Read
Refer to pages 598−600 of the textbook for an explanation of how to calculate the magnetic force acting on a charged particle.

 
Self-Check

Read the information below then answer the following self-check (SC) questions.  When ready, click the "Check your work" bar to assess your responses.

 

Experiments were conducted to see if flue gases from a power plant could be cleaned using a magnetic field.  In one experiment with particles of mass 2.0 × 10 -20 kg, and speed of 1.50 × 10 -2 m/s, the following data was collected:

 

Charge on Particle (×10 -17 c)

Radius of Curvature (×10 -3 m)

1

150

2

75

3

50

4

36

5

30

10

15

 

Use the data to answer the following questions.

 

SC 1.  

Graph the data and draw a best-fit curve through the data points.

 

SC 2.  

Is there an easy way for you to find the magnetic field strength from this information?

 

SC 3.  

Graph the data using the reciprocal of the charge in place of the charge and draw a best-fit curve through these data points.

 

SC 4. 

Is there an easy way for you to find the magnetic field strength from this new graph?

 

   Self-Check Answer

Contact your teacher if your answers vary significantly from the answers provided here.

 

SC 1.  

You can graph the data in several ways. You might

  • use graph paper and plot the points by hand

  • use a graphing calculator to graph the points

  • use a spreadsheet to graph the points


This graph uses a spreadsheet to graph the points. You may think of better titles for the graph and labels for the axes when you create your own graphs.

 

 

SC 2.  

With a curved graph, it is difficult to find the magnetic field strength.

 

SC 3.  

Again, the data can be graphed in several ways. This graph uses a spreadsheet to graph the points. You may think of better titles for the graph and labels for the axes when you create your own graphs.

 

 

SC 4.  

This graph is a straight line. The slope of this graph gives an easy way to find the magnetic field strength. The slope is equivalent to  , so the magnetic field strength can be found from  .

 

In this self-check question you used curve straightening to get useful information. You should consider using this technique whenever you need more information from a curved graph.

 

The Direction of the Magnetic Force

 

As you discovered earlier, the magnetic force causes the charged particle to travel in uniform circular motion.  As a review, determine the inward force on the following diagrams.  The first one (a) has been completed as an example.  The particles below are positively charged.


a.  
b. 
c.

When a charged particle is moving at right angles to a magnetic field, the force exerted on the particle by the field is perpendicular to both the particle's velocity and the magnetic field.  Refer again to the diagram on page 594 of the textbook.  To may visualize the orientation this way: two of the quantities will be in the same plane of motion (able to be drawn on the same piece of paper) and the third will be into or out of that plane (the piece of paper).

To predict the direction of the magnetic force, one only needs to know the direction of the particle's velocity and the direction of the magnetic field.  However, this does not completely define the direction of the force.  There is still an ambiguity because a perpendicular has two directions.  This ambiguity is resolved by the left-hand rule illustrated in Figure 2.  (There are several hand rules for this purpose.  The following is only one suggestion.)

 

Left -hand Rule for Deflection:  The direction of the force exerted on a negatively charged particle moving in a magnetic field can be visualized by the left-hand rule.

 

 

Figure 2

 

Hold your left hand flat with outstretched fingers in the direction of the magnetic field ( ) and with the thumb pointing off to one side in the direction of the particle's velocity ( ).  The palm of your hand will then be pointing in the direction of the magnetic force ( ).

 

This left-hand rule predicts the force that would act on negative charge.  For a positive charge, use your right hand with your fingers, thumb, and palm representing the same quantities.