Three concentric spherical metallic shells X, Y and Z of radii a, b and c (a

Question

Three concentric spherical metallic shells X, Y and Z of radii a, b and c (a < b < c) have surface charge densities +σ, −σ and +σ respectively. Shells X and Z are at the same potential. If a = 2 cm and b = 3 cm, find c in cm.

Physics · Circular Motion

JEE Mains 10 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Charges on the shells are q(X) = 4πσa² q(Y) = −4πσb² q(Z) = 4πσc² Equating the potentials of shells X and Z and simplifying gives c(a − b) = (a + b)(a − b) Since a ≠ b, c = a + b Therefore, c = 2 + 3 = 5 cm Final value: 5