Question

If a wire is connected between the inner and outer sphere, after electrostatic equilibrium is established. Find out the magnitude of total charge on the outer surface and inner surface of the outer sphere?

Answer 1

When outer and inner sphere are connected by wire, the entire charge is transferred to the outer surface from the inner sphere. In electrostatic equilibrium, charge does not reside inside a conductor. Total charge on the outer surface of the outer sphere is -5Q. Total charge on the inner surface is 0. The electric field at the surface of the inside sphere goes to zero after connection. Consider a Gaussian surface just on the surface of the inner sphere,
${\varphi }_E=E\left(4\pi r^2\right)=\frac{Q_{enclosed}}{{}_0}=0$ $\because Q_{enclosed}=0$
Thus, we have $E=0$