Question

Consider an LC circuit, with inductance $L=0.1H$ and capacitance $C=10^{-3}F$, kept on a plane. The area of the circuit is $1m^2$. 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 $\beta =0.04T{s}^{-1}$. The maximum magnitude of the current in the circuit is ___$mA$.

Answer 1

Answer: 4

Maximum energy will be
$\frac{q_0^2}{2C}=\frac{1}{2}L{I}_0^2$
$\frac{q_0^2}{CL}=I_0^2$
$I_0=\frac{q_0}{\sqrt{LC}}$
$I_0=\frac{CV}{\sqrt{LC}}$
$I_0=\sqrt{\frac{C}{L}}\times V$
$V=emf=\left|\frac{AdB}{dt}\right|$
$I_0=\sqrt{\frac{10^{-3}}{0.1}}\times 0.04$
$V=(1\times 0.04)$
Maximum current $I_0=0.004=4mA$