Question

The figure shows a square loop[ of resistance 1$\Omega$ side $1m$ being moved towards right at a constant speed of $1m/s$. The front edge enters the $3m$ wide magnetic field$(B=1T)$ at $t=0.$ draw the graph of current induced in the loop as time passes. (Take the anticlockwise direction of current as positive)

Answer 1

Time taken for the coil to completely enter the magnetic field
$=\frac{length}{speed}=\frac{1}{1}=1\sec$
Now side BC is $1m$ inside magnetic field
Time taken for side BC to reach other end= $\frac{2}{1}=2\sec$
While entering
$\begin{array}{c}E=\frac{d\varphi }{dt}=\frac{d}{dt}\left(B.A\right)=\frac{d}{dt}\left(Bxl\right)\\ =B.l\frac{dx}{dt}\\ =BlV\\ =1\times 1\times 1=1\\ i=\frac{E}{R}=\frac{1}{1}=1A\end{array}$