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

aligned q _ A & =4 a ^2 , q _ B & =-4 b ^2 , q _ C & =4 c ^2 , c = a + b V _ A & = 1 4 ₀ ( q _ A a + q _ B b + q _ C c ) & = 2 a ₀ ~V _ B & = 1 4 ₀ ( q _ A a + q _ B b + q _ C c ) aligned aligned & = ₀ ( a ^2 b - b + c ) & = ₀ ( a + a ^2 b ) V _ C & = 1 4 ₀ ( q _ A a + q _ B b + q _ C c ) & = ₀ ( a ^2- b c + c )= 2 a ₀ aligned So, V_C=V_A V_B