Dimensional formula of self inductance is

The correct option is [ML²T⁻²A⁻²].

To find the dimensional formula of self-inductance ($L$), we can start from the relation for the magnetic energy stored in an inductor:
$E=\frac{1}{2}L{I}^2$
where:
• $E$ is the energy stored,
• $L$ is the self-inductance,
• $I$ is the electric current.

Rearranging the equation to solve for self-inductance ($L$), we get:
$L=\frac{2E}{I^2}$

Now, we determine the dimensional formulas for each quantity involved:
1. Energy ($E$) has the same dimensions as work done (Force × Distance):
$\left[E\right]=\left[{\text{ML}}^2{\text{T}}^{-2}\right]$
2. Electric current ($I$) has the dimensional symbol:
$\left[I\right]=\left[\text{A}\right]$

Substituting these dimensions into the expression for $L$:
$\left[L\right]=\frac{\left[{\text{ML}}^2{\text{T}}^{-2}\right]}{{\left[\text{A}\right]}^2}$

Simplifying this expression:
$\left[L\right]=\left[{\text{ML}}^2{\text{T}}^{-2}{\text{A}}^{-2}\right]$

Thus, the dimensional formula of self-inductance is [ML²T⁻²A⁻²].