Lab Simulation: Coulomb's Experiment (Part A)

In this lab you will simulate what Coulomb did to derive the equation to describe the electrostatic force.  The first part of this lab investigates the relationship between the distance of separation ( r on the electrostatic force  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mfenced open=¨|¨ close=¨|¨» «msub» «mover» «mi»F«/mi» «mo»§#8594;«/mo» «/mover» «mi»e«/mi» «/msub» «/mfenced» «/math» , while the second part investigates the relationship between the amount of charge ( q1 and q2 and the resulting electrostatic force «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«/math»

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

 


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.


You will need a calculator, a pencil, an eraser, a straight edge or ruler, and a piece of graph paper (or 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.


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 then answer the following Self-Check questions.

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

The acceleration is caused by electrostatic force acting on sphere A. According to Newton's third law, an equal force is acting in the opposite direction on sphere B.


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

The force on sphere A will act to push it away from sphere B since each sphere has a negative charge and like charges repel.


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.)

Sphere A will rotate counterclockwise since it is repelled from sphere B.  If the arm on the torsion balance rotates, it will cause the torsion spring to tighten with a certain force. This is indicated on the scale. Coulomb had predetermined the graduation of the force scale in grains of force. In this simplified version, the scale is set in units of force that will be referred to as F units.



Spheres A and B on the torsion balance diagram are identical in size and both are made of metal.

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

  • Since sphere A and sphere B are conductors, electrons will flow from sphere B to sphere A until the charge on each is the same. This is an example of charging by contact.

  • The total charge must be  q B , in accordance with the law of conservation of charge.

  • Since the original amount of charge  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»q«/mi»«mi»B«/mi»«/msub»«/math»  is shared, the charge on sphere A will be  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«msub»«mi»q«/mi»«mi»B«/mi»«/msub»«/math»  and the charge on sphere B will be «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«msub»«mi»q«/mi»«mi»B«/mi»«/msub»«/math»


 


  • Sphere B is initially given a negative charge by touching it to a charged rubber rod that was rubbed with fur. Because 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.  Coulomb's actual apparatus, the angles of rotation were all less than 10°.

The following video will show you the results when Coulomb released sphere A from different distances.  You may pause the video at any time to record the data in a 2-column table.



From the video create a chart of data values showing the distance of separation and the corresponding force for each trial.

For scientific charts the Manipulated Variable is recorded in the left column and the Responding Variable is recorded in the right column.

Remember that you can use a graphing calculator or a spreadsheet instead of a paper chart.

Distance Between the Centers of Charge A and B, r
(cm)
Electrostatic Force Acting on Sphere A,«math style=¨font-family:stix¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mfenced open=¨|¨ close=¨|¨ mathcolor=¨#FFFFFF¨»«msub»«mover»«mi mathvariant=¨italic¨»F«/mi»«mo mathvariant=¨italic¨»§#8594;«/mo»«/mover»«mi mathvariant=¨italic¨»e«/mi»«/msub»«/mfenced»«/mstyle»«/math»
(N)
1.0 16.0
2.0 4.0
4.0 1.0
8.0 0.3



Using the data from your observations draw a graph of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«/math» as a function of r .


To create a graph in physics start by identifying the manipulate, responding and constant variables. For this lab this would be:

  • Manipulated variable: distance between the charges.
  • Responding variable: electrostatic force, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«/math», since the force acting on sphere A depended upon the distance value.
  • Constant variables: the charge on each of the spheres.
There are two ways to graph the results. Method 1 uses pencil and graph paper.  Method 2 uses a graphing calculator or computer. You are required to complete only one of the two methods.

When presenting your graph be sure to include the following:

  • The manipulated variable is on the x-axis
  • The responding variable is on the y-axis
  • Give your graph a title
  • Label the axis appropriately, include units
  • Create a scale for the axis and ensure that  all data points can be included and the graph is easy to read.

Method 1: Using Pencil and Paper



Method 2: Using Graphing Calculator or Spreadsheet



If you are using a Texas Instrument Graphing Calculator use the following steps.

Select the WINDOW button and adjust the window settings to the following:


Select the STAT button and select 1:Edit...
Enter the values for the distance in L1 and the values for the force in L2



Select the GRAPH button



 An inverse square relationship implies that if one variable increases by a factor of 2, then the other variable decreases by a factor of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math» . This is due to the fact that the inverse square of 2 is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math». This pattern is clearly shown between adjacent pairs of data points. For example, when the distance doubles from 1 cm to 2 cm, the value of the force is reduced from 16 force units to 4 force units, or by a factor of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math» .

It is difficult to gather meaningful information from curved graph but easy if the graph is a straight line of the form y=mx +b. To create a straight line graph from a inverse square relationship use one of the following methods in the tutorial Straightening the Curve of an Inverse Square Relationship.

To start add a third column to your previous observation graph and calculate the inverse square of the distances.

Distance Between the Centers of Charge A and B, r
(cm)
 Inverse square of distance, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mn mathvariant=¨bold¨»1«/mn»«msup»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mfenced open=¨[¨ close=¨]¨ mathcolor=¨#FFFFFF¨» «mfrac» «mn mathvariant=¨bold¨»1«/mn» «mrow» «mi mathvariant=¨bold¨»c«/mi» «msup» «mi mathvariant=¨bold¨»m«/mi» «mn mathvariant=¨bold¨»2«/mn» «/msup» «/mrow» «/mfrac» «/mfenced» «/math»
Electrostatic Force Acting on Sphere A,«math style=¨font-family:stix¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mfenced open=¨|¨ close=¨|¨ mathcolor=¨#FFFFFF¨»«msub»«mover»«mi mathvariant=¨italic¨»F«/mi»«mo mathvariant=¨italic¨»§#8594;«/mo»«/mover»«mi mathvariant=¨italic¨»e«/mi»«/msub»«/mfenced»«/mstyle»«/math»
(N)
1.0 1.0 16.0
2.0 0.25 4.0
4.0 0.063 1.0
8.0 0.016 0.3

Method 1: Using Pencil and Paper



Method 2: Using Graphing Calculator or Spreadsheet


If you are using a Texas Instrument Graphing Calculator use the following steps.

Select the WINDOW button and adjust the window settings to the following:


Select the STAT button and select 1:Edit...
Enter the values for the inverse of the distance squared in L1 and the values for the force in L2



To graph the data and determine the equation of the straight line, follow the instructions in the following link.

How to determine the equation of the line

The resulting graph will look like this


Part A Conclusion

Now that you have reviewed 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.
The electrostatic force, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«/math», is inversely proportional to the square of the distance, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/math».   Mathematically, this is written as «math style=¨font-family:`Courier New`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«mo»§#160;«/mo»«mi»§#945;«/mi»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mrow»«/mstyle»«/math» .