Question

A nonconducting insulating ring of mass $m$ and radius $R$, having charge $Q$ uniformly distributed over its circumference is hanging by an insulated thread with the help of a small smooth ring (not rigidly fixed with bigger ring). A time varying magnetic field $B=B_0\sin \omega t$ is switched on at t $=$ 0 and the ring is released at the same time. The induced EMF in loop at time $t=2\pi /\omega$ is:

• A. $0$
• B. $\frac{B_0\pi \omega R^2}{2}$
• C. $B_0\pi \omega R^2$
• D. $-\frac{B_0\pi \omega R^2}{2}$

Answer 1

Answer: (C)

$B_0\pi \omega R^2$

$\varphi =\overrightarrow{A}.\overrightarrow{B}V=-\frac{d\varphi }{dt}=-A{B}_0\omega \cos \omega t=\pi R^2{B}_0\omega cos\left(\omega t\right)att=2\pi /\omega ,V=\pi R^2{B}_0\omega$