Question

Consider an LC circuit, with inductance $L =0.1 H$ and capacitance $C=10^{-3} F$, kept on a plane. The area of the circuit is $1 \,m ^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t=0$, the magnetic field strength starts increasing linearly as $B=B_0+\beta t$ with $\beta=0.04\, Ts ^{-1}$. The maximum magnitude of the current in the circuit is ___$ m A$.

Answer 1

Maximum energy will be
$ \frac{ q _0^2}{2 C }=\frac{1}{2} LI _0^2$
$ \frac{ q _0^2}{ CL }= I _0^2 $
$ I _0=\frac{ q _0}{\sqrt{ LC }}$
$ I _0=\frac{ CV }{\sqrt{ LC }} $
$ I _0=\sqrt{\frac{ C }{ L }} \times V $
$ V = emf =\left|\frac{ AdB }{ dt }\right|$
$I_0=\sqrt{\frac{10^{-3}}{0.1}} \times 0.04 $
$ V=(1 \times 0.04)$
Maximum current $I _0=0.004=4 \,mA$