Three concentric spherical shells have radii a , b and c ( a < b < c ) and have surface charge densities σ , - σ and σ respectively. If V A , V B and V C denote the potentials of the three shells, then, for c = a + b , we have

Step-by-step solution

V A = 1 4 π ε 0 q A a + q B b + q C c = 4 π 4 π ε 0 a 2 σ a - b 2 σ b + c 2 σ c V A = 1 ε 0 a 2 σ a - b 2 σ b + c 2 σ c ⇒ V A = 1 ε 0 a σ - b σ + c σ = 2 a σ ε 0 V B = 1 ε 0 a 2 σ b - b 2 σ b + c 2 σ c V B = 1 ε 0 a 2 σ b - b σ + c σ V B = aσ ε 0 a b - 1 V C = 1 ε 0 a 2 σ c - b 2 σ c + c 2 σ c V C = σ ε 0 a 2 -b 2 a + b + c V C = σ ε 0 a-b + c V C = 2 σ a ε 0 V A = V C > V B