# Magnetic Moment

## What is Magnetic Moment?

Magnetic moment is a determination of its tendency to get arranged through a magnetic field. As we all know, a magnet has two poles, i.e., North and South. The distance between these two poles of a magnetic or a magnetic dipole is named as the magnet length and is given as the 2 ιι. If m is the power of any magnetic pole then the magnets magnetic dipole moment is provided by the vector M and it is articulated as

Where, m = Strength of any magnetic dipole

ιι = Magnet length.

## Magnetic Moment Units

In the definition for current loop, the Magnetic moment is produce of current flowing and the area,

M = I A

So the unit conferring to this definition is articulated by Amp-m2.

It can also be suggested in terms of torque and moment. Conferring to that, the torque is measured in Joules (J) and the magnetic field is measured in tesla (T) and thus the unit is J T -1.

So, these two units are equivalent of each other and is provided by : 1 Amp-m2 = 1 J T -1.

## Magnetic Dipole Moment

A Magnetic Dipole comprises of two unlike poles of equivalent strength and parted by a small distance.

For instance : The needle of a compass, a bar magnet, etc. are the magnetic dipoles. We shall show that a current loop works as a magnetic dipole.

Magnetic Dipole Moment is described as the product of pole strength and the distance amidst the two poles. The distance between the two poles of a magnetic or a magnetic dipole is named as the magnet length and is given as the 2 ι.

If m is the power of any magnetic pole then the magnetic dipole moment of the magnet is signified by the vector M and it is represented as

The Magnetic dipole moment is a vector as termed above and it has direction from the South Pole of the magnet to the north pole of the magnet as presented in the fig

## Expression for Magnetic Dipole Force:

The force on a magnetic dipole is because of both the poles of the magnet and we consider the magnetic dipole of a bar magnet and assume that the magnet is kept in a unbroken magnetic field B. In that situation, the force on the separate poles is articulated as

mB which is along the magnetic field B = Force on the N-pole

mB and this is opposite to magnetic field B = Force on the S-pole

These forces are equivalent in magnitude, but opposite in direction and they form a parallel couple which rotates the magnet clockwise and creates a net torque on the magnet because of the individual force in a couple thus we have torque acting on the bar magnet.

τ = Moment of the couple.

τ = mB × 2L sin θ

Where θ is the angle amid the magnet and the magnetic field therefore from the above discussion we have

M = m x 2L

Thus, Magnetic dipole moment is articulated by

ττ = MB sin θ

In vector form, it can be rephrased as

τ = M × B.

This is the required expression for the magnetic dipole force.

#### Practise This Question

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle, of  75. One of the fields has a magnitude of 2×102T. The dipole attains stable equilibrium at an angle of 30 with this field. What is the magnitude of the other field?