^Spherical capacitor inner earthed

Spherical capacitor inner earthed

Suppose a neutral metal sphere radius a is placed concentrically inside a metal shell of radius b having surface charge +q.

If inner sphere a is earthed then charge q/ appears on its surface from earth so that the potential of b becomes zero. i.e.,

Due to earthing & induction the final charge distribution will be

Due to this charge distribution electric field will be

1. E = 0 for r < a (i.e. inside a)

2. (radially outward) for a ≤  r ≤ b

3. (radially outward) for r > b

Due to earthing potential of a is zero & potential on b due to charge on outer surface of a & inner surface of b get cancelled & final potential on b is

Using C = q/V, capacitance for this system is

The above relation can be expressed as