Two coils have mutual inductance 0 . 002H . The current changes in...

The amount of flux induced in the second coil due to the first one is given by

$\begin{cases}{ϕ}_{2} & = & Mi \\ & = & M{i}_{0}sin\omegat . . . \left(1\right)\end{cases}$

where, $M$ is the mutual inductance of the coils.

The formula to calculate the emf induced can be written as

$ε = - \dfrac{d{ϕ}_{2}}{dt} . . . \left(2\right)$

From equation (2), it follows that,

\begin{cases}{ε}_\max & = & M{i}_{0}\omega \\ & = & 0 . 002 \times 5 \times 50\piV \\ & = & \dfrac{\pi}{2}V\end{cases}

Hence, $\alpha = 2$.