HPP Activity 73v1
Magnetic Fields and Forces
We have explored one method of seeing inside the human body in a destructive manner: use
ultrasound. Magnetism can also be used to visualize internal organs. The technology is called
magnetic resonance imaging, or MRI. It is based on hydrogen nuclei behaving as if they have a
little bar magnet on them. A strong magnetic field can orient these little magnets. Another
magnetic field can be turned on briefly to disorient the little nuclear magnets. As they become
aligned again they will emit detectable electromagnetic radiation which can give information that
can be turned into an image such as the one shown below. Unlike x-ray image technology, the
MRI technology will give good images of soft tissue.
Figure 1. Sagittal brain MRI. From Lahey Clinic Medical Center, Burlington, MA
To understand this technology better we must develop some expertise in describing magnetic
fields and their effects on matter.
Exploration
You have a bar magnet and some small compasses at your table. You may have investigated (i.e.
played with) magnets before, so now we have advanced playtime! You will need to study the
magnetic field lines. Magnetic field lines are exactly the same as electric field lines: they define
the magnitude and direction of the force on a "test" object. In the case of a magnet, the test object
is a small magnet (which will be a compass here). Also, as with electric charges, like poles of
magnets repel and opposite poles attract.
We know that a compass needle points north, so put your compasses on the table and determine
which is the north pole and which is the south pole of the needle. By definition, the north pole of
the compass needle points north. If you do not know which direction is north in the classroom,
your instructor will assist you. The small compasses tend to get their poles reversed sometimes,
so if some maverick compass needles point in the wrong direction, put them aside.
Activity Guide
© 2002-2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
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GE 1: Characteristics of Magnets
1. Use the compass to determine which ends (identify by color) of your
magnets are north(N) and south(S). Explain how you decided what is the N
pole and what is the S pole.
2. Map out the magnetic field lines using your compasses. You cannot
determine the magnitude of the force, but by finding the direction in many
places you can make a field map (just like an electric field map) and where the
field lines are close together, the force is greater.
The best method to use is to set up a grid along one side of the magnet (by
symmetry, both sides should be the same) and place the small compasses at
regular grid locations. Sketch the direction of each compass needle at that grid
point. When you have the grid complete, sketch the field lines. Remember that
the arrows are the tangent to a curve and that by convention, the field lines
come from the N pole and go to the S pole. A grid is drawn on the next page.
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GE 2.
Connect the coil of wire in a circuit with the battery and switch. When the
switch is closed current will run through the coil. Do not leave the switch on
for mor than a second.
Place the large compass in the middle of the coil and orient the arrangement
so that the compass needle points toward the wires in the coil.
Now turn on the switch and observe the compass needle.
1. Describe what happens.
2. Based on this observation, what is one way to create a magnetic field?
Invention
The sources of magnetic fields are materials in which the atoms themselves are permanent
magnets or moving electric charge (electric current). In each case the field is produced at each
point in the surrounding space. The magnetic field can produce a magnetic force on another
magnet placed at at point in space.
Magnetic field lines come out of the north end of a bar magnet and go into the south end of the
magnet, as shown in Figure 2.
Figure 2. Magnetic field lines for a bar magnet. From College Physics by Young & Geller.
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The direction of the magnetic field produced by a current-carrying wire is obtained by a righthand-rule:
Using your right hand, point your thumb in the direction of current flow in the wire.
Your fingers will wrap around in the direction of the field. Figure 3 shows the field lines for a
current-carrying coil.
Figure 3. Magnetic field from a current-carrying coil. From College Physics by Young & Geller.
Application
GE 3.
1. Think back to the activity where we mapped out electric fields. Was there a
charge configuration that produced an electric field similar to the magnetic
field produced by the bar magnet?
Exploration: Forces Exerted by a Magnetic Field
We now know that a magnetic field can exert a force on a magnet, but can it exert a force on
electric charges? Trying to investigate the force on a static charge is not possible in this
laboratory because the magnitudes of the charge and magnetic field needed are prohibitively
large. The results of any such experiment would show that there is no force exerted by a
magnetic field on a static charge. However, there is a force exerted on a moving charge, and we
will investigate this force.
At each table, there is a suspended wire connected to a battery and switch. When the switch is
closed, a current will travel through the wire. Do not leave the switch closed for more than a
second at a time. You also have two magnets: your bar magnet from the last section, and a
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horseshoe magnet (labeled N and S). With these two magnets you will investigate the force
exerted on a current in a wire.
GE 4: Force from a Magnetic Field
1. Place the horseshoe magnet around the wire with the current flowing
downward as shown in the figure below. The magnetic field from the magnet
is in the plane of the paper and directed from the N pole to the S pole. Tap the
telegraph switch and notice the direction that the wire moves. Rotate the
magnet through a small angle around the wire and tap the telegraph switch
and observe the direction of motion. Repeat for several angles. On the
diagram below, sketch the magnetic field and the direction of the force from
the magnetic field and current.
2. Make a general vector diagram showing the directions of B, I and F.
Signify a vector into the page with a circle with an x in the center (as shown in
the above drawing); and, signify a vector out of the page with a circle with a
dot in the center.
3. Verify your vector diagram by observing the force on the side wire and the
force on both wires with the magnet reversed. Sketch these situations below.
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4. But, a current is just charges in motion. From the definition of current (i.e.
what charge in what direction), draw the vector diagram for the force F from a
magnetic field B on a moving positive charge with velocity v.(This is rather
simple; just replace the current arrow with an arrow signifying the direction of
flow of positive charges in the wire.)
5. The actual magnitude of this force is F = qvB. But for this force, we had the
direction of B perpendicular to the direction of I. What if B and I are not
perpendicular. Place the horseshoe magnet next to the horizontal section of the
wire as shown in figure (a) below (note the this view shows the wire in front
of the magnet). Touch the switch and observe the motion of the wire away
from the magnet. The wire may move to the right, but this is from the B
interacting with the vertical sections of the wire, so ignore that motion (unless
you are curious why it moves to the right). Then rotate the magnet through
some small angle Ø as shown in figure (b) below, touch the switch, and
observe the motion away from the magnet. You should find that the force
depends on the orientation of B relative to I (and therefore to v of the
charges). Assuming that this dependence is a simple sine or cosine
dependence, determine which function it is: qvBsinθ or qvBcosθ. Explain
your reasoning.
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Invention
Moving electric charge can experience a force from a magnetic field. There must be a
component of the field perpendicular to the velocity in order for there to be a non-zero magnetic
force. The magnitude of the magnetic force is given by
where θ is the angle between B and v. The direction of the magnetic force on the moving charge
can be obtained by a right-hand rule. See Figure 4 below.
Figure 4. Right-hand rule for magnetic force direction. From College Physics by Young &
Geller.
Application
GE 5.
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Predict the direction of the magnetic force for each situation below. Assume
that the particle is positively charged.
1.
2.
3.
For the next situation, assume the particle is negatively charged.
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