Three concentric charged metallic spherical sheets A, B and C have radii a , b , c potentials V _ A , V _ B , V _ C and charge densities + ,- and + respectively. The value of potential V_A is ( ₀= permittivity of free space)

Step-by-step solution

The potential at the surface of shell A ( r = a ) is the sum of contributions from all three shells. For a spherical shell, the potential at distance r from its center is V = 1 4 ₀ Q r for r R and V = 1 4 ₀ Q R for r The charges are Q_A = 4 a^2 , Q_B = -4 b^2 , and Q_C = 4 c^2 . Since r = a lies on shell A ( r = R_A ), inside shell B ( a V_ A = 1 4 ₀ Q_A a + 1 4 ₀ Q_B b + 1 4 ₀ Q_C c Substituting the charges: V_A = 1 4 ₀ 4 a^2 a + 1 4 ₀ -4 b^2 b + 1 4 ₀ 4 c^2 c Simplifying each term yields V_A = ₀ (a - b + c) . The