Three concentric spherical shells have radii a, b and c(a < b < c) and have surface charge densities ,- and 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

Here, aligned & V _ A = 1 4 ₀ 4 a ^2 a - 1 4 ₀ 4 b ^2 ~b & + 1 4 ₀ 4 c^2 c & = ₀ (a-b+c)= ₀ (2 a) ( c=a+b) & aligned aligned & V _ B = 1 4 ₀ 4 a ^2 a - 1 4 ₀ 4 b ^2 ~b &+ 1 4 ₀ 4 c ^2 c aligned aligned & = ₀ ( a^2 c -b+c )= ₀ (2 a)( c=a+b) & and V_C= 1 4 ₀ 4 a^2 c - 1 4 ₀ 4 b^2 c & + 1 4 ₀ 4 c^2 c & = ₀ ( a^2 c - b^2 c +c )= ₀ (2 a)( c=a+b) & aligned Hence, V _ A = V _ C V _ B