Two coils have a mutual inductance of 0.005 H. The current changes in the first coil according to the equation $I = I_0sinωt,$ where $I_0 = 10 A$ and $ω = 100 \pi  rad/s$. The maximum value of emf in the second coil is :

$5\pi $

The correct answer is option (2) : $5\pi $

emf induced in the second coil $(\epsilon_s)$

$\epsilon_s=-L\frac{di_f}{dt}$

$⇒|\epsilon_s|=L\frac{di_s}{dt}$

$=L\frac{d}{dt}(I_0sin \omega t)$

$=L I_0\omega cos \omega t$

$⇒|\epsilon_s|_{max}=LI_0\omega $

$= 5\pi $