Question

A square-shaped copper coil has edges of length $50cm$ and contains $50$ turns. It is placed perpendicular to a $1.0T$ magnetic field. It is removed from the magnetic field in $0.25s$ and restored in its original place in the next $0.25s$. Find the magnitude of the average emf induced in the loop during (a) its removal, (b) its restoration and (c) its motion.

Answer 1

during removal
${\varphi }_1=B.A=1\times 50\times 0.5\times 0.5-25\times 0.5=12.5Tesla-m^2;{\varphi }_2=0,\tau =0.25$
$e=-\frac{d\varphi }{{dt}^{}}=\frac{{\varphi }_2-{\varphi }_1}{dt}=\frac{12.5}{0.25}=50V$
(b) during restoration
${\varphi }_1=0;{\varphi }_2=12.5Tesla-m^2;t=0.25s$
$E=\frac{12.5-0}{0.25}=50V$
(c) During the motion
${\varphi }_1=0;{\varphi }_2=0$
$E=\frac{d\varphi }{{dt}^{}}=0$