A coil of resistance $400 \mathrm{\Omega }$ is placed in a magnetic field. If the magnetic flux $\varphi \left(\mathrm{wb}\right)$ linked with the coil varies with-time $t\left(\sec \right)$ as $\varphi =50t^2+4$. The current in the coil at t = 2 sec is :

Given,

Coil resistance R= $400 \mathrm{\Omega }$ 

It is placed in magnetic field. 

Time t= 2 sec 

Magnetic flux,

$\varphi =50t^2+4$. 

Here, the Induce emf ,

 $\epsilon =-\frac{d\varphi }{dt}=-\frac{d}{dt}\left(50t^2+4\right)$

$=-100t \mathrm{V}$

Thus, induce current in coil at 2 sec,

$$\begin{gathered} I=\frac{\left|\epsilon \right|}{R} \\ I=\frac{200\mathrm{V}}{400\mathrm{\Omega }} \\ I=\frac{1}{2}\mathrm{A} \\ \mathrm{I}=0.5\mathrm{A} \end{gathered}$$