Magnetic Fields
and
Force on a Moving Charged Particle in a Magnetic Field
Studio Physics I
Introduction to Magnetic Fields
We will begin our investigation of magnetic fields by using a compass to map out the
shape and direction of magnetic fields. A compass needle is a small magnet. It aligns
itself parallel with a magnetic field.
1. Does the red end of the compass needle point toward or away from a south pole of a
magnet? Does it point toward or away from the north pole of a magnet? Use the bar
magnet you have been given to determine this. Also take a minute to play with two
bar magnets. Try to make one of bar magnets spin around on your desktop by
attracting or repelling it with the other magnet.
2. If you face the screen at the front of your classroom, you will be facing
(approximately) north. Does the red end of the compass needle point toward the
geographic north pole? (Did it point toward a magnetic north pole?) Based on this
observation, would you say that the geographic north pole is a north or south magnetic
pole?
You should have found that for our compasses, the red end of the needle points in the
direction of the magnetic field. That is, it will point away from the north pole of a magnet
and toward the south pole of a magnet. We will use this information to map the shape
and direction of simple magnetic fields.
3. Take a single bar magnet and use the compass to map out a sketch of the magnetic
field. Be sure to put arrows on your lines showing the direction of the field. (Remember
that the compass needle points in the direction of the magnetic field).
4. Now take two bar magnets and put them together, north pole to south pole. Use the
compass to map out a sketch of the magnetic field of the combined magnet. Be sure to
put arrows on your lines showing the direction of the field. (Remember that the compass
needle points in the direction of the magnetic field).
5. In what ways are the two fields similar? In what ways are they different?
6. Suppose we were to cut one of the bar magnets in half. What do you think the field
would look like for this magnet? Justify your reasoning.
7. Now consider the coil of wire on your table. Pass the maximum possible current
through the coil. Is a magnetic field produced? Cite your evidence that a field is present
with current flowing and not present when it is not flowing.
8. Carefully investigate the direction of the field in the space inside the coil. What is the
direction of the field at the location of the black platform at the center of the coil? (Be
careful in determining this direction. The field produced by the coil is small enough that
it does not completely overpower the earth’s magnetic field.)
How does the magnitude of the magnetic field from a bar magnet along
one of its axes depend on the distance from the magnet?
You will have a bar magnet, a meter stick, a Hall probe, computer and compass. The
Hall probe looks like a clear plastic wand. At the end of the wand is an electronic
microchip which can measure magnetic field strength. The analysis of the data form this
chip is done through the software. Details regarding the use of the probe are attached.
Be sure to look at them. You should already know the shape of the magnetic field of a
bar magnet. You will now use the Hall probe to determine how the magnitude of the
magnetic field varies as you move away from the magnet along each of the axes of the
bar magnet.
9. Sketch a prediction (doesn’t have to be right, just carefully thought through) of
how you expect a graph of magnetic field strength as a function of distance to
look along each axis of the bar magnet.
Get the file Magnet.mbl from the course web page under the activities icon. This file
takes one data point every three seconds. Remember to use Internet Explorer when
transferring the file. Take one of the bar magnets and use the probe to check out the
variation of the magnetic field. Based on your prior knowledge of the shape of the
magnetic field for the bar magnet and the information provided for the Hall probe, be
sure to orient the probe correctly.
10. Where around the perimeter of the magnet is the field strongest? Where is the
field weakest? How far away from the magnet can you get and still measure the
field?
11. Choose an axis of the bar magnet and take measurements of the magnetic field
strength in a straight line along the axis of the magnet. Be sure that the field is
always perpendicular to the probe. Plot a graph of magnetic field strength versus
distance away from the magnet for each axis.
12. Repeat the step above for the other axis of the magnet.
13. Along which axis of the bar magnet does the magnet field fall off faster?
14. Did your measured graph agree with your predicted graph? If not, why
15. State your results in the most general terms supported by your analysis.
Force on a Moving Charged Particle in a Magnetic Field
Consider a piece of equipment that can produce a stream of electrons by heating a piece of
metal. The electrons are then given some kinetic energy (velocity) by passing through an
electric potential. This is a very simple description of an electron tube, oscilloscope or
cathode ray tube. If the stream of particles in the tube moves through a magnetic field, the
electrons will experience a force and hence be deflected. The force is known as the Lorentz
force
 and for
 a particle of charge q moving with velocity v in a magnetic field B,


F  qv  B . The standard unit for B that follows from this cross product is newtons per
coulomb-meter per second. This unit of magnetic field is known as the tesla, or T for short.
16. If a magnet is held with its north pole pointed toward the top of the page as shown
at the bottom of the figure above, What is the direction of the magnetic field? What
will be the direction of the force on an electron (remember an electron is negative)?
Up toward the top of the page? Down toward the bottom of the page? Out of the
page? Into the page? To the right? To the left?
17. If a magnet is held with its south pole pointed toward the top of the page, what is
the direction of the magnetic field? What will be the direction of the force on an
electron? Up toward the top of the page? Down toward the bottom of the page? Out
of the page? Into the page? To the right? To the left?
18. If a magnet is held with its north pole pointed to the left as shown at the right of
the figure above, what will be the direction of the force on an electron (remember an
electron is negative)? Up toward the top of the page? Down toward the bottom of the
page? Out of the page? Into the page? To the right? To the left?
19. If a magnet is held with its north pole pointed to the left as shown at the right of
the figure above, what will be the direction of the force on a proton? Up toward the
top of the page? Down toward the bottom of the page? Out of the page? Into the
page? To the right? To the left?
Understanding why a charge moving perpendicular to a magnetic
field moves in a circle.

20. Consider an electron that is shot with velocity v from left to right in the presence of a
uniform magnetic field B that is into the paper. This is indicated by the X’s in the figure
below.
In the next moment after it is launched, will the electron still be traveling in the same straight
line? Why or why not? Sketch this figure on your paper and show what its trajectory might
be in the next moment.
21. If the force on the moving charged particle due to the magnetic field is perpendicular to
the direction of motion of the electron in the first moment, is it still perpendicular in the
second moment? In the third moment? Why or why not?
22. If the force is always perpendicular to the direction of motion, is any work done on the
particle as it moves in a short but curved path (not a complete circle)? Recall that
 the formal


definition of work for a small displacement ds is given by the equation dW  F • ds . If so,
how much work is done? If not, why not?
23. If no work is done on the electron as it moves, does its speed (that is, the magnitude of its
velocity) change or remain the same? Does this particle undergo an acceleration? Why or
why not?
24. The displacement of an electron bending in a magnetic field is shown in the figure below
for two moments. Copy this diagram onto your paper and complete the diagram for the next
several moments of time. Thus show the shape of the path of the electron in the magnetic
field.
25. Suppose, you broke the path above up into a huge number of tiny steps. What
would the shape of the path be? How might it change if you increase the magnitude
of the magnetic field? Why?