1. We use the standard relation for magnetic energy density:

$u = \frac{B^2}{2\mu_0}$

So, the dimensions of

$\frac{B^2}{\mu_0}$

are the same as the dimensions of energy per unit volume.

2. Now, dimensions of energy are:

$[\text{Energy}] = [M L^2 T^{-2}]$

and dimensions of volume are:

$[\text{Volume}] = [L^3]$

Therefore,

$\left[\frac{\text{Energy}}{\text{Volume}}\right] = \frac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}]$

3. Hence,

$\left[\frac{B^2}{\mu_0}\right] = [M L^{-1} T^{-2}]$

4. Comparing with the options:

• A: $[M L^2 T^{-2}]$ ❌
• B: $[M L T^{-2}]$ ❌
• C: $[M L^{-1} T^{-2}]$ ✅
• D: $[M L^2 T^{-2} A^{-1}]$ ❌

Therefore, the correct option is C.