Question

The dimensional formula for the magnetic moment of a magnet is.

Answer 1

Magnetic moment

1. It is a vector quantity that is a measure of the torque exerted on a magnetic system (such as a bar magnet or dipole) when placed in a magnetic field
2. In the case of a magnet, it is the product of the distance between its poles and the strength of either pole.

1. We know that the magnetic moment for a solenoid is $=N.I.S$,
2. Where $N$ is the number of loops, $I$ is current and $S$ is the vector area
3. Now, dimensional formula for current = $\left[M^0{L}^0{T}^0{A}^1\right]$
4. Dimensional formula for area = $\left[M^0{L}^2{T}^0{A}^0\right]$
5. Hence, by combining the above formulas, we get dimensional formula for the magnitude of the magnetic moment.
6. $\left[M^0{L}^0{T}^0{A}^1\right]\left[M^0{L}^2{T}^0{A}^0\right]=\left[M^0{L}^2{T}^0{A}^1\right]$

Hence, the dimensional formula for the magnitude of the magnetic moment= $\left[M^0{L}^2{T}^0{A}^1\right]$.