Question

A small metallic sphere carrying charge + Q is located at the centre of a spherical cavity in a large uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of the shell. Write the expression for the electric field at the point P₁.

Answer 1

Charge on inner surface: - Q

Charge on outer surface : + Q

Electric field at point P₁ 

Answer 2

The uniform charge −Q will be induced on inner surface of the shell and +Q will be induced on outer surface. This is follows from conservation of charge and no static charges resides in the interior of a metal in electrical equilibrium.

Using Gauss's law the field at P₁​:

\(E.4\pi r^2_1 = \frac{Q_{en}}{\varepsilon_0}\) where Q_en = +Q, charge inside gaussian surface of radius r₁​.

Thus, \(E = \frac{Q}{4 \pi \varepsilon_0 r_1^2}\)