Question

A long solenoid has magnetic field induction $10\, T$ at its centre. A $100$ turn close-packed coil of area $1\, cm ^{2}$ is placed at the centre of the solenoid. This coil is arranged so that at the centre of the solenoid is parallel to its axis. The current in the solenoid is reduced to zero and then raised to its initial value in other direction at a steady rate over a period of $0.05\, s$. What induced emf appears in the coil while the current is being changed, in volt.

Answer 1

Given $B =3.8 \times 10^{-2} T$
$\Delta t =0.05\, s$
$r =1\, cm$ of coil
$N=100$ turns;
Change in flux when current in solenoid reduced to zero $= NBA$
$=100 \times 3.8 \times 10^{-2} \times \pi \times\left(10^{-2}\right)^{2}$
$\phi=3.8 \pi \times 10^{-4}$ weber.
again when current in other direction to same value
$\phi=3.8 \pi \times 10^{-4}$ weber.
Total change in flux $=7.6 \pi \times 10^{-4} wb$.
So emf induced
$e =-\frac{d \phi}{d t}=-\frac{7.6 \times 10^{-4}}{0.05}$
$=\frac{-23.84 \times 10^{-4}}{0.05}$
$=-48\, mV$.