Physics - Electrostatics Question with Solution | TestHub

When $-{\mathrm{Q}}_{\mathrm{t}}$ charge is induced at inner surface at time t, then electric field in the material of shell is $\mathrm{E}=\frac{{\mathrm{q}}_0-{\mathrm{Q}}_{\mathrm{t}}}{4\pi {ϵ}_0{\mathrm{r}}^2}$ where r is distance of point under consideration from centre of shell.

Current through shell at this moment (discussed in option A) is $\mathrm{I}=\frac{{\mathrm{q}}_0-{\mathrm{Q}}_{\mathrm{t}}}{{ϵ}_0\rho }$

At time t we can write $\frac{{\mathrm{dQ}}_{\mathrm{t}}}{{\mathrm{q}}_0-{\mathrm{Q}}_{\mathrm{t}}}=\frac{\mathrm{dt}}{{ϵ}_0\rho }$

At time t , value of ${\mathrm{Q}}_{\mathrm{t}}$ is given by ${\mathrm{Q}}_{\mathrm{t}}={\mathrm{q}}_0\left(1-{\mathrm{e}}^{-\frac{\mathrm{t}}{{ϵ}_{0\mathrm{p}}}}\right)$