A magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or other object that produces a magnetic field. More precisely, a magnetic moment refers to a magnetic dipole moment, the component of magnetic moment that can be represented by a magnetic dipole. A magnetic dipole is a magnetic north pole and a magnetic south pole separated by a small distance.

Magnetic dipole moments have dimensions of current times area or energy divided by magnetic flux density. The unit for dipole moment in metre–kilogram– second–ampere is ampere-square metre. The unit in centimetre–gram–second electromagnetic system, is the erg (unit of energy) per gauss (unit of magnetic flux density). One thousand ergs per gauss equal one ampere-square metre.

## Derivation of Magnetic Dipole Moment Formula

Magnetic Dipole moment- The magnetic field, **B** due to a current loop carrying a current i of radius, R at a distance l along its axis is given by:

B = \( \frac {Î¼_0 i R^2}{2(R^2~+~l^2 )^{\frac32}}\)

Now if we consider a point very far from the current loop such that l>>R, then we can approximate the field as:

B = \( \frac{Î¼_0 i R^2}{2l^3 \left( \left(\frac{R}{l} \right)^2~+~1\right)^\frac 32 }\)

Now, the area of the loop, A is

A = \( Ï€R^2 \)

Thus, the magnetic field can be written as

B = \( \frac {Î¼_0}{4Ï€} \frac Â {2i A}{l^3} \)

We can write this new quantity Î¼ as a vector that points along the magnetic field, so that

**\( \overrightarrow{B}\) = \( \fracÂ {Î¼_0}{4Ï€} \frac {2 \overrightarrow{Î¼}}{l^3}\)**

Notice the astounding similarity to the Â electric dipole field:

**\( \overrightarrow{E}\) = \( \frac {1}{4 \pi \epsilon_0} \frac {2 \overrightarrow {p}}{r^3}\)**

Thus we call this quantity \(\overrightarrow{Î¼}\)

Most elementary particles behave intrinsically as magnetic dipoles. For example, the electron itself behaves as a magnetic dipole and has a Spin Magnetic Dipole moment. This magnetic moment is intrinsic as the electron has neither an area A (it is a point object) nor does it spin around itself but is fundamental to the nature of the electronâ€™s existence.

We can generalize the magnetic moment for â€˜Nâ€™ turns of the wire loop as

**Î¼ = NiA**

The magnetic field lines of a current loop look similar to that of an idealized electric dipole:

If you have ever broken a magnet into two parts, you would have found that each piece forms a new magnet. The new pieces also contain a north and a south pole. You just canâ€™t seem to be able to obtain just a North Pole. Can you find the answer in this article?

To study science by applying it to everyday phenomena download BYJUâ€™s â€“ The Learning App!