The magnetic moment has the dimensions of

The correct option is [L²A].

To find the dimensional formula of the magnetic moment, we can use the formula for the magnetic moment of a current-carrying loop:

$M=I\times A$

Where:
• $M$ is the magnetic moment
• $I$ is the electric current
• $A$ is the area of the loop

Now, let's write the dimensions of the quantities on the right-hand side:
• The dimension of electric current ($I$) is represented as $\left[A\right]$.
• The dimension of area ($A$) is length squared, represented as $\left[L^2\right]$.

Substituting these dimensions into our formula:
$\left[M\right]=\left[I\right]\times \left[A\right]$
$\left[M\right]=\left[A\right]\times \left[L^2\right]$
$\left[M\right]=\left[L^{2}A\right]$

Thus, the dimensional formula of the magnetic moment is $\left[L^{2}A\right]$.