This document is a student's project report on building a vibration magnetometer to determine the magnetic dipole moment of a bar magnet and the horizontal intensity of the Earth's magnetic field. It includes an introduction explaining the apparatus, theory behind tangent law relating torque and oscillation period, procedure, observations and calculations section, results, precautions, and an index of references. The student successfully completed the project under guidance of their physics teacher to analyze the bar magnet's oscillation and calculate the magnetic field intensity and dipole moment.

1. PHYSICS
INVESTIGATORY
PROJECT

2. CERTIFICATE
This is to certify that B.BHUVANESH a student
of class XII A has successfully completed
project on topic “vibration magnetometer”.
This report is result of his effort and endeavors
under the guidance of Mr.K.I JOHN. The report
has been examined.
Signature of external examiner
Signature of Physics teacher

3. ACKNOWLEDGEMENT
I would like to express thanks and gratitude to my
project guide Mr. KI JHON for guiding me
immensely through the course of the project. His
constructive advice and constant motivation have
been responsible for the successful completion of
project.
I also thanks to my parent for their motivation and
support. I must thanks to my classmate and friends
for their timely help, advice and support for
completion of project.
Last but not the least, I would like to thanks all
people who directly or indirectly helped me in
completion of project.

4. Declaration
I hereby declare that the project work “vibration
magnetometer” submitted to Kendriya
Vidyalaya A.S.C Centre, Bangalore is prepared by
me. All the observation and calculation given are
my personal effort.

5. Index
1) Aim
2) Apparatus

6. 3) Theory
4) Procedure
5) Observation and calculation
6) Results
7) Precautions
8) Inference
AIM
To determine the magnetic dipole

7. moment (m) of a bar magnet and
horizontal intensity (BH) of earth’s
magnetic field using a deflection
magnetometer.
Apparatus

8. 1)Box-typevibrationmagnetometer
2) Timer
3) Barmagnet

9. Theory
The horizontal component of earth's magnetic
field, BH, is the component of the magnetic field of
the earth along a horizontal plane whose normal
vector passes through the center of the earth. BH is
measured in Tesla, T.
The magnetic dipole moment m of a magnetic
dipole is the property of the dipole which tends to
align the dipole parallel to an external magnetic
field. m is measured in Ampere-square meters (A
m2) or, equivalently, in Joules per Tesla (J/T).
Tangent law
Consider a bar magnet with magnetic
moment m, suspended horizontally in a
region where there are two perpendicular
horizontal magnetic fields, and external
field B and the horizontal component of the

10. earth’s field BH. If no external magnetic
field B is present, the bar magnet will align
with BH. Due to the field B, the magnet
experiences a torque τD, called the deflecting
torque, which tends to deflect it from its
original orientation parallel to BH. If θ is the
angle between the bar magnet and BH, the
magnitude of the deflecting torque will be,
The bar magnet experiences a torque τR due
to the field BH which tends to restore it to its
original orientation parallel to BH. This torque
is known as the restoring torque, and it has
magnitude.
The suspended magnet is in equilibrium
when,
(1)
The above relation, called the tangent law,
gives the equilibrium orientation of a magnet
suspended in a region with two mutually
perpendicular fields.
Vibration Magnetometer
The equation of motion of the bar magnet
suspended horizontally in the earth’s
magnetic field is
Thus its period of oscillation, for small θ, is
approximately.
(2)
Where I = moment of inertia of the magnet
about the axis of oscillation
m = magnetic moment of the magnet

11. BH = horizontal intensity of the earth's
magnetic field.
For a rectangular bar magnet,
(3)
Where
M = mass of the magnet
L = length of the magnet (longest horizontal
dimension)
b = breadth of the magnet (shortest
horizontal dimension)
Squaring equation (2)
(4)
Which gives
us?
(5)
Thus, by measuring vibration (oscillation)
period T and calculating the moment of
inertia I of the bar magnet, mBH is
determined using the vibration
magnetometer. We will call this value x.

12. Procedure
1) The direction of BH is drawn on the table using a
compass needle.
2) The box-type vibration magnetometer is placed
with its length parallel to this direction.
3) The bar magnet is then suspended horizontally
in the vibration magnetometer with its north
pole pointing north.
4) The magnet is set into vibration by momentarily
bringing another bar magnet near to it.
5) The time taken for 10 oscillations is determined
twice and the mean of t is to be found and period

13. of oscillation (T) can be calculated using
equation (2).
6) The mass of the magnet is determined.
7) The length and breadth of the magnet are
measured by using vernier calipers.
8) The moment of inertia of the magnet is
calculated.
9) From these observations, the value of mBH is
calculated using equation (5).
Observations and calculations
Readings of Vibration magnetometer=
Mass of the magnet=
Length of the magnet=
Breadth of the magnet=
=
=
Results

14. 1. The horizontal intensity of earth's magnetic
field at a place, BH =................... Wbm-2
2. The moment of the bar magnet, m =
...................... Am-2
Precaution

15. 1) While finding North Pole of the earth, keep all
magnets far away so that compass does not get
affected.
2) After placing the vibration magnetometer once, do
not disturb it while experiment.
3) Take readings carefully.
Inference
1. Amrita.vlab.co.in
2. www.scribd.com
3. www.google.com