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} $