Question

What is the magnetic moment of a bar magnet? How to measure it?

Answer 1

Hint: Magnetic field is the space around the magnet where the effect of the magnet can be felt by another magnet or iron piece. The magnetic field can also be produced by a moving charge whose intensity can be determined by the velocity and magnitude of charge or using a magnet having definite pole strength. The S.I unit of the magnetic field is Tesla (T) whereas the C.G.S unit is Gauss (G).

Complete step-by-step solution:
Every material of magnet has a defined magnetic field associated with it. This can be measured by its pole strength. Hence the amount of magnetic field a magnet will produce is directly associated with its pole strength. In physics, moment means the torque, if it is associated with some force. Hence magnetic moment is the measure of torque that a bar magnet will experience when placed in an external magnetic field. It is a vector quantity. Mathematically, the cross product of the magnetic moment and magnetic field will give the torque on the bar magnet i.e.
$\vec\tau = \vec\mu \times \vec B$
It's S.I. unit is $N-m T^{-1}\ or \ Am^2$
It is also equal to the product of the length of the magnet and its pole strength i.e. $\mu = l m$
It can be measured by measuring the time period of the bar magnet when placed in a magnetic field ‘B’.
The time period is given by:
$T = 2\pi\sqrt{\dfrac{I}{mB}}$
Where ‘I’ is the moment of inertia and m is the pole strength of the bar magnet.

Note: We can easily measure the time period for small oscillations and moment of inertia. By putting the values in the formula, we can easily solve for ‘m’, and multiplying it with the length will give the magnetic moment of the bar magnet. Note that pole strength is a scalar quantity.