Magnets and Magnetic Fields Extension
Overview:
In the Tutorial “Magnets and Magnetic Fields”, you used a compass to map the field around a bar
magnet. In this activity, you will extend the ideas you learned in that tutorial to quantitatively
measure the field strength at various positions around a bar magnet.
How can a compass be used to measure magnetic field strength?
It might seem implausible, but you can use a compass to determine the magnitude of a magnetic
field. Here’s how it works. Place a compass on the table far from any magnets (or other strong local
sources of magnetic fields). Place a magnet a long distance from the compass directly east or west of
the compass. Orient the magnet so that it points East-West.
N
S
N
Very far apart
If the magnet is sufficiently far from the compass, the compass needle points North. If the magnet
is moved closer to the compass, the compass needle no longer points North. By measuring the angle
between the compass needle and North (call this angle α ), you get an indirect measure of the
strength of the bar magnet’s field at the location of the compass (call this field strength Bbar ).
•
Predict how α will vary as you bring the magnet in from far away along the East-West line.
Explain the reasoning behind your prediction.
•
Derive an expression that can be used to calculate Bbar from the angle α between North
and the compass needle direction. (If you get stuck, hints for the derivation are on the back
of this page).
•
Check your prediction.
developed 2/2/04 for P16
as a companion for Washington Tutorial “Magnets and Magnetic Fields”
Magnets and Magnetic Fields Extension
How does the field strength from a bar magnet depend on distance?
As you have observed, the strength of the magnetic field from a bar magnet decreases as you get
farther from the magnet. But what is the mathematical relationship? In this section, you will use the
technique you developed in the first part of this extension to measure the magnetic field of the bar
magnet as a function of distance from the magnet. To keep things simple, you will confine your
study to points along the axis of the magnet.
S
N
P
x
•
Measure the field strength as a function of the distance to the magnet. You should measure
the center-center distance and the resulting compass angle. (Why measure center-to-center
distance rather than, say, the distance to the end of the magnet?) For simplicity, express Bbar
in units of Bearth (rather than in Tesla or some other unit).
•
Use Excel to plot the field strength of the bar magnet as a function of distance. You will
likely find that the relationship is non-linear.
•
Determine the functional relationship between the field strength of the bar magnet and
distance. (Hint: “Linearize” the graph. Some possible candidates for the relationship between
field strength and distance are Bbar ∝ x − n , where n is a constant, and Bbar ∝ e − λx , where λ
is a constant). Interpret the slope of your “linearized” graph.
Derivation Hints:
1. The magnetic field at the compass’ position consists of two contributions: one from the Earth (call this
magnet (call this
!
Bearth ) and another from the bar
!
!
!
Bbar ). Sketch the magnetic field vectors for Bearth and Bbar when the magnet is far from the compass. Explain how
you determined the directions and relative magnitudes of the two contributions to the magnetic field at the compass’ position.
2. Suppose the magnet is moved closer to the magnet. Sketch the magnetic field vectors for the two contributions, using the same scale as in the
previous diagram. (Contributions of equal strength should be represented by arrows of equal length). Explain how you determined the directions
and relative magnitudes of the vectors.
3. Use your vector diagrams and trigonometry to relate
!
Bbar
,
!
Bearth
and
α.
developed 2/2/04 for P16
as a companion for Washington Tutorial “Magnets and Magnetic Fields”
Homework for Magnets and Magnetic Fields Extension
In the Extension, you measured the magnetic field strength at points along the axis of the magnet
(such as points A and B) using just a compass. To do this, you started with the magnet a long way
away from the compass. The magnet was aligned with its poles pointing East-West and the magnet
was positioned directly West of the compass.
C
D
E
S
N
A
B
Now your lab group wants to measure the field at points on the center line perpendicular to the axis
of the magnet (such as at points C and D). Three students are discussing how to proceed:
Student 1: Let’s orient the magnet so that it points North-South. We’ll start
with the magnet a long way away from the compass at a point directly West of the
compass. As the magnet is moved in, the compass will always be positioned along
the line that includes points C and D.
Student 2: I disagree. I think we should orient the compass East-West and
bring it in from the North. The compass will still be along the line we want, but
!
!
now Bearth and Bbar will be parallel and the compass direction will reflect the
strength of the field.
Student 3: Wait a minute! I don’t think either of these methods will work
because both methods rely on knowing the direction of the bar’s magnetic field at
!
both C and D. Imagine if we had tried to find Bbar for point E during lab. The
method we used relied on the fact that the bar’s magnetic field points directly EastWest.
What should you tell these students? Does either method have a chance of working? Evaluate their
statements and develop a method for measuring the field at C and D. Explain why the method will
work.
developed 2/2/04 for P16
as a companion for Washington Tutorial “Magnets and Magnetic Fields”