanations of the first three Van de Graaff generator demonstrations, reconsider the behaviour of the soap bubbles.

 

 

The behaviour of the soap bubbles is much more complex than that of the animal fur, the pie plates, or the confetti because the soap bubbles are subject to a sequence of interconnected events.

 

These events have been organized into the four steps listed below. In each step, describe what is happening and then explain. You can check your answers by clicking on the Description and Explanation buttons.

 

Step 1: Neutral soap bubbles are attracted to the negative globe.

 

 

For more information, click on Description and Explanation.

 

 

 

Step 2: The first soap bubble collides with the globe and becomes negatively charged.

 

 

For more information, click on Description and Explanation.

 

 

 

Step 3: The repelled tiny negative droplets collide with incoming soap bubbles.

 

 

For more information, click on Description and Explanation.

 

 

 

Step 4: Incoming bubbles are repelled and move away from the negatively charged globe.

 

 

For more information, click on Description and Explanation.

 

 

 

 

Big Picture Reflection

 

Connecting Bubbles and Lightning Strikes

 

In the previous section you worked at describing and explaining what happens to a soap bubble near the negatively charged globe of a Van de Graaff generator.

 

You might be surprised to know that the principles explained in this demonstration can also be applied to lightning.

 

Read

 

Carefully read the section called “How Lightning Gets Its Charge” on page 522 of your physics textbook. As you read this section, look for similarities between lightning and the soap bubble demonstration.

 

Discuss

 

D 1. Summarize the piece from the textbook called “How Lightning Gets Its Charge” by writing or illustrating a series of steps that will concisely describe and explain what occurs in this process. Your result should be in a format similar to the steps used to describe and explain the soap bubble in the previous activity. Remember to add the answer to this question to your course folder.

 

D 2. Post your summary to the discussion area set up by your teacher. Compare your summary to at least one other explanation produced by another student. Identify similarities and differences between your work and the work of other students. Remember to add the answer to this question to your course folder.

 

D 3. If you were to update your explanation of lightning based on what you learned in D 2, what changes would you make? Remember to add the answer to this question to your course folder.

 

Module 3: Lesson 1 Assignment

 

Remember to submit the answer to D 4 to your teacher as part of your assignment.

 

D 4. Use your answers to Discuss questions D 1, D 2, and D 3 to revise your explanation of how lightning gets its charge. Submit your revised summary to your instructor as part of your assignment.

 

 

Module 3: Lesson 1 Assignment

 

Remember to submit your Module 3: Lesson 1 Assignment, including question A 4 to your teacher for marks.

 

A 4. Do question 10 of “10.1 Check and Reflect” on page 523 of your physics textbook.

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Module 3—Electrical Phenomena

 

Lesson Summary

 

At the start of this lesson you were asked two essential questions:

• Can the concepts that explain large-scale phenomena like lightning be explored using small-scale equipment like a Van de Graaff generator?
  
  
• How can these concepts explain what happens to charges within a cloud during a lightning strike?

You have seen that charged balloons, soap bubbles, and machines like a Van de Graaff generator can effectively model many of the key concepts that are essential to understanding electrostatics. These concepts include the attraction and repulsion of charges, the law of conservation of charge, and the three methods of transferring charge—by friction, by conduction, and by induction. All of these ideas come into play to describe how lightning gets its charge.
 

In the next lesson you will have an opportunity to develop a more precise description of the interactions between charges as you explore the equation that describes the electric force between two charges.

 

Lesson Glossary

 

grounding: the process of transferring charge to and from Earth

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Module 3—Electrical Phenomena

 

Lesson 2—Investigating Coulomb’s Law

 

Get Focused

 

This is the young woman at the observation platform of a national park whom you met in the previous lesson. Recall that charges in a nearby thundercloud caused her hair to stand on end. Although the exact details of what happened that day are unknown, the following diagram shows what this scene may have looked like from a different perspective.

 

This illustration shows a hiker standing far below the platform, somewhere in the valley. Since the hiker is about four times as far from the negative charges in the cloud, the hiker is in a much safer location than the people on the platform. For the hiker in the valley, it would be unlikely that the charge in the cloud could induce a charge on strands of hair. There wouldn’t be a large enough force to make these hairs stand on end. If the distance were four times farther, how would the electrostatic force be affected? Would the force be ¼ as large for the hiker as for the people on the observation platform?

 

Charles de Coulomb, in 1785, investigated the precise relationship between electrostatic forces and distance of separation. Coulomb was a former military engineer. He used his engineering skills to design and build a precision device to explore the variables that affect electric forces. The results of his work provide a precise description of the electric force that exists between two charged objects separated by a known distance.

 

In this lesson you will focus on the following essential questions:

• What is Coulomb’s law, and how was this law determined using the results of experiments?

• Can Coulomb’s law predict the effect on electrostatic force if the distance of separation increases by a known amount? What does the answer to this question suggest about lightning safety?

Module 3: Lesson 2 Assignment

 

Your teacher-marked Module 3: Lesson 2 Assignment requires you to submit a response to the following questions:

• Assignment—A 1 and A 2

You must decide what to do with the questions that are not marked by the teacher.

 

Remember that these questions provide you with the practice and feedback that you need to successfully complete this course. You should respond to all the questions and place those answers in your course folder.

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Module 3—Electrical Phenomena

 

Explore

A Link Between Electrostatics and Gravitation

 

Coulomb did not begin his work on determining the electric force law on his own. As the following timeline indicates, other scientists had already done much of the essential groundwork. You might be surprised to know that the essential ideas came from Isaac Newton’s work on gravitation.

 

Date	Scientist	Contribution to Coulomb’s Work
1687	Isaac Newton	Published his great book Mathematical Principles of Natural Philosophy, which included his three laws of motion and his law of universal gravitation:
1775	Benjamin Franklin	Franklin noticed that a small cork inside a hollow, charged can experiences no force. The same cork experiences a force outside the can. He wrote to Joseph Priestly and asked him to repeat the experiment.
1776-1777	Joseph Priestley	Priestley verified Franklin’s results and realized a connection to Newton’s law of universal gravitation. Newton had explained in his book that an object would experience no force of gravity inside a hollow planet. He was able to show that this was the consequence of the “inverse squares law,” which says that gravitational force acting on two masses is inversely proportional to the square of the distance between their centres.  Priestly instantly likened the cork to the object and the hollow can to the planet. Priestley suggested that this indicated that the force of electricity could also be an inverse square law.

 

Read

 

To review the key features of Newton’s law of universal gravitation and to better understand what it means to say that this law is an “inverse square law,” read “10.2 Coulomb’s Law” on page 524 of your textbook. Pay special attention to the “Physics Insight” on the left-hand side of the page.

 

Self-Check

 

You can check your understanding by answering these questions:

 

SC 1. List all the variables that influence the magnitude of the force of gravity.

 

SC 2. Describe how increasing the size of both masses influences the magnitude of the force of gravity.

 

SC 3. Describe how increasing the distance (r) between the two masses influences the magnitude of the force of gravity

 

SC 4. Mathematically express how increasing the size of both masses influences the magnitude of the force of gravity. In other words, write a proportionality statement.

 

SC 5. Mathematically express how increasing the distance (r) between the two masses influences the magnitude of the force of gravity. In other words, write a proportionality statement.

 

 

Making Predictions about the Electrostatic Force

 

Given your answers to the previous questions, you should be able to speculate about the nature of the electrostatic force. The following graphic shows the possible connections between the gravitational force acting on two masses (m1 and m2) and the electrostatic force acting on two charges (q₁ and q₂).

 

 

 

Try This

 

TR 1. Identify the variables that will likely influence the magnitude of the electrostatic force.

 

TR 2. Speculate on how increasing the size of charges q1 and q2 will influence the size of the electrostatic force.

 

TR 3. Speculate on how increasing the distance between the two charges would influence the magnitude of the electrostatic force.

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Module 3—Electrical Phenomena

 

Verifying Predictions about the Electrostatic Force

 

Although the thought processes used to answer the previous questions are very helpful as a starting point, it is important to verify these hypotheses with data collected from an experiment. Coulomb did this using a torsion balance. A detailed illustration of the torsion balance is shown in the following illustrations.

 

 

In Coulomb’s torsion balance, a horizontal, insulated rod is suspended by a thin, stiff fibre of silver wire. The wire twists when a force is exerted on sphere A, which is shown at the end of the rod. The force on sphere A causes the rod to rotate horizontally. The twisting of the wire can be measured at the suspension head at the top, which indicates the force acting on sphere A.

 

A simplified representation of this apparatus focuses on the suspension head at the top and the two charged spheres at the bottom. This simplified version shows how the variables of distance of separation (r) and charge (q) could be used to measure the electrostatic force .

 

 

In this simplified scheme, the ruler can be used to measure the distance from the centre of sphere A to the centre of sphere B. If sphere A and sphere B were given like charges, a force would act on each sphere. This force would push the spheres apart. If sphere A were free to move, then it would be forced to rotate away from sphere B, causing the wire to twist. A larger force acting on sphere A would produce a greater twist in the wire, which could be indicated by the scale on the top.

 

Although Coulomb had no way of determining the exact amount of charge on an object, he did devise an ingenious method of varying the charge in a controlled way.

 

Read

 

To learn more about Coulomb’s method for varying charge, read page 528 in your textbook.

 

Self-Check

 

You can check your understanding by answering this question:

 

SC 6. Coulomb used a third sphere, C, which was identical to sphere A and sphere B. Explain how Coulomb used sphere C to vary the charge on sphere B.

 

 

You will have an opportunity to collect data from a virtual torsion balance apparatus in the next investigation.

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Module 3—Electrical Phenomena

 

Lesson 2 Lab: Simulating Coulomb’s Experiment

 

In this lab activity you will simulate what Coulomb did to derive the equation to describe the electrostatic force. This activity will be broken into two parts. The first part of this lab investigates the relationship between the distance of separation (r) on the electrostatic force , while the second part investigates the relationship between the amount of charge (q1 and q2) and the resulting electrostatic force .

 

Part A: How the Electrostatic Force is Affected by Distance of Separation (r)

 

Purpose

 

In this part of the investigation you will examine how Coulomb gathered data from a torsion balance experiment to determine the relationship between the distance of separation and the electrostatic force. You will be given sample data to graph and analyze to find the relationship.

 

Materials

 

You will need a calculator, a pencil, an eraser, a straight edge or ruler, and a piece of graph paper. If you decide not to use graph paper, you will need a graphing calculator or a computer that has spreadsheet software to do graphing. Below is a diagram of Coulomb’s torsion balance apparatus set up for the experiment.

 

 

Variables

Before starting the experiment Coulomb had to identify the manipulated variable and predict what would happen when metal sphere A was released. Study the previous diagram, and answer the Self-Check questions about it.

 

Self-Check

 

SC 7. Identify the type of force that causes the acceleration of sphere A.

 

SC 8. Determine if the force will push sphere A away from sphere B or toward sphere B. Support your answer.

 

SC 9. Assume that sphere B is fixed in position and that sphere A is free to rotate. Determine if the arm holding sphere A will rotate clockwise or counterclockwise (if viewed from above as shown in the illustration.)

 

 

Procedure

• Sphere B is initially given a negative charge by touching it to a charged rubber rod that was rubbed with fur. Since Coulomb did not have a precise value for the charge on sphere B, he simply referred to this charge as qB.

• Touch Sphere B momentarily to sphere A, which was initially neutral.

• With sphere A held stationary, place sphere B 1.0 cm away. Release sphere A, allowing the arm on the torsion balance to rotate. Measure the force acting on sphere A on the scale at the top of the torsion balance.
  

• Repeat the preceding step with sphere B set at the following distances from sphere A’s positions: 2.0 cm, 4.0 cm, and 8.0 cm.

• The results of all the trials are indicated in the diagrams shown in the Observations section. Note that the angles of rotation have been made large enough for you to make force measurements. In Coulomb’s actual apparatus, the angles of rotation were all less than 10°.

Self-Check

 

SC 10. Remember that spheres A and B are identical in size and both are made of metal.

1. Describe what happens to the charge when sphere B is touched to sphere A.
   
   
2. Determine and explain the total charge that is present on both spheres A and B after they touch.
   
   
3. Determine and explain the charge that would be on each sphere after they were touched and separated.

 

Observations

 

The following multimedia will show you the results when Coulomb released sphere A from different distances. Click on the “Next” button to see the different force and distance values and fill in the results for Self-Check 11.

 

Data

 

Self-Check

 

SC 11. Study the diagrams, and create a chart of data values showing the distance of separation and the corresponding force for each trial. Remember that you can use a graphing calculator or a spreadsheet instead of a paper chart.

 

 

Analysis

 

SC 12. Draw a graph of  as a function of r. You can use the following steps as a guide:

1. Explain which variable is the manipulated variable, which variable is the responding variable, and which variables are held constant.
   
   
2. Label the axis with the manipulated variable on the x-axis and the responding variable on the y-axis.
   
   
3. Scale the axis and plot the points.
   
   
4. Draw the line of best fit for this data.

 

SC 13. Earlier in this lesson, the suggestion was made that the equation describing the electrostatic force that acts on one charge due to the presence of a second charge could be an inverse square relationship.

1. Use adjacent pairs of data points to illustrate that  varies as .
   
   
2. Instead of sampling individual data points, a better way to demonstrate that Fe varies as is to manipulate the original data chart to produce a straight-line graph. Build a new data chart with columns for the distance (r), the new values that you will be plotting, and the electrostatic force, .
   
   
3. Use the manipulated data from SC 13. b. to draw a straight line graph illustrating the inverse square relationship.

 

Part A Conclusion

 

Now that you have seen Coulomb’s observations and learned how to change the curved electrostatic force vs. distance of separation graph into a straight line graph you should have an understanding of how the two variables relate.

 

SC 14. Based upon your results for SC 13, write a mathematical expression describing the relationship between  and r.

 

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Part B: How Electrostatic Force is Affected by Charge Strength (q)

 

Purpose

 

In this part of the lab you will examine sample data from Coulomb’s torsion balance experiment to determine how varying the charge on one sphere can influence the electrostatic force on the other.

 

Materials

 

The only material needed is sample data from a torsion balance-type experiment. This data is provided for you in this investigation. To determine these values Coulomb used his torsion balance.

 

Background Information

 

In part A Coulomb used a negatively charged rod to give sphere A and sphere B the same charge. He used a third neutral sphere called sphere C, which was otherwise identical to spheres A and B, to vary the amount of the charge on sphere B.

 

Each time sphere C was touched to sphere B, the original charge on sphere B was split between spheres B and C. After sphere C was removed, sphere B was left with only half of the charge that it had before touching sphere C. Grounding sphere C each time and repeating this process provided a method for varying the charge on sphere B. Sphere A’s charge remained the same throughout the process.

 

Procedure

 

The first three steps of the procedure are the same as part A. Step four is where the two procedures differ:

• Give sphere B an initial negative charge by touching it to a charged rubber rod that was rubbed with fur. Since Coulomb did not have a precise value for the charge on sphere B, he simply referred to this charge as qB.
  

• Touch sphere B momentarily to sphere A, which was initially neutral.

• With sphere A held stationary, place sphere B 2.0 cm away. Release sphere A, allowing the arm on the torsion balance to rotate. Measure the force acting on sphere A on the scale at the top of the torsion balance.

• Ground sphere C, which is identical in size to sphere A and sphere B, to give it a charge of zero. Touch it to sphere B and then remove it.

• Return sphere A to a distance 2.0 cm away from sphere B and release it, allowing the arm on the torsion balance to rotate. Measure the force again.

• Repeat the preceding two steps to observe how the new charges on sphere B affect the electrostatic force.
  

Observations

 

The following table summarizes these results.

 

Data

 

Charge on Sphere A (qA) (q units)	Charge on Sphere B (qB) (q units)	Product of the Charges (qA qB) (q2 units)	Electrostatic Force on Sphere A (F units)
		=0.25	4
		=0.125	2
		=0.0625	1
		=0.03125

 

Analysis

 

Self-Check

 

SC 15. Plot a graph of the electrostatic force versus the product of the two charges (qA qB).

 

 

Part B Conclusion

 

Now that you have seen the observations and analyzed them by graphing you should be able to describe the relationship.

 

SC 16.

1. Describe the shape of the graph that you plotted.
   
   
2. Use the shape of the graph to state the mathematical relationship between the electrostatic force and the product of the two charges.

 

Lab Conclusion

 

Now that you have completed Part A, you understand the relationship between the electrostatic force and the distance of separation. Since you have completed Part B, you also understand the relationship between the electrostatic force and the product of the charge. Now you need to combine your results to determine the equation that describes Coulomb’s law.

 

SC 17.Consider your conclusion for Part A and your conclusion for Part B. Based upon your results, state the mathematical relationship among the variables , qA, qB, and r.

 

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Reflect and Connect

 

The conclusions of Coulomb’s experimental work with the torsion balance enabled him to describe the factors that determined the magnitude of the electrostatic force.

 

 

 

Coulomb’s law: the magnitude of the electrostatic force between two charged objects is directly proportional to the product of the two charges on the objects and inversely proportional to the square of the distance of separation between their centres.

 

Coulomb’s law can provide insights into the circumstances described in the Get Focused section.

 

 

 

 

 

Try This

 

TR 4. Recall your work from Lesson 1. Describe the process that caused the top surfaces of the objects under the thundercloud to develop a positive charge.

 

TR 5. The circumstances in this illustration are much more complex than the carefully controlled environment of Coulomb’s experiment. Identify at least two differences between the circumstances in the illustration and Coulomb’s work.

 

The answers to the previous question indicate that applying Coulomb’s law to the circumstances in the illustration will only yield a rough approximation of what may be occurring in terms of electrostatic forces.

 

Even with these limitations in mind, some valuable insights can be gained into lightning safety.

 

Self-Check

 

SC 18. The illustration shows that the hiker is four times farther from the negative charges in the thundercloud than the people on the observation platform.

1. Use Coulomb’s law to provide a rough comparison of the electrostatic force that would act on a similarly charged strand of hair in each location.
   
   
2. Do you think it is reasonable to assume that a strand of hair would have a similar charge in each location? Explain concisely.
   
   
3. How does your answer to SC 18.b. affect your estimates of forces in SC 18.a.?

 

Big Picture Reflection

 

 

Imagine you are out hiking and are surprised by a sudden thunderstorm. Based on Coulomb’s law, what are the strategies for protecting yourself?

 

The strategies are:

• Avoid high spots, or very open areas; look for low areas.
  
  
• Sit down in a tucked position to get further from the clouds and prevent charge build up on extremities (arms, head and legs).
  
  
• Wear and/or sit on some insulating plastic, if possible.
  
  
• Get rid of metal objects that could conduct electric charges.
  
  
• Close your eyes and cover your ears to protect yourself from any nearby lightning strikes.
  

Does Coulomb’s law validate the recommendations shown in this illustration?

 

Store your thoughts in your Physics 30 course folder.

 

Module 3: Lesson 2 Assignment

 

Remember to submit your Module 3: Lesson 2 Assignment to your teacher for marks. If you are not familiar with curve straightening refer back to Self Check 13 for an example.

 

A 1. Answer questions 25. a., b., c., and d. on page 541 of your textbook.

 

A 2. A student is investigating Coulomb’s law. The student measures a force of +2.00 × 10−3 N between the two charged spheres. 

1. Explain how you can tell whether the charges are both positive, both negative, or positive and negative.
   
   
2. Describe two methods that the student could use to increase the force to 64 times its current value.
   
   
3. The student touches one of the spheres with an equally sized neutral sphere and then removes the neutral sphere. The student then moves one of the spheres so the distance is three times the original distance. What is the ratio of the original force to the new force?

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Lesson Summary

 

At the start of this lesson you were asked two essential questions:

• What is Coulomb’s Law, and how was this law determined using the results of experiments?

• Can Coulomb’s law predict the effect on electrostatic force if the distance of separation increases by a known amount? What does the answer to this question suggest about lightning safety?

You examined sample data from a Coulomb-type experiment, and you analyzed this data using the techniques of graphical analysis. This work illustrated the essential characteristics of Coulomb’s law:

 

 

This law means that if the charges are held constant and the distance of separation increases by some factor, then the effect on the resulting electrostatic force can be predicted. For example, if the distance increases by a factor of four, then the electrostatic force would be th its original value. In terms of lightning safety, a wise strategy is to seek low ground—maximize the distance of separation between you and the cloud.

 

In the next lesson you will continue your work with Coulomb’s law as you consider how much charge is actually transferred in a lightning strike.

 

Lesson Glossary

 

Coulomb’s law: the magnitude of the electrostatic force between two charged objects is directly proportional to the product of the two charges on the objects and inversely proportional to the square of the distance of separation between their centres

 

torsion balance: an instrument designed to measure small forces by the twisting of a thin wire

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Module 3—Electrical Phenomena

 

Lesson 3—Applying Coulomb’s Law

 

Get Focused

 

This photograph was taken the day after a thunderstorm. Lightning struck the pole and then followed the guy wire down into the sandy soil. Closer inspection reveals one of the effects of the lightning—some of the sand was turned into glass.

When lightning strikes the sandy soil, the extremely high temperature causes the silica in the sand to melt. The rapid cooling of this molten material forms glass. The next photograph shows a close-up of white silica glass formed by a lightning strike. Note the grains of sand melded to the outside surface of the glass.

Although the white glass has a smooth appearance, on the atomic scale, the silica in the glass has formed crystals with the main building block being a pyramid shape. In the following ball-and-stick model, the white ball in the centre represents a silicon atom; the four red balls surrounding it represent oxygen atoms. The oxygen atoms are actually much larger than the silicon atom, but they have been reduced in size to make the detail of the inner structure more visible.

Each bond forms because of an unequal sharing of electrons. Each oxygen atom has a slightly negative charge, and the central silicon atom has a slightly positive charge. The result is a tetrahedral shape that is perfectly symmetrical: the values for the angles and the distances of separation are the same for each oxygen-silicon bond. Why does nature produce this kind of symmetry? The answer has to do with Coulomb’s law.

 

In this lesson you will apply Coulomb’s law to the exploration of both large-scale and extremely small-scale phenomena:

• How much charge is transferred in a lightning strike, and how is this amount of charge measured?
  
  
• How can Coulomb’s law be applied to predict the net force acting on one point charge due to the presence of other point charges? How does this sort of analysis relate to the symmetry found in crystals?

Module 3: Lesson 3 Assignments

 

Your teacher-marked Module 3: Lesson 3 Assignment requires you to submit a response to the following questions:

• Assignment—A 1, A 2, A 3, and A 4

You must decide what to do with the questions that are not marked by the teacher.

 

Remember that these questions provide you with the practice and feedback that you need to successfully complete this course. You should respond to all the questions and place those answers in your course folder.

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Module 3—Electrical Phenomena

 

Explore

 

An Equation for Coulomb’s Law

 

How would you describe the amount of charge delivered in a lightning strike or calculate the forces that act on the tiny charged particles within a crystal? You need values that can be described with units of measure and an equation for the electrostatic force. In the last lesson you learned that Coulomb’s work enabled him to describe the factors that affected the magnitude of the electrostatic force.

 

 

Although this mathematical expression describes Coulomb’s law, it is not an equation. The left-hand side does not equal the right because a proportionality constant (k) is missing. The proportionality constant enables the left side to be equal to the right by taking into account the units for charge, distance, and force.

 

Read

 

You can learn how units were considered in building the equation for Coulomb’s law by reading from the top of page 529 to the middle of page 530 in your textbook.

 

Self-Check

 

You can check your understanding by answering these questions.

 

SC 1. Complete the following graphic to summarize the quantities in the equation for Coulomb’s law as well as the units for each of these quantities.

 

 

 

Quantity	Units
electrostatic force	Newtons (N)
Coulomb’s constant
charge
distance

 

SC 2. Provide two examples that illustrate the size of a coulomb as a unit for charge.

 

 

Try This

 

TR 1. Starting with Coloumb’s law derive the units for Coulomb’s constant .

 

As you saw in Get Focused, this piece of glass was formed as lightning penetrated sand. The presence of air and moisture in the silica resulted in an explosive expansion of the silica as many coulombs of charge surged into the ground. Note the swollen lumps formed by the rapid expansion of super hot bubbles. This sample is, in fact, hollow—a fragile glass tube.

 

The precise arrangement of the silicon and oxygen atoms within the glass crystals is a consequence of Coulomb’s law. However, the analysis is quite complex, requiring you to consider the vector nature of forces.

 

To prepare for this, the next part of this lesson will lead you through a series of examples that will gradually increase in complexity. By the time you have completed the last example, you should be ready to revisit the arrangement of the atoms in the crystal of glass.

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Module 3—Electrical Phenomena

 

Calculations with Coulomb’s Law

 

Dealing with Signs of Charges

 

It is truly remarkable that two of the most fundamental laws in physics, which describe completely different phenomena and are based on completely different observations, should be so similar. The reasons for these similarities remain a mystery. However, it would be misleading to say that these forces are identical because there are some important differences.

 

When you solve problems with Coulomb’s law, it is important to substitute only the magnitude of the charges into the equation. The signs of the charges are considered after the calculation is complete to determine the direction of the resulting force.

 

Read

 

Do “Example 10.1” on page 530 in your textbook.

 

Self-Check

 

Use this question to confirm your understanding of example 10.1.

 

SC 3. Complete the “Practice Problem” on page 530 of your textbook.

 

 

Calculations with Coulomb’s Law

Using the Law of Conservation of Charge

 

Sometimes the law of conservation of charge plays a role in Coulomb’s law calculations. The two objects with different charges are first touched together and then separated before an electrostatic force is calculated.

 

Read

 

Do “Example 10.2” on page 531 of your textbook.

 

Self-Check

 

Use this question to confirm your understanding of example 10.2.

 

SC 4. Complete the “Practice Problem” on page 531 of your textbook.

 

 

Module 3: Lesson 3 Assignment

 

Remember to submit your answer to A 1 as part of your Module 3: Lesson 3 Assignment to your teacher for marks.

 

A 1. Answer question 12 on page 540 of your textbook.

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Module 3—Electrical Phenomena

 

Calculations with Coulomb’s Law

 

Three Charges Forming a Line

 

If there are three charges arranged along a straight line, then the calculation of the net electrostatic force on any one of the three charges requires you to take into consideration the vector nature of forces.

 

Read

Read the first two paragraphs on page 532 of your physics textbook, and then read “Example 10.3.” Be sure to follow the solution carefully.

 

Self-Check

 

Use these questions to confirm your understanding of “Example 10.3.”

 

SC 5. Complete “Practice Problems” 1 and 2 on page 532 of your textbook.

 

 

In the previous example and the practice problems, the fact that two of the charges had the same magnitude allowed symmetry to simplify the solution. The next problems are slightly more complex because this symmetry is not present.

 

Read

 

Do “Example 10.4” on page 533 of your textbook. Be sure to follow the solution carefully.

 

Self-Check

 

Use this question to confirm your understanding of “Example 10.4.”

 

SC 6. Complete “Practice Problem” 1 on page 533 of your textbook.

 

 

Module 3: Lesson 3 Assignment

 

Remember to submit your answers to A 2 and A 3 as part of your Module 3: Lesson 3 Assignment to your teacher for marks.

A 2. Do “Applications” problem 8 on page 538 of your textbook.

 

A 3. Do “Knowledge” problem 13 on page 540 of your textbook.

 

 

Calculations with Coulomb’s Law

Three Charges Forming a Triangle

 

The glass crystal from the Get Focused section did not have the charges arranged in a straight line; instead, they were arranged in triangular shapes.

When three charges form a triangle, a calculation of the electrostatic force requires a two-dimensional vector treatment. This means that directions need to be expressed using either the polar method or the navigator method.

 

Read

 

Do “Example 10.5” on page 534 of your textbook. Be sure to follow the solution carefully.

 

Self-Check

 

Use this question to confirm your understanding of “Example 10.5.”

 

SC 7. Complete “Practice Problem” 2 on page 534 of your textbook.

 

 

The previous example and practice problem show how powerful a systematic approach to problem solving can be. Did you recognize that this method of dealing with vectors using the polar or the navigator methods stemmed directly from your work with momentum earlier in the course? Even though the topic is no longer momentum, the same techniques work. This isn’t good luck—it is by design. Remember, the whole idea is to use the same overall strategies throughout the course so that you can become a successful problem solver.

 

As long as you take your time and consistently follow the recommended approach, even the most complicated problems can be solved. The key is to make effective use of diagrams—both vector diagrams and free-body diagrams.

 

Keep this in mind as you attempt the most complicated type of Coulomb’s law problem.

 

Open the multimedia learning object called Coulomb’s Law in 2D.

 

Read

 

Read “Example 10.6” on pages 535 to 537 of your textbook. Read the solution carefully. As you read, try to anticipate the next step in the solution.

 

Module 3: Lesson 3 Assignment

 

Remember to submit the answer to A 4 as part of your Module 3: Lesson 3 Assignment to your teacher for marks.

 

A 4. Do “Applications” question 24 on page 540 of your textbook.

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Module 3—Electrical Phenomena

 

Reflect and Connect

 

In the Get Focused section you were asked to consider the symmetry of a crystal within silica glass. In the ball-and-stick model that was presented, a red ball represented each oxygen atom. These atoms have a slight negative charge. The central white ball represents a silicon atom that has a slight positive charge.

 

Try This

 

TR 2. Consider the electrostatic force exerted by the top-most oxygen atom on the central silicon atom. Identify the direction of this force.

 

TR 3. Consider the net electrostatic force exerted by the three oxygen atoms on the bottom of the central silicon atom. Use your knowledge of vectors to explain how it could be possible for the direction of this net force to be straight down, in the opposite direction of the force exerted by the oxygen atom on the top.

 

TR 4. Given your answers to the previous two questions, explain how, because of the four oxygen atoms, it could be possible for the net force acting on the silicon atom to be zero.

 

TR 5. Suppose someone attempted to apply Coulomb’s law to calculate the net force on the silicon atom due to all four oxygen atoms in this crystal. Would it be sufficient to work only with x and y components of the individual forces? Suggest a more successful approach.

 

TR 6. Each of the oxygen atoms in this crystal has a slight negative charge. Therefore, each oxygen atom experiences a net repelling force due to the presence of the other three oxygen atoms. Identify a force that could counter this net repelling force.

 

Big Picture Reflection

 

Take a few moments and think about your answers to the questions in the Reflect and Connect section. The fact that the oxygen atoms are negatively charged and the central silicon atom is positively charged means that electrostatic forces apply to this situation. However, the net electrostatic force on each atom is zero. In other words, the forces are in a state of equilibrium. The angles and distances between the atoms simply describe the overall state of this system when the forces are balanced.

 

Given the central role played by the electrostatic force, it is not a stretch to say that the shape of this crystal is a direct consequence of Coulomb’s law. The same thinking could apply to almost any crystal. Keep this in mind the next time you look at a snowflake.

 

Going Beyond

 

Other Effects of Lightning on the Environment

 

In this lesson you learned about some of the effects of lightning striking the ground. The silica in sand can be turned into glass because the temperature inside a single lightning bolt can exceed 30 000°C—that’s five times hotter than the surface of the sun!

 

 

These high temperatures explain why lightning strikes are often a source of wildfires. In both the boreal forest ecosystem and the prairie grassland ecosystem, a fire started by lightning can have a rejuvenating effect since fires started by lightning strikes burn away dead and overcrowded trees, clearing the way for new growth; the combustion reaction also releases nutrients into the soil to nourish the next generation of the forest, leading to a healthy diversity in both the plant and animal communities.

 

Using Lightning as a Technology

 

First Nations people have lived in Alberta for thousands of years. They knew about the connections between the fires produced by lightning strikes and their beneficial long-term effects on the ecosystem. Where lightning caused a fire, there would be exceptionally lush vegetation in following years, which would attract animals such as bison, drawn to feed on the vegetation. Clearly, lightning was a natural phenomenon that was to be respected for both its destructive and beneficial effects.

 

Self-Check

 

SC 8. The traditional ecological knowledge of the First Nations people developed through living in the environment for hundreds of generations. Part of this knowledge was informed by the natural cycle of forest rejuvenation of which fire is a part. Suggest a reason why this knowledge would be crucial to the survival of indigenous people in this environment.

 

 

Module 3: Lesson 3 Assignment

Remember to submit your Module 3: Lesson 3 Assignment to your teacher for marks.

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Module 3—Electrical Phenomena

 

Lesson Summary

 

At the start of this lesson you were asked some essential questions:

• How much charge is transferred in a lightning strike, and how is this amount of charge measured?

• How can Coulomb’s law be applied to predict the net force acting on one point charge due to the presence of other point charges? How does this sort of analysis relate to the symmetry found in crystals?

In this lesson you’ve learned more about the enormous amounts of charge that a lightning strike can deliver between cloud and Earth. Although a strike of 1 C is typical, it is not unheard of for a single strike to deliver more than 30 C of charge. The high temperatures associated with this phenomenon can turn ordinary sand into crystals of silica glass and initiate wildfires.

 

Coulomb’s law can be used to calculate the net force on one point charge due to other point charges. The solutions to these sorts of problems require you to consider the vector nature of the electrostatic forces. The shapes of crystals are a consequence of charged particles aligning themselves so that the electrostatic forces are balanced.

 

In the next lesson you will use Coulomb’s law to explain electric fields and electrical phenomena.

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Module 3—Electrical Phenomena

 

Lesson 4—Electric Fields

 

Get Focused

 

Have you ever been on an airplane as it flew through a lightning storm? You may have seen an eerie blue glow on the wing tips. This unusual effect is an electrostatic phenomenon called St. Elmo’s fire.

 

St. Elmo’s fire was thought to indicate good luck to sailors in ancient times, because the tall masts of the ships would sometimes glow with a blue light following a bad storm. They believed it was a sign of salvation from the patron saint of sailors, St Ermo—the mispronunciation of the saint’s name was given to the fiery glow.

 

Although it is generally harmless, St.Elmo’s fire may have played a role in an airplane crash in 1959; an airplane flew into a stormy Italian sky and crashed just 12 minutes later.

 

The investigators who examined the crash site concluded that the accident was likely caused by an electrical discharge from St. Elmo’s fire, which they suspected had ignited vapors from the aviation fuel. The accident prompted Lockheed, the aircraft’s manufacturer, to install a flame-arrester screen on the vent pipe openings of its aircraft to eliminate the potential for St. Elmo’s fire to become a bad omen in stormy skies.

 

Though such accidents can now be prevented, St. Elmo’s fire still shows up on airplane wing tips and propellers. The explanations of this phenomenon involve the effects of strong electric fields.

 

In this lesson you will answer the following essential questions:

• What is an electric field, and how can it be described and analyzed?
• What exactly is St. Elmo’s fire, and why does it occur at the end of pointed surfaces?

Module 3: Lesson 4 Assignments

Your teacher-marked Module 3: Lesson 4 Assignment requires you to submit a response to the following:

• Assignment—A 1, A 2, A 3, and A 4
• Discuss—D 4

You must decide what to do with the questions that are not marked by the teacher.

 

Remember that these questions provide you with the practice and feedback that you need to successfully complete this course. You should respond to all the questions and place those answers in your course folder.

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Module 3—Electrical Phenomena

 

Explore

 

Action at a Distance

 

Throughout this course, you have had many opportunities to observe electrostatic forces acting on charged objects. In many cases, the force was able to produce an observable effect even though the objects were not touching.

 

 

How were the positive charges on the sweater able to exert an electrostatic force on the negative charges on the balloon, even though the sweater was not touching the balloon? How was the negatively charged globe of the Van de Graaff generator able to exert forces on the soap bubbles, even though the Van de Graaff generator was not touching the bubbles?

 

These questions illustrate an important property of the electrostatic force: the force can act on a distant object without any apparent contact. This property has been called “action at a distance.” But naming this property is not the same as explaining it. After all, how does “action at a distance” work? What mechanism enables the electrostatic force to act through space? The answer to these riddles relates to an idea that you studied in previous courses—the concept of a field.

 

Read

 

You can learn more about how the concept of a field explains “action at a distance” by reading pages 542, 544, 545, and the bottom of page 546 of your textbook.

 

Self-Check

 

SC 1. Electrostatics is not the only branch of physics that utilizes the concept of a field.

1. Identify another type of force that uses the field concept to explain “action at a distance.”
   
   
2. Support your answer to the previous question by briefly describing an example of how the concept of a field is used to explain action at a distance for the force you identified.

 

Reviewing Gravitational Fields

 

Before you begin your study of electric fields, you may find it helpful to review what you have learned about gravitational fields from previous courses. A satellite in orbit around Earth is a good example of gravitational fields at work.

 

The Hubble Space Telescope moves at about 8 km/s as it orbits about 600 km above Earth’s surface. It’s natural to wonder why an object moving so quickly, so far from the planet, stays in orbit. Shouldn’t this satellite just fly off into space?

 

Read

 

To answer this question, think about Earth’s gravitational field. If you need help remembering how Earth’s gravitational field acts on objects in orbit, read pages 200 and 201 of your textbook.

 

Self-Check

 

SC 2. Earth’s gravitational field can be described by a field diagram and by an equation.

1. Describe the direction of Earth’s gravitational field.
   
   
2. Although Earth’s gravitational field is invisible, it can be represented with a diagram showing gravitational field lines. Sketch a diagram representing Earth’s gravitational field. Use this diagram to compare the strength of Earth’s gravitational field at locations close to the planet and far from the planet.
   
   
3. Compare the direction of the gravitational force of Earth acting on the Hubble Space Telescope to the direction of Earth’s gravitational field at the same location.
   
   
4. Define gravitational field strength.
   
   
5. State the equation for gravitational field. How does this equation support your answer to part c?
   
   
6. Explain the difference between gravitational force and gravitational field.

 

Equations for Gravitational Field

 

A vector equation emphasizes that the gravitational field and the gravitational force act in the same direction.

 

 

This equation provides a way to calculate the strength of the gravitational field in newtons per kilogram. Gravitational field strength can also be calculated in another way. Substituting Newton’s law of universal gravitation into the previous equation leads to an alternative equation that describes gravitational field strength.

 

 

Both equations for calculating the magnitude of the gravitational field for a point in space contain a mass variable, but these masses refer to different things.

 

 

Self-Check

 

How well do you remember gravitational fields? Try the Self-Check problems to review gravitational fields.

 

SC 3. Use the data from “Table 4.1” on page 218 of your textbook to calculate the gravitational field strength on the surfaces of Mars and Jupiter.

 

SC 4. An astronaut in her space suit has a mass of 105.5 kg. Use your answers from the previous question to determine the force of gravity that would act on this astronaut on the surface of each planet.

 

SC 5. Suppose a space probe moves from an initial position orbiting a planet to a final position that is only ¼ the distance away. Use the ratio method to determine how the value of gravitational field in the final position compares to the value of gravitational field in the initial position.

 

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Describing Electric Fields

 

 

 

Try This: Exploring Electric Field Lines

 

A simulation will be used to help visualize both the magnitude and direction of the electric field surrounding a single point charge. Consider the large, coloured charge the source charge for the electric field. The small, grey dots represent positive test charges influenced by the field.

 

You may be required to enter a username and password. Contact your teacher for this information. Open the Electric Field Point Charge simulation.

 

TR 1. Press the “grid” button (), and drag the positive charge randomly around the display area. Notice the vector arrows that extend outwards when the charge passes near all the points on the grid. The vector arrows represent the electric field produced by the spherical charge. Sketch the electric field vectors on diagrams like those shown below.

 

 

TR 2. In what direction does the electric field always point for a positive source charge?

 

TR 3. On the simulation, switch the charge to negative by dragging the charge slider (Q) to the left until the charge becomes blue. Sketch the electric field vectors on diagrams like those shown below.

 

 

TR 4. In what direction does the electric field always point for a negative source charge?

 

Read

You can learn more about electric fields and how they differ from gravitational fields by reading “Magnitude and Direction of an Electric Field” on pages 546 and 547 of your textbook.

 

Self-Check

 

SC 6.

1. Explain why gravitational field lines are always drawn toward the centre of the source.

2. Explain why this simple rule cannot always apply in the case of electric fields.

3. Explain how the direction of an electric field vector is determined for a given location outside a source charge.

4. State the equation for the electric field. Label each of the variables in this equation.

 

Read

 

Read “Example 11.1” on page 548 of your textbook. As you go through this example, first identify the key steps and then focus on the details in each step.

 

SC 7.

 

Try “Practice Problems” 1 and 2 on page 548 of your textbook.

 

 

The magnitude of the electric field at some distance from a point charge can be determined from another equation that is derived from Coulomb’s law. The process of deriving this equation is similar to your earlier work deriving a second equation for gravitational field from Newton’s law of universal gravitation.

 

Read

 

To see how this second equation for electric field is derived and applied, read from the bottom of page 548 to the end of “Example 11.2” on page 549 of your textbook. As you go through this derivation, first identify the key steps and then focus on the details in each step. Note how this work parallels your previous practice with gravitational fields.

 

Try This

 

TR 5. Calculate and illustrate the electric field strength at a distance of 4.25 × 10–1 m from a +3.00 μC charged particle. Use the simulation to verify your field diagram.

 

TR 6. Calculate the electric field strength 6.50 × 10–2 m from a –5.00 μC charged particle. Sketch the electric field lines around the source. Use the simulation to verify the directions of your field lines.

 

Module 3: Lesson 4 Assignment

Remember to submit the answer to A 1 and A 2 to your teacher as part of your Module 3: Lesson 4 Assignment.

 

A 1.  Calculate and illustrate the electric field strength at a distance of 8.25 m from a +6.50 μC charged particle. Use the simulation to verify your field diagram.

 

A 2.  Calculate how far from a –5.00 μC charged particle the electric field strength 7.2 × 107 N/C is toward the charge.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lightning and Earth’s Electric Field

 

© Brandon Poleski/shutterstock

 

Each day, there are about 45 000 thunderstorms worldwide. Earth has acquired a net charge from the lightning strikes and therefore surrounds itself with a weak electric field.

 

Investigations of this phenomenon indicate that, near the surface, Earth’s electric field is typically 150 N/C directed straight down toward the centre of the planet. When the field is constant, the field lines are evenly spaced, as indicated in this diagram.

 

Under the right circumstances, a tiny, charged droplet of water could be suspended in Earth’s electric field. In this circumstance, the electrostatic effects counteract the effects of gravity, so the drop would no longer be accelerating toward Earth’s surface.

 

You have the tools to analyze this situation, but you have to be careful to use the equations for electric field correctly. It is important to remember that one equation deals with the charge on a test body, while the other equation deals with the charge on the source of the electric field.

 

 

Self-Check

 

SC 8. Use the diagram of Earth’s electric field to determine the sign of the net charge on Earth.

 

 

The Vector Addition of Electric Fields

 

St. Elmo’s fire is very difficult to photograph; a camera does not detect the faint blue glow very well, and St. Elmo’s fire occurs in circumstances that make photography difficult. A photographer would have to be close to the top of a ship’s mast in a thunderstorm or just behind the trailing edge of an aircraft wing in flight!

 

An alternative approach is to photograph a phenomenon that is similar to St. Elmo’s fire. Strictly speaking, the blue streamers of light visible in the photo of this plasma lamp are not St. Elmo’s fire. Nevertheless, the ribbons of light in a plasma lamp do have many things in common with St. Elmo’s fire:

• The effects are due to the presence of strong electric fields.

• The electric fields strip some electrons from gaseous molecules producing a hot, ionized gas called plasma.

• Light is emitted when electrons drop to lower energy levels within atoms.

• The colour of the emitted light depends upon the particular atoms affected.
  

 

Since the atmosphere is comprised mostly of nitrogen, the light emitted from St. Elmo’s fire is blue, which is the characteristic colour emitted when nitrogen atoms are ionized. The manufacturers of plasma lamps deliberately introduce other gases to produce dramatic effects.

 

The streamers of light in this close-up photograph of a plasma lamp are particularly beautiful, not only because the colour is so striking but also because of the graceful, twisting shapes. These shapes are caused by charged particles within the streamers that are under the influence of more than one electric field. St. Elmo’s fire also involves overlapping electric fields that simultaneously influence many charges.

 

Read

 

To see what happens when electric fields with only x components overlap, read from the bottom of page 549 to the end of “Example 11.3” on page 550 of your textbook. As you read through this example, first identify the key steps and then focus on the details in each step.

 

Self-Check

 

SC 9. Refer to the previous photos of the plasma lamp. Simplify the situation and suppose that the charged particles within the streamer were only under the influence of the electric field of the negatively charged central orb. If this simplification were true, what shape would the streamers have?

 

SC 10.  Try “Practice Problems” 1 and 2 on page 550 of your textbook. For question 2 remember the charge on a proton and electron is equal to the elementary charge on your datasheet.

 

 

Read

 

To see what happens when electric fields are described with both x and y components, read “Example 11.4” on pages 551 and 552 of your textbook. As you read through this example, first identify the key steps and then focus on the details in each step.

 

Self-Check

 

SC 11.  Do “Practice Problem” 1 on page 551 of your textbook.

 

 

Module 3: Lesson 4 Assignment

Remember to submit the answer to A 3 and A 4 to your teacher as part of your Module 3: Lesson 4 Assignment.

 

A 3. Point P is collinear with a +2.80 μC and a −8.50 μC as shown in the following diagram. Point P is 10 cm to the left of the positive charge and 20 cm to the left of the negative charge. What is the electric field at point P?

 

 

A 4. The following diagram shows two charged spheres arranged to the left of a point in space labelled P. Use the information on the diagram to calculate the magnitude and direction of the net electric field at point P.

 

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Electric Field Lines in Nature

 

St. Elmo’s fire is not the only natural phenomenon that is explained using electric field lines. Sharks are capable of detecting the weak electric fields that other animals produce through their muscle activity. This ability enables sharks to detect prey that has buried itself under shallow sand on the seabed.

 

Just as a source mass surrounds itself with gravitational field lines, a source charge surrounds itself with electric field lines. Since muscle activity is triggered by the moving charges in nerve cells, muscle contractions produce electric fields. In this case, the source charges are very weak, so the resulting electric fields are also very weak.

 

Hammerhead sharks have sensors located in their snouts that allow this predator to detect very weak electrical fields. The hammerhead shark swims close to the seabed seeking prey that has hidden itself under the sand. The electric field lines produced by the prey can extend up into the water above the sand. As the shark swims past a location where the density of the electric field lines suddenly change, the sensors in the shark’s snout are triggered. The shark uses this information to pinpoint the exact location of its hidden prey.

 

 

 

Scientists have verified this ability of sharks by burying pairs of oppositely charged sources in the sand. As the shark swims closer to the sources, the special sensors in its snout detect a change in the density of electric field lines. Where the field lines are most concentrated, the shark disturbs the sand looking for a meal. Astonishingly, this type of behaviour was observed with electric fields as weak as 5 × 10–7 N/C.

 

Read

 

You can learn more about electric field lines and the patterns they form by reading page 554 of your textbook.

 

Self-Check

 

SC 12.

1. Are the field lines in the illustration with the shark drawn in a way that is consistent with the rules for drawing electric field lines listed on page 554 of your textbook?
   
   
2. Use the rules listed on page 554 of your textbook to identify the location in the illustration where the magnitude of the electric field would be greatest.
   
   
3. Use your answer to SC 12.b. to identify the location that would likely draw the shark.

 

Read

 

Read the instructions in “Minds On: Drawing Electric Field Lines” on page 555 of your textbook.

 

Self-Check

 

SC 13. On a sheet of paper, sketch the patterns of the electric field lines shown in each of the situations illustrated in the “Minds On: Drawing Electric Field Lines” activity. Complete each illustration by adding arrowheads to each of the electric field lines.

 

 

 

Electric Fields on the Surfaces of Conductors

 

Recall that St. Elmo’s fire has been observed on the wing tips of aircraft that are flying near large concentrations of charge within a thunderstorm. The reason this phenomenon occurs on wing tips, as it does at the ends of other sharply pointed projections, has to do with the distribution of charge on the surface of the aircraft.

 

As an aircraft flies through thunderclouds, the metal surface of the aircraft can become charged. If electrons are transferred to the aircraft, these excess negative charges will move as far apart as possible due to like charges repelling one another. On a flat metallic surface, the negative charges spread out evenly. So, the resulting pattern of electric field due to these charges is also evenly distributed.

 

 

If the same surface is slightly bent, more charges can be added. Can you think why this would be the case? The reason has to do with the fact that charges on opposite sides of the curved surface are unable to repel one another as effectively as they can when the surface is completely flat. On curved surfaces, the electrostatic force that repels each charge away from the others has a component that is no longer parallel to the surface. This means that the parallel component of the force is less and therefore there is less force acting to separate each individual charge away from the others. The result is that the charges can be packed closer together. It follows that the density of the field lines also increases.

 

 

To pack more charges on the surface, and get an even denser pattern of field lines, the same surface could be bent into a more pronounced curve. As the curvature of a given surface increases, so does the capacity of the surface to concentrate charge and produce regions of intense electric fields.

 

 

Read

You can learn more about the role of the electrostatic force in explaining the patterns illustrated in the previous diagrams by reading pages 555 to 558 of your textbook. Note the explanation of the electric field inside a hollow conductor as well as the electric field between two charged parallel plates.

 

Self-Check

 

SC 14. Record the following diagrams in your notebook. Complete each diagram by sketching the electric field lines within each object.

 

 

SC 15. Refer to the “infoBIT” in the margin on page 558 of your textbook. Explain the role of the flexible metal shielding in the cable that is used to bring TV signals into a home.

 

SC 16. Electric fields are a key component of radio waves. Other than convertibles, most vehicles on the roadway can be thought of as metal boxes with holes cut in them for windows. Use this information to explain why the antenna for a vehicle’s radio must be mounted outside of the vehicle or built into the windshield.

 

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Reflect and Connect

 

As was mentioned earlier in the lesson, the blue streamers emitted by a plasma lamp have many things in common with St. Elmo’s fire. One key difference is that, within a plasma lamp, the strong electric fields are produced artificially within the glass by the circuitry at the base of the lamp. In the case of St. Elmo’s fire, the strong electric fields are produced naturally at the edges or at the pointed tips of conductors near large concentrations of charge in a thundercloud.

 

Discuss

 

D 1. Use the information presented in this lesson to explain why St. Elmo’s fire is observed at the ends of sharply pointed exterior surfaces of aircraft such as wing tips and propellers. Be sure to explain why St. Elmo’s fire is not observed on surfaces that are flat or on interior parts of the aircraft.

 

D 2. Post your summary to the discussion area set up by your teacher. Compare your summary to at least one other explanation produced by another student. Identify similarities and differences between your work and the work of other students.

 

D 3. If you were to update your explanation of St. Elmo’s fire, what changes would you make?

 

Module 3: Lesson 4 Assignment

Remember to submit the answer to D 4 to your teacher as part of your Module 3: Lesson 4 Assignment.

 

D 4. Use your answers to D 1, D 2, and D 3 to revise your explanation of why St. Elmo’s fire occurs on sharply pointed projections of aircraft and not on flat exterior surfaces or interior surfaces.

 

 

Module 3: Lesson 4 Assignment

 

Remember to submit the Module 3: Lesson 4 Assignment to your teacher for marks.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson Summary

 

At the beginning of this lesson you were asked the following essential questions:

• What is an electric field, and how can it be described and analyzed?
• What exactly is St. Elmo’s fire, and why does it occur at the end of pointed surfaces?

You have learned that an electric field is the property of space surrounding a source charge that enables the source charge to exert forces on other charges that enter this region. One way to describe electric fields is to use equations:

 

 

The direction of an electric field is determined by the direction of the electrostatic force experienced by a small positive test charge. This can be used to describe electric fields in terms of patterns of electric field lines around source charges.

 

St. Elmo’s fire is a consequence of the strong electric fields that develop along the sharp edges and points of conductors. These electric fields are strong enough to ionize molecules of air, leading to the emission of light when free electrons combine with positively charged ions.

 

Lesson Glossary

 

electric field: a property of the space around a source charge that enables the source charge to exert forces on test charges in the region

 

field: a region of influence surrounding an object through which a force operates

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson 5—Electric Potential Energy

 

Get Focused

 

Danger signs are always placed near high-voltage equipment. What makes this equipment so dangerous? Why are high-voltage power lines more dangerous to humans than the 120-volt power lines commonly found in houses and stores?

 

The truth is that high voltages are, in fact, not always dangerous. For example, when you rub a balloon on your head, you can generate thousands of volts completely safely.

 

Other devices, such as electric fencing for livestock, operate at tens of thousands of volts yet never cause any permanent damage to livestock that come into contact with it. This is in contrast to the relatively low voltage found in homes, which, as it turns out, is much more dangerous. When is high voltage dangerous? Why?

 

In this lesson you will explore the following essential questions:

• What is electric potential energy?
• How is electric potential energy similar to gravitational potential energy?
• What is voltage?
• How is voltage calculated?

Module 3: Lesson 5 Assignments

 

Your teacher-marked Module 3: Lesson 5 Assignment requires you to submit a response to the following:

•  Lab—LAB 1, LAB 2, LAB 3, LAB 4, LAB 5, LAB 6, LAB 7, LAB 8, and LAB 9

You must decide what to do with the questions that are not marked by the teacher.

 

Remember that these questions provide you with the practice and feedback that you need to successfully complete this course. You should respond to all the questions and place those answers in your course folder.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Explore

 

These BASE (building, antenna, span, earth) jumpers are about to enjoy a “huge dose of adrenaline” as they accelerate toward Earth’s surface before opening their parachutes. When they reach their highest speed, the kinetic energy of the jumpers will be electrifying. What is the source of this vast amount of kinetic energy?

 

You could say that the peak kinetic energy enjoyed by each jumper on the way down was earned by the work done in the climb on the way up. Recall from previous courses that when work is done to change the position of an object, the system containing the object gains potential energy. In this case, since each jumper does work against the force of gravity, each jumper increases the gravitational potential energy of the “jumper-Earth system” as they climb to the top of the platform.

 

In previous lessons, you have seen many similarities between the gravitational field and the electric field. It’s natural to wonder if a charged object could store potential energy by doing work in an electric field, similar to the way that the BASE jumpers stored potential energy by doing work in a gravitational field.

 

You will have an opportunity to solve this problem in the next lab activity.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson 5 Lab: Storing Energy in Non-Uniform Electric Fields

 

There are two parts to this Lab activity. The first part is a simulation that examines how a charged particle behaves in a non-uniform electric field due to the force caused by the field. The second part is a simulation that examines the energy transfer from kinetic energy and potential energy between the charged particle and the non-uniform electric field.

 

Part A: Motion in a Non-Uniform Electric Field

 

Purpose

 

In this part of the lab activity you will use a computer simulation to collect data enabling you to answer the following questions:

• How does a test charge move in a non-uniform electric field?
• How can this motion be explained using physics principles?

Procedure

 

Step 1: You may be required to enter a username and password. Contact your teacher for this information. Open the Electrical Field Potential, Non-Uniform simulation, and enter the following settings:

• Reset the simulation (). Note that the source is the larger charge on the left and the test body is the smaller charge on the right.
  
  
• Turn on the grid ().

• Click on the “velocity mode” button () until the velocity is displayed in the polar method (), showing a velocity in m/s and a direction in degrees.

• Drag the test charge to the following location: (x,y) = (100,0).

• Click on the “initial” button () to have this position be the point where initial values are determined.

• Note that if you use the “rewind” button ( ), you can return to these initial settings at any time during this lab activity. However, if you choose to reset (), you will have to re-enter all these initial settings.

If these settings have been applied, the screen should look like this.

 

Step 2: Collect the following data from the screen, which you will use in the Analysis:

qsource= __________                qtest= ____________

 

mtest= ___________                 = _____________

 

Step 3: Press “play” (), and observe the motion of the test charge until it reaches the point (x,y) = (300,0). Then press the “pause” button (). Record the final velocity for the particle once it has reached this point. You will use this value in the Analysis.

= ___________

Analysis

 

Self-Check

 

SC 1.

1. Describe the motion of the test charge as it moved from (100,0) to (300,0).
   
   
2. Explain the motion of the particle using Newton’s laws of motion.
   
   
3. Draw a free-body diagram to show the force acting on the particle at the points (100,0) and (300,0).
   
   
4. Explain how the source charge was able to exert a force on the test charge even though the particles were not touching.

SC 2.

1. Calculate the magnitude and direction of the electric field of the source charge at the locations (100,0) and (300,0).
   
   
2. Explain how your answers to the previous question demonstrate that electric field varies inversely to the square of the distance from the source.
   

SC 3.

1. Use your values for electric field from SC 2.a. to calculate the magnitude and direction of the electrostatic force acting on the test charge at the locations (100,0) and (300,0).
   
   
2. Use your answers from SC 3.a. to calculate the acceleration of the test body at the locations (100,0) and (300,0).

 

Part A Conclusion

 

Non-uniform electric field

 

Module 3: Lesson 5 Assignment

 

Remember to submit the answers to LAB 1 and LAB 2 to your teacher as part of your Module 3: Lesson 5 Assignment.

 

LAB 1. Describe the motion of a test charge in a non-uniform electric field.

 

LAB 2. Explain the motion of a test charge in a non-uniform electric field.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Part B: Storing Potential Energy in a Non-Uniform Electric Field

 

Purpose

 

In this part of the lab activity you will continue to use electric field potential, non-uniform simulation to collect data enabling you to answer the following question:

• In which direction must a test charge be moved within an electric field if potential energy is to be stored in the system?

Procedure

 

Step 1: If you still have the computer simulation open from Part A of this lab activity, continue with the next step. If you need to re-open the simulation, you will need to enter the settings described in Part A.

 

Step 2: To return the particle to its initial position, (100,0), press “rewind” (). Press “data” () to view a data chart describing the particle, as well as a set of bar graphs of potential energy (in blue), kinetic energy (in red), and voltage (in yellow).

 

If these settings have been applied the screen should look like these settings:

 

Step 3: Press “play” (), and observe the changing energy values until the test charge reaches the point (x,y) = (300,0). Then press “pause” (). You may simply press “rewind” () to return the test charge to its starting position if you need to try again. Collect the following data, which you will use in the Analysis, for these two locations:

 

Data for the Test Charge at (100,0)	Data for the Test Charge at (300,0)
Kinetic Energy = Ek =	Kinetic Energy = Ek=
Potential Energy = Ep =	Potential Energy = Ep=
Total Energy = Etotal =	Total Energy = Etotall =

 

Step 4: Even though you will be properly introduced to voltage later in this lesson, this is a good opportunity to gather voltage data from the simulation. You will use this voltage data in the Analysis. Collect the following additional data for these two locations:

 

Data for the Test Charge at (100,0)	Data for the Test Charge at (300,0)
Potential Energy = Ep =	Potential Energy = Ep =
Test Charge = qtest =	Test Charge = qtest=
Voltage = V =	Voltage = V =

 

Step 5: Return the particle to its initial position, (100,0), by pressing “rewind” (). Enter the highest value of initial velocity that the simulation will accept, 30.0 m/s. Press “play” (), and let the simulation run in the background while you answer the next three questions.

 

Analysis

 

Self-Check

 

SC 4.

1. As the test charge moves from (100,0) to (300,0), calculate the change in the potential energy, kinetic energy, and the total energy.
   
   
2. Identify the physics principle that explains your results in SC 4.a.

SC 5. If the test charge were to be moved toward the source from (300,0) to (100,0) work would have to be done. The applied force would have to overcome the electrostatic force at each point between (300,0) and (100,0).

1. Explain the difficulties in using the equation to solve for the work in this case.
   
   
2. Use the idea that the potential energy is equal to the work done to change the position of an object to solve for the work in this case.

SC 6. Press “pause” (), and record the following values:

• position of the test charge: (x,y) = (________ m, __________ m)
  
  
• potential energy of the system = ____________

The simulation does not display potential energy values less than 1 J. If the system could display values of potential energy that were in millijoules or even in microjoules, you would be waiting forever for the potential energy of the system to reach zero. That’s because potential energy is defined to be zero at infinity—it takes an infinitely long time for a particle to move infinitely far away. Speculate on why infinity was chosen as the reference point having zero potential energy for this system.

 

 

Part B Conclusion

Module 3: Lesson 5 Assignment

Remember to submit the answer to LAB 3 to your teacher as part of your Module 3: Lesson 5 Assignment.

 

LAB 3. In which direction must a test charge be moved within an electric field if potential energy is to be stored in the system? Why?

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Storing and Releasing Potential Energy

 

© Vasily Smirnov/shutterstock (jumper)

Both of these photos show objects accelerating in fields. The BASE jumper is accelerating to Earth due to the force of gravity acting through Earth’s gravitational field. The charged soap bubbles are accelerating away from the charged globe of the Van de Graaff generator due to the electrostatic force acting through the electric field of the Van de Graaff generator. In both cases, potential energy stored in the system is being transformed into kinetic energy.

 

Read

 

You can find out more about the similarities between the potential energy stored in these two situations by reading pages 560 to 562 of your textbook. Pay special attention to “Example 11.5” and to the connections to the previous lab activity.

 

Self-Check

 

SC 7.

1. Define electric potential energy.
   
   
2. Solve “Practice Problem” 2 on page 561 of your textbook.
   
   
3. Explain why it is important to indicate the reference position when stating a value for potential energy.

SC 8. When it comes to calculations, the textbook uses a particular method for defining the reference point for electric potential energy. Describe this method, and relate it to your experiences with the simulation in the previous lab activity.

 

 

Electric Potential or Voltage

 

The following diagram summarizes some of the key findings from the previous lab investigation.

 

 

It takes 180 J of work to move a positive test charge from a point infinitely far away to a location 300 m from the source charge. Since this work was done against the electric field, the electric potential energy of the system is 180 J at this point. Note that electric potential energy is defined to be zero at infinity.

 

It takes even more work, 539 J, to move the same positive test charge from a point infinitely far away to a location 100 m from the source charge. The electric potential energy of the system is said to be 539 J at this point.

 

Although this system accurately describes the situation, it is impractical to make these sorts of measurements in practice. Measuring the work done moving tiny particles with minute amounts of charge is a problem. A more practical way to describe these situations is to use a new quantity called voltage (or electric potential).

 

 

Try This

 

TR 1. The volt is not a base SI unit. Break the volt down into C, kg, m, and s.

 

The following graphic illustrates how the voltage would be calculated for the results of the previous lab activity:

 

 

The number of volts describes the amount of energy required to move a coulomb from infinity to each location in the field—a value of “90 000 volts” means “90 000 joules per coulomb.”

 

Self-Check

 

SC 9. Suppose the test charge shown in the previous diagram was +4.0 mC instead of +2.0 mC.

1. Explain how this new value for the test charge would affect the amount of work required to move the test from infinity to each location.
   
   
2. Given your answer from SC 9.a., explain how this new value for test charge would affect the value of the voltage at each location.
   
   
3. Does the value of the voltage depend upon the value of the test charge?

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson 5 Lab: Electric Potential as a Function of Distance

 

Background Information

In the previous lab activity you collected data for a positive test charge that was forced to move in the electric field of a positive source charge. As the test charge was moved closer to the source charge, work was done and potential energy was stored in the system. Since the potential energy increased, the electric potential also increased as the test charge was brought closer to the source.

 

In the analysis of this system, it was noted that the electric field of the source and the electrostatic force exerted on the test charge both varied as the inverse of the distance squared from the source. Do you think that the electric potential also varies as the inverse square of the distance of separation?

 

Purpose

 

In this lab activity you will design an experiment and collect data to answer the following question:

• Does the electric potential between a source charge and a test charge vary as the inverse square of the distance of separation?

You may be required to enter a username and password. Contact your teacher for this information. You will use the capabilities of the Electric Field Potential, Non-Uniform simulation as a tool to gather the necessary data. Make the initial settings of the simulation identical to those used in the previous investigation.

 

In this set-up, you can collect data along the x-axis from 100 m to 600 m.

 

Module 3: Lesson 5 Assignment

 

Remember to submit the answers to LAB 4, LAB 5, and LAB 6 to your teacher as part of your Module 3: Lesson 5 Assignment.

 

LAB 4. Does the electric potential between a source charge and a test charge vary as the inverse square of the distance of separation? Describe a procedure that would enable you to collect the necessary data to answer this question.

 

LAB 5. Collect the necessary data, according to the steps of the procedure that you described in LAB 4.

 

LAB 6. Analyze the data that you collected so that you can answer the question posed in LAB 4.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Potential Difference

 

Electronic technicians complete a number of tasks when assembling circuit boards. A voltmeter is frequently used when testing circuits. The word voltage stems from the fact that potential difference is measured in volts with a voltmeter.

 

In these cases, the voltage is describing the amount of work required per unit of charge to move a test charge from one point to another within a circuit. Since the calculation involves subtracting one potential value from another, this quantity is called electric potential difference (or just potential difference for short).

 

 

In terms of an equation, electric potential difference is described as

 

 

The following calculation shows how to calculate the electric potential difference if the test charge in the previous lab activity was moved from an initial location 300 m from the source to a final location 100 m from the source.

 

 

Read

 

You can find out more about voltage by reading the sections called “Electric Potential” and “Electric Potential Difference” on pages 563 to 566 of your textbook. Pay close attention to the explanation of the electron volt and to “Example 11.8.”

 

Self-Check

 

SC 10.An electron is accelerated to high velocities within the picture tube of an old-style CRT (cathode ray tube) computer monitor. The potential difference used in the picture tube is 375 V.

1. The charge of an electron is 1.60 × 10–19 C. Calculate the energy gained by the electron in joules.
   
   
2. Calculate the energy gained by the electron in electron volts.
   
   
3. Consider your answers to SC 10.a. and SC 10.b. Suggest a reason why the electron volt is considered to be a convenient unit for researchers studying the behaviour of electrons and other particles in electric fields.

SC 11. a. Complete “Practice Problem” 2 on page 566 of your textbook.

2. Use your answer from SC 11.a. to determine the final velocity of the electron assuming that it started at 8.00×107 m/s. Remember that you can find the mass of the electron on your data sheet.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson 5 Lab: Storing Energy in Uniform Electric Fields

 

Purpose

 

In this lab activity you will use a computer simulation to collect data enabling you to answer the following questions:

• How does a test charge move in a uniform electric field?
• How can this motion be explained using physics principles?

Procedure

 

Step 1: You may be required to enter a username and password. Contact your teacher for this information. Open the Electric Field Potential, Uniform simulation, and enter the following settings:

• Reset the simulation (). Note that in this simulation the electric field is not varying as it is in the region surrounding a single point charge. The electric field in this simulation is uniform in strength and direction once the “play” button () is pressed.
  
  
• Turn on the grid ().
  
  
• Click on the “mode” button () for both the electric field and velocity until both of these quantities are displayed in the polar method (), showing a direction in degrees.
  
  
• Enter the following values for the electric field: 10.0 V/m at 0°. (Note that the unit for field used here, the volt per metre, is equivalent to a newton per coulomb. You’ll learn more about this later in the lesson.)
  
  
• Click on the vectors button, and turn on the electric field vector from the “Visible Vectors” option box.
  
  
• Enter the following values for the initial velocity: 5.0 m/s at 0°.
  
  
• Drag the test charge (red dot) to the following location: (x,y) = (100,0).
  
  
• Click on the “initial position” button () to have this position be the point where initial values are determined.
  
  
• If you choose to rewind (), you can return to these initial settings at any time during this lab activity. However, if you use the “reset” button (), you would have to re-enter all these initial settings.

If these settings have been applied, the screen should look like these settings.

 

Step 2: For the Analysis, you will need to collect the following data from the screen:

= __________                   = ____________

 

qtest = ___________          mtest = _____________

 

Step 3: Press play (), and observe the motion of the test charge until it reaches the point (x,y) = (300,0). Then press the “pause” button (). Use “rewind” () if it takes several attempts to get this right. Record the final velocity for the particle once it has reached (300,0). You will use this value for the Analysis.

= ___________

Analysis

 

Self Check

 

SC 12.

1. Calculate the magnitude and direction of the electrostatic force acting on the test charge at the locations (100,0) and (300,0).
   
   
2. Draw a free-body diagram to show the force acting on the particle at the points (100,0) and (300,0).
   
   
3. Refer to your answer to SC 12.b. How is this free-body diagram different from the one that you drew in the previous lab activity when the electric field was non-uniform?
   
   
4. Use your values for electrostatic force to calculate the acceleration of the test charge at the locations (100,0) and (300,0).

 

Conclusion

 

Uniform electric field

 

Module 3: Lesson 5 Assignment

 

Remember to submit the answer to LAB 7 to your teacher as part of your Module 3: Lesson 5 Assignment.

 

LAB 7. Describe the motion of a test charge in a uniform electric field.

 

LAB 8. Explain the motion of a test charge in a uniform electric field.

 

LAB 9. Explain why the equation cannot be applied in this situation.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

The Electric Field Between Charged Plates

 

Many graphic artists prefer to use the old-style CRT monitors because these monitors often give a truer representation of colours than LCD monitors.

 

The key component of a CRT monitor is the picture tube, which uses two oppositely charged parallel plates to accelerate a beam of electrons toward the screen. When the electrons hit the phosphor coatings on the inside of the screen, many colours of light are produced. Controlling the voltage regulates the electric field between the parallel plates in the picture tube. How does the voltage across two parallel plates relate to the strength of the electric field between those plates?

 

Read

 

To learn how potential difference can be used to develop a new equation describing the electric field between parallel plates, read pages 567 and 568 of your textbook.

 

Self-Check

 

SC 13. Produce a flowchart to show how potential difference can be used to derive a new equation describing the electric field between charged plates.

 

SC 14. Complete a unit analysis to show that one volt per metre is equivalent to one newton per coulomb.

 

SC 15. Complete “Practice Problem” 2 on page 568 of your textbook.

 

 

Try This

 

Researchers in a physics lab were experimenting with charged particles moving between parallel plates. In the course of their research, they decided to modify the apparatus to increase the strength of the electric field between the two plates.

 

The researchers doubled the potential difference across the plates and then reduced the separation of the plates to a third of its original value. As the following analysis with ratios demonstrates, the final arrangement of the apparatus resulted in producing an electric field that was six times stronger than the electric field in the initial arrangement of the apparatus.

 

 

 

 

 

Try This

 

TR 2. Suppose the researchers made further modifications to the apparatus. This time, they made the potential difference across the plates four times larger than the initial apparatus and they reduced the separation of the plates to a fifth of the initial value. Use a ratio analysis to determine how the electric field strength in this final arrangement compares to the electric field strength in the initial arrangement.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Reflect and Connect

 

Now that you have a better understanding of voltage, you should be able to explain some of the statements that were made in Get Focused.

 

SC 16. Explain the following statement: “When you rub a balloon on your head, you can generate thousands of volts completely safely.”

 

 

In general, sources of voltage are dangerous when large numbers of charges are involved because the energy is transferred through the motion of the charges. High-voltage power lines are certainly in this category because large numbers of charges have been given huge amounts of energy. It is not unusual for some power lines to operate at 250 kV. This combination of extremely high voltage with a huge number of charges makes these structures particularly dangerous. It’s important to have a comprehensive safety program when working near high-voltage power lines that conduct significant amounts of charge and energy.

 

 

Module 3: Lesson 5 Assignment

 

Remember to submit your Module 3: Lesson 5 Assignment to your teacher.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson Summary

 

At the beginning of this lesson you were asked the following essential questions:

• What is electric potential energy? How is it similar to gravitational potential energy?
• What is voltage? How is voltage calculated?

Both electric potential energy and gravitational potential energy result when work is done to move an object in a field. In both cases, work is done by applying an external force on the object that is opposite to the force that the field would exert on the object. Gravitational potential energy can be increased when a mass is moved up, away from Earth’s surface, parallel to the gravitational field. Electric potential energy can be gained by moving a positive charge toward a positive source, or by moving a negative charge away from a positive source. In both cases, the distance moved is parallel to the electric field.

 

While potential energy is measured in joules, electric potential is measured in volts. A volt is a joule per coulomb because electric potential is the change in electric potential energy stored per unit of charge. Many people prefer to use the term voltage for electric potential because it reminds them how this quantity is measured. In most applications, potential difference is used instead of electric potential because the change in energy stored per charge is measured relative to some other point in the electric field rather than using infinity as the reference point.

 

Dangers associated with high voltage increase with increasing amounts of charge. At very high voltages, the amount of energy per unit of charge is high, but the total amount of electrical energy can be limited by having few charges held at this voltage. In the case of high-voltage power lines, the product of high energy per unit of charge and the high number of charges can lead to electrocution and death.

 

Lesson Glossary

 

electric potential difference: the change in electric potential experienced by a charge moving from one point to another in an electric field

 

It is sometimes called potential difference.

 

voltage: the value, in volts, of the change in electric potential energy stored per unit of charge

 

It is also called electric potential.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson 6—The Motion of Charges in Uniform Electric Fields

 

Get Focused

 

The Genesee power plant at Wabamun Lake near Edmonton, Alberta, can generate 1.315 billion watts of power. To put that into perspective, this is enough power to supply the electrical energy needs of nearly 1.5 million homes in Alberta! The source of all this energy is coal from nearby surface mines. The coal seen in the next photo is being delivered, via conveyor, to a supercritical boiler, where it is crushed and mixed with oxygen at high pressure before being burned.

 

The useful energy output from the boiler is in the form of high-pressure steam. The steam is used to drive the turbines connected to the generators that produce electricity.

 

Electricity generating stations that burn pulverized coal as fuel often have particulate matter, such as bits of uncombusted coal, in the exhaust gas that leaves the furnace. This exhaust gas is called flue gas, and the particulate matter in flue gas can be a significant source of air pollution if it is not removed before entering the environment.

 

There are technologies designed to remove particulate matter from flue gas. The most common technology is called an electrostatic precipitator. This device works by first charging the tiny particles in the flue gas and then by removing these particles using strong electric fields.

 

How strong would the electric fields have to be to effectively remove over 99% of the particulate matter from the flue gas? The answer to this question depends on typical values for charge, mass, and initial velocity for individual particles. In other words, the answer depends on combining what you have been learning about electrostatics in this lesson, along with the physics of Newton's laws and projectile motion from previous courses.

 

In this lesson you will answer the following essential questions:

• How do charged particles move in a uniform electric field? How is this motion similar to a mass moving in a gravitational field?
  
  
• Is it possible to predict the velocity, acceleration, and displacement of charged particles moving in electric fields?

Module 3: Lesson 6 Assignments

Your teacher-marked Module 3: Lesson 6 Assignment requires you to submit a response to the following:

• Lab—LAB 1, LAB 2, LAB 3, LAB 4, LAB 5, LAB 6, and LAB 7
• Assignment—A 1 and A 2

You must decide what to do with the questions that are not marked by the teacher.

 

Remember that these questions provide you with the practice and feedback that you need to successfully complete this course. You should respond to all the questions and place those answers in your course folder.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Explore

 

 

An electrostatic precipitator works using positively charged parallel plates, which sandwich negatively charged metal rods that hang between the plates. As the particles in the flue gas pass the negatively charged rods, the particles pick up negative ions and become negatively charged. These negatively charged particles are then attracted to the positive plates where they are collected. By the time the flue gas has passed through a long column of rods and plates, over 99% of the particulate matter has been removed. Periodically, the large positive plates are rapped with automated hammers, causing the particles to drop into the hoppers below the plates.

 

The pattern of the electric field lines within an electrostatic precipitator is a combination of the patterns formed by field lines between parallel plates with the patterns that surround negative sources.

 

 

Self-Check

 

SC 1. Classify the pattern of electric field lines close to the negatively charged rod as being either "uniform" or "radial.”

 

SC 2. Classify the pattern of electric field lines close to the positively charged plates as being either “uniform” or “radial.”

 

 

The Motion of Charged Particles in Radial Electric Fields

 

To develop an understanding of how an electrostatic precipitator works, you will first take a look at the motion of charged particles in radial electric fields.

 

Read

 

You can learn how the motion of charged particles can be analyzed in non-uniform electric fields by reading pages 570 and 571 of your textbook. Pay special attention to the way that the law of conservation of energy is used in “Example Problem 11.10.”

 

Self-Check

 

SC 3. Explain why the equations for accelerated motion could not be used for situations like the one described in “Example Problem 11.10.”

 

SC 4. Solve “Practice Problem” 2 on page 571 of your textbook.

 

 

 

 

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

The Motion of Charged Particles in Uniform Electric Fields

 

The motion of an individual charged particle in a uniform electric field is not something that most people observe on a daily basis. However, the motion of a mass in a uniform gravitational field is something that almost everyone has experienced but may not know it.

 

Think back to the last time you were watching or playing sports when a ball was given a velocity and then allowed to move through Earth's gravitational field. If the batter in the photo connects her bat with the ball, what additional information would you need in order to predict the motion of the ball?

 

If spinning effects can be ignored, the motion of the ball depends upon the direction of the initial velocity of the ball once it leaves the bat. As you'll see in the next question, the path of the ball is a consequence of Newton's laws of motion.

 

Self-Check

 

SC 5. In each of the following diagrams, the initial velocity of a softball is shown relative to the direction of the gravitational field. Make your own copy of each diagram, and add the following information:

• the direction of the force of gravity on the ball
• the path of the ball
• the concise explanation of the path that you drew

Ignore the effects of air resistance, and consider the force of gravity to be the only force acting on the ball.

 

 

 

Read

 

You can learn how the motion of charged particles can be analyzed in uniform electric fields by reading pages 572 and 573 of your textbook. Note how kinetic and potential energy are assigned zero values in “Example Problem 11.11.”

 

Self-Check

 

SC 6. Solve “Practice Problem” 1 on page 573 of your textbook.

 

 

The same physics principles used to analyze the motion of a softball in the gravitational field of Earth can be used to analyze the motion of a charged particle moving in a uniform electric field. When a charge travels through a uniform electric field, the type of motion that results depends on the direction of the force acting on the particle relative to the direction of the particle's initial velocity. In the next lab activity you will have an opportunity to investigate this further.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson 6 Lab: Motion of Charges in Uniform Electric Fields

 

This lab consists of four parts. In Part A, you will examine the motion of a positively charged particle when it initially moves parallel to the electric field. In Part B you will examine the motion of a positively charged particle when it initially moves perpendicularly to the electric field. In Part C you will examine how a negatively charged particle will move when it starts parallel to the electric field. Finally, in Part D you will examine the motion of a negatively charged particle when it initially moves perpendicularly to the electric field.

 

Part A: Positive Particle Moves Parallel to the Electric Field

 

Purpose

 

In this part of the lab activity, you will use a computer simulation to collect data enabling you to answer the following questions:

• How does a positive particle move when the direction of its initial velocity is opposite to the direction of the electric field?
  
  
• How can this motion be explained using physics principles?

Procedure

 

Step 1: Open the Electric Field Potential simulation, and enter the following settings:

• Reset the simulation ().
  
  
• Set the direction of the electric field to 0° W of S using the drop-down menu in the electric field display panel. Press the “enter” button on the keyboard to change the value in the textbox. Enter a value of 75 V/m for the magnitude of the electric field in the electric field display panel. Note that the electric field vector is shown as a large, green arrow. The small, green arrows indicate that the field has the same value at all locations on the screen.
  
  
• Set the direction of the initial velocity to 0° E of N using the drop-down menu in the velocity display panel. Enter a value of 150 m/s for the magnitude of the initial velocity in the velocity display panel. The velocity vector is shown as a magenta (purplish red) arrow.
  

• Set the particle's charge and mass to + 2.0 C and 3.0 kg, respectively.

• Drag the particle to a position low on the screen.

• Note that if you use “rewind” (), you can return to these initial settings at any time during this lab activity. However, if you use “reset” (), you will have to re-enter all these initial settings.

If these settings have been applied, the screen should look like this:

 

 

 

Step 2: Given these initial conditions, make a prediction as to how you think the particle will move if it is released. Press the “play” button () to confirm your prediction.

 

Step 3: Use “rewind” () to return to the initial settings. Repeat the previous step, but use “pause” () to stop the motion at the instant the particle reaches its highest point. Use “data” () to display information about the elapsed time, Δt, the x and y components of the acceleration (x, y), and the x and y components of the displacement (dx, dy) from the start of the motion.

 

Step 4:  Collect the following data:

 

elapsed time   Δt = ________ s

 

charge   q = ____________ C

mass   m = ___________ kg

Express the remaining values in terms of x and y components:

 

electric field    = ___________V/m

acceleration   (ax, ay) = ___________m/s2

initial velocity   (vix, viy) = (0, 150) m/s

final velocity   (vfx, vfy) = ____________m/s

maximum displacement   (Δdx, Δdy) = __________m

 

Press the green button beside the once to see the final velocity in terms of x and y components.

final velocity              (vfx, vfy) = ____________m/s

 

Note that the acceleration due to gravity is ignored in this simulation.

 

Analysis

 

Self-Check

 

Note that the values will be close to, but not necessarily exactly the same as, the answers shown. This is because you might have a slightly different time, ±0.20 s. However, your results will match the simulation’s values.

 

SC 7. Use Newton's laws of motion to verify the x and y components of the acceleration.

 

SC 8. Use calculations to verify the x and y components of the maximum displacement.

 

SC 9. Describe and explain a situation involving gravitational fields that could produce a similar type of motion.

 

 

Module 3: Lesson 6 Assignment

 

Remember to submit the answers to LAB 1 and LAB 2 to your teacher as part of your Module 3: Lesson 6 Assignment.

 

LAB 1. Summarize what you have learned from this simulation by stating what will happen when

• a positive particle has an initial velocity opposite to the direction of the electric field.
• a positive particle has an initial velocity in the same direction as the electric field.

LAB 2. Use physics principles to explain the motion you described in LAB 1.

 

Part B: Positive Particle Moves Perpendicular to the Electric Field

 

Purpose

 

In this part of the lab activity you will use a computer simulation to collect data enabling you to answer the following questions:

•  How does a positive particle move when the direction of its initial velocity is perpendicular to the direction of the electric field?
  
  
• How can this motion be explained using physics principles?

Procedure

 

Step 1: Open the Electric Field Potential, Uniform simulation, and enter the following settings:

• Reset the simulation ().
  
  
• Set the direction of the electric field to 0o W of S using the drop-down menu in the electric field display panel. Enter a value of 75 V/m for the magnitude of the electric field in the electric field display panel.
  
  
• Set the direction of the initial velocity to 0o S of E using the drop-down menu in the velocity display panel. Enter a value of 150 m/s for the magnitude of the initial velocity in the velocity display panel.
  
  
• Set the particle's charge and mass to +2.0 C and 3.0 kg, respectively.
  
  
• Drag the particle to a position on the left of the screen and centred vertically.
  
  
• Note that if you use “rewind” (), you can return to these initial settings at any time during this lab activity. However, if you use “reset” (), you will have to re-enter all these initial settings.

If these settings have been applied, the screen should look like this.

 

 

Step 2: Given these initial conditions, make a prediction as to how you think the particle will move if it is released. Press the “play” button () to confirm your prediction. To see the path that the particle followed, use the “rewind” button (). Then use the “trace” button ().

 

Step 3: Use “rewind” () to return to the initial settings. Repeat the previous step, but use “pause” () to stop the motion at the instant the particle starts to leave the display. Use “data” () to display information describing the particle in this location.

 

Step 4: Collect the following data:

 

 

Express the remaining values in terms of x and y components:

 

 

Note that the acceleration due to gravity is ignored in this simulation.

 

Analysis

 

Self-Check

 

SC 10.

1. Use calculations to verify the x component of the displacement.
   
   
2. Use calculations to verify the y component of the displacement.

SC 11. Use calculations to verify the y component of the final velocity.

 

SC 12. Use calculations to verify the magnitude and the angle of the final velocity as displayed in the velocity display panel.

 

SC 13. Describe a situation involving gravitational fields that could produce a similar type of motion.

 

 

Module 3: Lesson 6 Assignment

 

Remember to submit the answers to LAB 3 and LAB 4 to your teacher as part of your Module 3: Lesson 6 Assignment.

 

LAB 3. Describe the motion of a positive particle when the direction of its initial velocity is perpendicular to the direction of the electric field.

 

LAB 4. Use physics principles to explain the motion you described in LAB 3.

 

Part C: Negative Particle Moves Perpendicular to the Electric Field

 

Purpose

 

In this part of the lab activity you will use a computer simulation to collect data enabling you to answer the following question:

• How does a negative particle move when the direction of its initial velocity is perpendicular to the direction of the electric field?
  
  
• How can this motion be explained using physics principles?

Procedure

 

Step 1: If you still have the simulation open from Part B of this lab activity, continue with the next step. Otherwise, re-open the Electric Field Potential, Uniform simulation, and enter the settings described in Step 1 of Part B.

 

Step 2: To return the particle to its initial position, press “rewind” ().

 

Step 3: Make the following adjustments to the initial settings:

• Change the charge of the particle to –2.0 C.
  
  
• Set the direction of the initial velocity to 0o N of E using the drop-down menu in the velocity display panel. Enter a value of 150 m/s for the magnitude of the initial velocity in the velocity display panel.

If these settings have been properly applied, the screen should look like this:

 

 

Step 4: Given these initial conditions, predict how the particle will move if it is released. Press the “play” button () to confirm your prediction.

 

Step 5: Use “rewind” () to return to the initial settings. Repeat the previous step, but use “pause” () to stop the motion at the instant the particle starts to leave the display. Use “data” () to display information describing the particle at this location.

 

Step 6: Collect the following data:

 

 

Express the remaining values in terms of x and y components:

 

 

Note that the acceleration due to gravity is ignored in this simulation.

 

Analysis

 

Self-Check

 

SC 14. a. Use calculations to verify the x component of the displacement.

2. Use calculations to verify the y component of the displacement.

SC 15. Use calculations to verify the y components of the final velocity.

 

SC 16. Use calculations to verify the magnitude and direction of the final velocity as displayed in the velocity display panel.

 

SC 17. In this part of the lab, a particle that had an initial velocity perpendicular to a field moved through a parabolic trajectory so that it accelerated in a direction opposite to the external field. Explain why this situation could never happen in a gravitational field.

 

 

Module 3: Lesson 6 Assignment

 

Remember to submit the answers to LAB 5 and LAB 6 to your teacher as part of your Module 3: Lesson 6 Assignment.

 

LAB 5. Describe the motion of a negatively charged particle when the direction of its initial velocity is perpendicular to the direction of the electric field.

 

LAB 6. Use physics principles to explain the motion you described in LAB 5.

 

Part D: Producing an Un-deflected Path Through an Electric Field

 

Purpose

 

In this part of the lab activity you will use a computer simulation to collect data enabling you to answer the following question:

• If a particle is given an initial velocity perpendicular to an electric field, under what circumstance could this particle move un-deflected with uniform motion through the electric field? Assume the electric field is the only field present.

Procedure

 

Step 1: If you still have the simulation open from this lab activity, continue with the next step. Otherwise, re-open the Electric Field Potential, Uniform simulation, and enter the settings described in Step 1 of Part B.

 

Step 2: To return the particle to its initial position, press “rewind” ().

 

Step 3: Without changing the settings for the electric field or the velocity, what adjustment could you make so that the particle moves with only uniform motion when you release the particle? Make the necessary adjustment and press “play” () to confirm your prediction.

 

Step 4: Use “rewind” () to return to the initial settings. Repeat the previous step, but use “pause” () to stop the motion at the instant the particle starts to leave the display. Use “data” () to display information describing the particle in this location.

 

Self-Check

 

SC 18. Identify the values on the data chart that confirm that the particle is only moving with uniform motion.

 

 

Module 3: Lesson 6 Assignment

Remember to submit the answer to LAB 7 to your teacher as part of your Module 3: Lesson 6 Assignment.

 

LAB 7. Explain the circumstances that enable an article to move un-deflected with uniform motion through an electric field if it is given an initial velocity perpendicular to the electric field. Assume the electric field is the only field present.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Pulling it All Together: Charges, Fields, and Projectile Motion

 

As a soccer ball arcs through the air from one end of the field to the other, its path follows the characteristic pattern of a projectile, a parabolic trajectory. In the previous lab activity you used a computer simulation to discover that a charged particle can also move through a parabolic trajectory. The analysis of the data from the simulation revealed that the same equations that you used to analyze projectile motion in previous courses can be applied to a charged particle moving through a uniform electric field.

 

Now it’s time to apply these analytical skills to problem solving. In the next activity you will have an opportunity to apply what you learned to a variety of new situations.

 

Sketching the Paths of Charged Particles in Uniform Electric Fields

 

In the previous lab activity you developed some general statements that described how charged particles would move in specific circumstances. In this activity you will have a chance to apply those statements as you predict the motion of individual particles moving through electric fields.

 

Purpose

 

In this activity you will sketch the paths of charged particles in a number of different circumstances.

 

Procedure

 

Answer the following Assignment question.

 

Module 3: Lesson 6 Assignment

 

Remember to submit the answer to A 1 to your teacher as part of your Module 3: Lesson 6 Assignment.

 

A 1. In your Module 3: Lesson 6 Assignment, diagrams show the initial position and the velocity vector of a charged particle within a uniform electric field. For each diagram, follow each of these steps:

• Sketch a free-body diagram showing the net force that acts on the particle.
  
• Sketch the path of the particle.
  
  

Self-Check

 

SC 19. The following diagram shows an electron entering the region between two oppositely charged plates. The plates are 55.0-mm long and are separated by 19.5 mm. A potential difference of 0.133 V across the plates generates a uniform electric field in the region between the plates. The electron is given an initial velocity of 8.50 × 105 m/s in the positive ydirection. Use this information to determine the final velocity of the electron when it leaves the region between the plates.

 

Be sure to begin your solution with a free-body diagram and an analysis of the physics principles that will support your solution.

 

 

 

Module 3: Lesson 6 Assignment

 

Remember to submit the answer to A 2 to your teacher as part of your Module 3: Lesson 6 Assignment.

 

A 2. The following diagram shows a proton entering the region between two oppositely charged plates. The plates are 45.0 mm long and are separated by 17.5 mm. A potential difference of 0.208 V generates an electric field between the plates. The proton is given an initial velocity of 1.35 × 104 m/s in the positive x direction. Use this information to determine the y component of the displacement of the proton when it leaves the region between the plates. (Note: This displacement is how far the proton has moved above or below the x-axis the instant it leaves the region between the plates.)

 

Be sure to begin your solution with a free-body diagram and an analysis of the physics principles that apply.

 

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Reflect and Connect

 

The engineers who design electrostatic precipitators for coal-fired generating stations have to balance the need to significantly reduce the particulate matter that enters the air with the need to run the units efficiently. Since the electric fields within the units are sustained by high-voltage sources, it makes sense to create a design that effectively removes the particulate matter using the minimum amount of electrical energy. Keep these ideas in mind as you answer the following questions.

 

 

Try This

 

TR 1. The electric field between the negatively charged rods and the positively charged plates of an electrostatic precipitator has to be strong enough to generate negatively charged ions that can be picked up by the particles in the flue gas. If the field is not strong enough, then the some of the particles might remain uncharged while in the electrostatic precipitator. Explain the outcome for a microscopic bit of coal dust within the electrostatic precipitator if it remains uncharged.

 

TR 2. A key consideration for the design engineers is the speed of the particles within the flue gas. The faster the charged particles move, the more difficult it is to deflect them toward the collector plates.

1. Produce a simple sketch to illustrate why it is more difficult to deflect a fast-moving charged particle than a slow-moving charged particle in a given electric field. Assume that each particle has the same mass and charge.
   
   
2. Identify two reasons why increasing the strength of the electric field within the electrostatic precipitator makes it easier to deflect the particles in the flue gas.
   
   
3. Explain why it is easier to deflect particles within the flue gas to the collector plates if the collector plates are kept close together and made as long as possible.
   
   
4. Post your solutions to the discussion area. Read some of the other solutions from other students. Choose which of the solutions from the postings is best and identify why you think so.

Module 3: Lesson 6 Assignment

 

Remember to submit the answers to your assignment questions to your teacher.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Lesson Summary

 

At the beginning of this lesson, you were asked the following essential questions:

• How do charged particles move in a uniform electric field? How is this motion similar to a mass moving in a gravitational field?
  
  
• Is it possible to predict the velocity, acceleration, and displacement of charged particles moving in electric fields?

Charged particles in uniform electric fields move according to Newton’s laws of motion. This makes the motion of a charged particle very similar to the motion of a mass in a gravitational field. In both cases, the test body accelerates in the direction of an unbalanced force as described by Newton’s second law. If there is no unbalanced force, then the test body maintains its velocity as described by Newton’s first law. If one component of the velocity of a test body is maintaining a constant velocity, while another component is accelerating, then the test body will move through a parabolic trajectory or projectile motion.

 

The equations used to analyze projectile motion in previous courses can be applied to the motion of a charged particle in a uniform electric field.

 

For example, the equation Δd =½aΔt2 can be applied not just to projectile motion in a gravitational field, but also to the motion of a charged particle in a uniform electric field. To apply the formula to the motion of a charged particle, you simply take the variable a to refer to the acceleration due to the force of the uniform electric field.

 

The formula for projectile motion can be used to calculate the velocity, displacement, and acceleration of the motion of charged particles. The engineers who design electrostatic precipitators use the formulas of projectile motion to ensure that these devices work to effectively remove over 99% of the particulate matter from the flue gases produced at coal-fired generating stations.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Module Summary

 

In Lesson 1 you looked at key concepts that are essential to understanding electrostatics, including the attraction and repulsion of charges, the law of conservation of charge, and the three methods of transferring charge: by friction, by conduction, and by induction.

 

In Lesson 2 you worked with Coulomb’s law:

 

This law says, if the charges are held constant and the distance of separation increases by some factor, then the effect on the resulting electrostatic force can be predicted. For example, if the distance increases by a factor of four, then the electrostatic force would be 1/16th its original value.

 

In Lesson 3 you learned more about the enormous amounts of charge that a lightning strike can deliver from a cloud to Earth. You also saw that Coulomb’s law can be used to calculate the net force on one point charge due to other point charges. You looked at solutions to these sorts of problems, which required you to consider the vector nature of electrostatic forces.

 

In Lesson 4 you learned that an electric field is the property of space surrounding a source charge that enables the source charge to exert forces on other charges that enter this region. One way to describe electric fields is to use equations:

 

 

The direction of an electric field is determined by the direction of the electrostatic force experienced by a small positive test charge. This can be used to describe electric fields in terms of patterns of electric field lines around source charges.

 

In Lesson 5 you saw that both electric potential energy and gravitational potential energy result when work is done to move an object in a field. In both cases, work is done by applying an external force on the object that is opposite to the force that the field would exert on the object. Gravitational potential energy can be increased when a mass is moved up, away from Earth’s surface, and parallel to the gravitational field. Electric potential energy can be gained by moving a positive charge toward a positive source, or by moving a negative charge away from a positive source. In both cases the distance moved is parallel to the electric field.

 

While potential energy is measured in joules, electric potential is measured in volts. A volt is a joule per coulomb. Many people prefer to use the term voltage for electric potential because it reminds them how this quantity is measured.

 

In Lesson 6 you learned that charged particles in uniform electric fields move according to Newton’s laws of motion. This makes the motion of a charged particle very similar to the motion of a mass in a gravitational field. In both cases the test body accelerates in the direction of an unbalanced force. If there is no unbalanced force, then the test body maintains its velocity. The equations used to analyze projectile motion in previous courses can be applied to the motion of a charged particle in a uniform electric field.

 

For example, the equation Δd =½aΔt2 can be applied not just to projectile motion in a gravitational field, but also to the motion of a charged particle in a uniform electric field. The formula for projectile motion can be used to calculate the velocity, displacement, and acceleration of the motion of charged particles.

 

Module Assessment

 

As your module assessment do the following two questions. The first is a graphing question, and the second is a holistic question.

 

Use the following information to answer this graphing question.

 

 

• Show that the results verify Coulomb’s law by manipulating the data and providing a new table of values that, when plotted, will produce a straight-line graph.
  
  
• Plot the new data with the responding variable on the vertical axis.
  
  
• Calculate the slope of your graph.
  
  
• Using the slope value or another suitable averaging technique, determine the charge on sphere B if the charge on sphere A is 3.08 × 10–7 C
  
  
• Determine the magnitude of the force between spheres A and B when they are at a distance of 2.00 m apart. Use the hypothetical value of 4.00 × 10–6 C for the charge on sphere B if you were unable to determine the actual value.

 

Use the following information to answer this holistic question.

 

 

• Compare and contrast how each gun charges the paint powder.
  
  
• Why are corona guns affected by the Faraday cage effect whereas tribo guns are not?
  
  
• Explain why electrostatic spraying of powdered paint is far more efficient in terms of the amount of paint that attaches to the target than sprayed liquid paint.

 

Your answers must clearly communicate your understanding of the physics principles you used to solve these questions. You may communicate this understanding mathematically, graphically, and/or with written statements.

Physics 30 Learn EveryWare © 2009 Alberta Education

Module 3—Electrical Phenomena

 

Module Glossary

 

Coulomb’s law: the magnitude of the electrostatic force between two charged objects is directly proportional to the product of the two charges on the objects and inversely proportional to the square of the distance of separation between their centres

 

electric field: a property of the space around a source charge that enables the source charge to exert forces on test charges in the region

 

electric potential difference: the change in electric potential experienced by a charge moving from one point to another in an electric field

 

It is sometimes called potential difference.

 

field: a region of influence surrounding an object through which a force operates

 

grounding: the process of transferring charge to and from Earth

 

torsion balance: an instrument designed to measure small forces by the twisting of a thin wire

 

voltage: the value, in volts, of the change in electric potential energy stored per unit of charge

 

It is also called electric potential.

Physics 30 Learn EveryWare © 2009 Alberta Education