Physics 2402
Department of Physics and Geology
Magnetic Moment of a Dipole
Objective:
There are three main objectives to this experiment. The first is to demonstrate that in a uniform magnetic
field, this is no net force on a magnetic dipole, only a net torque. Secondly, this experiment demonstrates that there
is a net force on a magnetic dipole when it is in the presence of a magnetic field gradient. The third objective is to
measure the dipole moment, using the fact that net force on a magnetic dipole in a magnetic field gradient is
proportional to the magnetic moment.
Materials:

Frederiksen Power Supply 0-24V AC/DC 3630.00

Teach Spin Magnetic Force Apparatus MF1-A

Package of Five (5) 0.1 gram steel balls

One Red connecting wire

One Blue/Black connecting wire
Theory:
The principal player in this experiment is the magnetic dipole. With the dipole we will be able to
find the magnetic moment of a magnetic dipole.
Magnetic Moment (μ) as per Oxford Dictionary of Physics is, the ratio between the maximum
torque (τMax) exerted on a magnet, current-carrying coil, or moving charge situated in a *magnetic field
and the strength of that field. It is thus a measure of the strength of a magnetic or current-carrying coil.
We will use the Kennelly approach also called the magnetic dipole moment.
In the case of a magnet placed in a magnetic field of field strength B, the maximum torque (τMax) occurs
when the axis of the magnet is perpendicular to the field. In the case of a coil of N turns and area A carrying a
current I, the magnetic moment can be shown to be
(1)
(magnetic moments are measured in SI Units A m2)
We know that when the magnetic field is parallel to the plane of the loop we can write
magnetic dipole moment (equation (29.15 page 823) Serway and Jewett)
⃗⃗
⃗
We can write an expression of a total magnetic force on a length of wire L as
⃗
⃗
⃗⃗
Where ⃗ is a vector that points in the direction of the Current I and has a magnitude equal to the length of
L of the segment. We can differentiate each side and result in
⃗
Where
⃗
⃗⃗
is a small segment of vector in the presence of ⃗⃗ .
For simplicity sake we will say the force of the magnetic field along a vector of displacement is
(
)
(
Where
(2)
)
in equation 2.
If we call to Physics 1, we were introduced to Hooke’s Law that states
Where k is spring constant, and x being the displacement, the negative sign reminds us this is a restoring
force.
The fact that there are two opposite forces acting on the magnet means that the magnet will displace either
upward or downward until the spring forces equal the magnetic force. At that point the magnet will cease
it acceleration, and if one stops its motion it will come to a rest. At this displacement x, the following
expression can be written (which will inadvertently cancel out the negative sign in Hooke’s Law)
or
(3)
with this equation we will be able to solve for the magnetic moment of this system by measuring the
change in displacement, and the change in the magnetic fields. (*Note, the variable x is there just to
denote a displacement, some books will use y, as a vertical displacement, or a z. Just remember that any
variable can be used to represent something as long as you are consistent throughout the equations and
expressions.)
The radius of the coils is 7.0cm with a resistance of 2.8
with 168
.
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Created By Sjon Clinton 2012
Experimental Procedure:
1) Plug the Frederiksen Power Supply 0-24V AC/DC 3630.00 to the wall socket using universal power cable.
2) Plug the Red connecting wire into the Red port on the Frederiksen Power Supply 0-24V AC/DC 3630.00
on the DC side.
3) Plug the Blue/Black connecting wire into the Black port on the Frederiksen Power Supply 0-24V AC/DC
3630.00 on the DC side.
4) Plug the Red connecting wire into the Red port on the
Teach Spin Magnetic Force Apparatus MF1-A Lower
Coil.
5) Plug the Blue/Black connecting wire into the Black port
on the Teach Spin Magnetic Force Apparatus MF1-A
Lower Coil
6) Inside the plastic tube on the Teach Spin Magnetic
Force Apparatus MF1-A is a magnet attached to a
spring that is attached to a metal rod this is protruding
from a white plastic cap at the top.
7) Attached to the cap is a screw. Loosen the screw
enough so that the rod will move up and down.
8) Align the bottom of the magnet with the position zero
on the plastic tube. This will be your initial starting
point for all your motion of the magnet.
9) Once the bottom of the magnet is aligned with the zero position, tighten the screw on the white cap so
that the rod will not move during the experiment. DO NOT OVER TIGHEN IT!
10) Remove the white cap from the tube with everything still attached without moving the rod from its
position.
11) Add a single 1.0 gram steel ball to the magnet
12) Record on the table the mass in kilograms.
13) Replace the magnet and spring back into the tube making sure the white cap is placed correctly.
14) Once the motion of the spring has settled down, note the displacement of the addition of the 0.1gram
steel ball in the table.
15) Repeat steps 11 through 14 by adding a new steel ball each time. Your final displacement should have
the weight of all five (5) steel balls.
16) In the table figure out the Force on each set of weights added to the magnet.
17) Plot in a graph the force per displacement to determine
. Hint- Expect a Linear Graph
18) Remove all five (5) steel balls from the magnet and place back in the bag.
19) Turn on the Frederiksen Power Supply 0-24V AC/DC 3630.00.
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Created By Sjon Clinton 2012
20) Make sure the Voltage and Current are reading zero on the Frederiksen Power Supply 0-24V AC/DC
3630.00 display
21) Slowly turn the Voltage Knob to increase the Voltage.
22) Stop when the Current is at 0.5 Amps on the LED Displace. If there is a red light by the Ampere Knob,
then slowly turn the knob to the left till the knob cans no longer move.
23) Measure the displacement of the magnet with the current running at 0.5 Amps
24) Repeat step 22 for all currents up to 4.0 Amps.
25) Record all displacements in the Magnetic Dipole Moment Table.
⃗
26) Create a graph of the data of displacement per
. Hint- Expect a Linear Graph
27) Using the equation 2 in the theory section, solve for the magnetic dipole moment.
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Created By Sjon Clinton 2012