Question

A uniform magnetic field $B=0.5T$ exists in a circular region of radius $R=5m$. A loop of radius $R=5m$ encloses the magnetic field at $t=0$ and then pulled at uniform speed $V=2m$ $s^{-1}$ in the plane of the paper. Find the induced emf (in $V$) in the loop at time $t=3s$

Answer 1

$\epsilon =-\frac{d\varphi }{dt}=-B\frac{dA}{dT}$
$A=2r^2{\cos }^{-1}\frac{x}{2r}-\frac{x}{2}\sqrt{4R^2-x^2}$
$x=vt$
$x=6m,v=2m/s,r=5m,B=0.5T$
$Solvetoget\epsilon =8V$