Magnetism- Inverse Cube Law
Course:
Section:
Name(s):
Instructor:
Date:
Introduction:
In this lab we will study how the magnetic field intensity of a bar magnet changes with distance.
Theory:
Consider a point P which lies along eh axial line of a bar magnet as shown in figure below. Let 2𝑙 be the
length of the magnet with O as center so that OP =𝑑.
2𝑙
S
O
P
N
If m is the magnetic strength of each pole, then magnetic field at P due to N pole of the magnet is given
𝜇 𝑚
0
by: 𝐵 = 4𝜋(𝑑−𝑙)
2
Also, Magnetic field at P due to S-pole of the magnet is given by
𝐵′ =
𝜇0 𝑚
4𝜋(𝑑 + 𝑙)2
Thus, resultant magnetic field at P will be
𝐵1 = 𝐵 − 𝐵′ =
4𝜇0 𝑚𝑙𝑑
4𝜋(𝑑 2 −𝑙 2 )2
…………………. (1)
If 𝑑2 ≫ 𝑙 2 , then,
𝐵1 =
4𝜇0 𝑚𝑙
4𝜋𝑑 3
…………………………………… (2)
Similarly if the magnet lies along the equatorial line as in figure below, we can show that the net
magnetic field at point P is given by
2𝑙
P
𝐵2 =
2𝜇0 𝑚𝑙
3
4𝜋(𝑑 2 +𝑙2 ) ⁄2
………………………………….. (3)
If 𝑑2 ≫ 𝑙 2 , then,
𝐵2 =
2𝜇0 𝑚𝑙
4𝜋𝑑 3
…………………………………… (4)
Procedure:
For this lab we assume that the length of the magnet is small compared to the distance to point P, and
see if the magnetic field strength obeys Inverse cube law.
1) Make sure that the Magnetic sensor
is connected to the INPUT “A” of
PASCO-850 box.
2) Open “Magnetism-Inverse Cube
Law.cap” file.
3) Keep the bar magnet far away from
the magnetic sensor and press the
ZERO button located on the magnetic
sensor. Set the magnetic sensor to
Axial switch. Now, place the magnet
in axial configuration at a distance of
1 cm from the Magnetic Field Sensor
as shown in the figure and press
Preview. Once a stable point is seen
on the graph. Press Keep. Do not click
Figure 1: Axial Orientation
on STOP sign. Now move the magnet
to 2 cm and once a stable point is seen in the graph, press KEEP. Continue until the magnet is 10
cm from the sensor. Now press STOP.
4) The top graph shows the variation of Magnetic field with distance whereas the bottom graph
shows the variation of magnetic field with cube of distance. This graph in theory should be a
straight line passing through the origin.
5) Do a linear fit (Seventh button from left on the graph screen) on this graph and record the slope
on the table below. Do a linear fit, click on “Take a screenshot” of the program and paste it here.
6) Now ZERO out the sensor again after moving the magnet very far away from the sensor.
7) Place the magnet in equatorial configuration and repeat steps 3-5. Record the slope in the table
below.
8) Take a screenshot of the program and paste it here.
Table 1:
Slope of Magnetic field vs. distance cubed graph during axial configuration =
Slope of Magnetic field vs. distance cubed graph during equatorial configuration =
Ratio of the two slopes = axial slope/equatorial slope =
Theoretical Ratio of these two slope = Equation 2/ Equation 4 =
Percentage Difference =