The dimension of mutual inductance is

We need to find the dimensions of mutual inductance.

The emf induced in a coil is related to mutual inductance by:

$$\varepsilon = M \frac{dI}{dt}$$

So: $$M = \frac{\varepsilon \cdot dt}{dI}$$

The dimension of emf ($$\varepsilon$$) is the same as voltage:

$$[\varepsilon] = [V] = ML^2T^{-3}A^{-1}$$

The dimension of $$\frac{dt}{dI}$$ is:

$$\left[\frac{dt}{dI}\right] = \frac{T}{A} = TA^{-1}$$

Therefore, the dimension of mutual inductance is:

$$[M] = ML^2T^{-3}A^{-1} \times TA^{-1} = ML^2T^{-2}A^{-2}$$

Hence, the correct answer is Option B.