The dimension of mutual inductance is

The formula for mutual inductance is given by, $ε = M\dfrac{dI}{dt} ⇒ M = \dfrac{ε}{\left(\dfrac{dI}{dt}\right)}$

Dimension of emf or voltage is \left[M{L}^{2}{T}^{- 3}{A}^{- 1}\right]$,<br />Dimension of current is \left[A\right]$,
Dimension of time \left[T\right]$.</p><p>Therefore, the dimension of$M$is<br />$M = \dfrac{\left[{ML}^{2}{T}^{- 3}{A}^{- 1}\right]}{\left[A\right]{\left[T\right]}^{- 1}}$<br />$= \left[{ML}^{2}{T}^{- 2}{A}^{- 2}\right]$