## What is Magnetic Moment?

**Magnetic moment**Â 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**Â andÂ **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 2Â Î¹Î¹. IfÂ **m**Â is the power of any magnetic pole then the magnets magnetic dipole moment is provided by the vectorÂ **M**Â and it is articulated as

Where, m = Strength of any magnetic dipole

Î¹Î¹Â = 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 byÂ **Amp-m ^{2}**.

It can also be suggested in terms of torque and moment. Conferring to that,Â the torque is measured in JoulesÂ **(J)**Â and the magnetic field is measured in teslaÂ **(T)**Â and thus the unit isÂ **J TÂ ^{-1}**.

So, these two units are equivalent of each other and is provided by**Â :Â 1 Amp-m ^{2}Â = 1 J T^{Â -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 2Â Î¹.

IfÂ **m**Â is the power of any magnetic pole then the magnetic dipole moment of the magnet is signified by the vectorÂ **M**Â 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 fieldÂ **B**. In that situation, the force on the separate poles is articulated as

**m _{B}**Â which is along the magnetic fieldÂ

**B**=Â Force on the N-pole

**m _{B}**Â and this is opposite to magnetic fieldÂ

**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.

Ï„Â = Moment of the couple.

Ï„Â = m_{B}Â Ã—Â 2L sinÂ Î¸

WhereÂ Î¸Â 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

Ï„Ï„Â = MB sinÂ Î¸

In vector form, it can be rephrased as

Ï„Â = MÂ Ã—Â B.

This is the required expression for the magnetic dipole force.