Question

Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities σ, – σ and σ respectively.

(i) Find the potential of three shells A, B and C.

(ii) If the shells A and C are at the same potential, obtain the relation between the radii a, b and c.

Answer 1

The three shells are shown in figure.

(i) Potential of A

Potential of B = (Potential due to + σ on A) + (Potential due to – σ on B)

Potential of C = (Potential due to + σ on A) + (Potential due to – σ on B) + (Potential due to + σ on C)

(ii) Given that V_A = V_C 

Solving we get, c = (a + b).