Emf induced in the circuit is
$
\begin{aligned}
& |E|=\left|\frac{d \phi}{d t}\right|=\frac{d}{d t}\left(\left(B_0+\beta t\right) A\right) \\
& =\beta \times A \\
& =0.04 \mathrm{~V}
\end{aligned}
$
So the circuit can be rearranged as
Using Kirchhoff's law we can write
$
\begin{aligned}
& E=L \frac{d i}{d t}+\frac{q}{C} \\
& L \frac{d i}{d t}=E-\frac{q}{C} \\
& \text { or } \frac{d^2 q}{d t^2}=-\frac{1}{L C}(q-C E)
\end{aligned}
$
Using SHM concept we can write
$
\begin{aligned}
& q=C E+A \sin (\omega t+\phi)\left(\text { where } \omega=\frac{1}{\sqrt{L C}}\right) \\
& \text { at } t=0, q=0 \& i=0 \\
& \text { So } A=C E \& \phi=-\frac{\pi}{2} \\
& q=C E-C E \cos \omega t \\
& \text { so } i=\frac{d q}{d t}=C E \omega \sin \omega t \\
& i_{\max }=\frac{10^{-3} \times 0.04}{\sqrt{0.1 \times 10^{-3}}}=4 \mathrm{~mA}
\end{aligned}
$
