Consider three concentric metal shells A, B and C having radii a, b and c respectively, as shown in the figure (a

Question

Consider three concentric metal shells A, B and C having radii a, b and c respectively, as shown in the figure (a < b < c). Their surface charge densities are σ, -σ and σ respectively. Calculate the electric potential on the surface of shell A.

Accepted Answer

(3) σ/(ε₀)(a-b+c). Given: shells A, B, C of radii a < b < c with surface charge densities σ, -σ, σ. Charges: q_A = 4π a²σ, q_B = -4π b²σ, q_C = 4π c²σ. Idea: a shell of charge q and radius R gives V = q/(4πε₀R) on its surface and everywhere inside it. The surface of A is on shell A and inside shells B and C, so each shell contributes q/(4πε₀×(its own radius)). V_A = 1/(4πε₀)((q_A)/a + (q_B)/b + (q_C)/c) = σ/(ε₀)(a - b + c). So the potential on shell A is σ/(ε₀)(a-b+c).

Consider three concentric metal shells A, B and C having radii a, b and c respectively, as shown in the figure (a < b < c). Their surface charge densities are σ, -σ and σ respectively. Calculate the electric potential on the surface of shell A.

Step-by-step solution

Why the other options are wrong