There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively (c>b>a) and they are charged with charge q₁, q₂ and q₃ respectively. The potentials of the spheres A, B and C respectively, are :

Step-by-step solution

The potential at any point due to a charged spherical shell of radius R and charge Q is V = 1 4 _o Q R for points inside or on the surface ( r R ), and V = 1 4 _o Q r for points outside ( r > R ). Let k = 1 4 _o . The potentials of the three shells A, B, C with radii a For shell A ( r = a ): Shell A is on its own surface, while it is inside shells B and C . V_A = k q₁ a + k q₂ b + k q₃ c = 1 4 _o ( q₁ a + q₂ b + q₃ c ) For shell B ( r = b ): Shell B is outside shell A , on its own surface, and inside shell C . V_B