Three concentric spherical shells have radii a, b and c (a

Question

Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ, -σ and σ, respectively. If Vₐ, Vᵦ and V𝒸 denote potentials of respective shells, the correct relation is: [Diagram: Image]

Options

G1 Physics · Accepted Answer

Step 1: Charge on shell radius R carrying density σ is Q = 4πR²σ. Step 2: At any position, sum potential kQ/R for outside shells and kQ/r for inside shells. Step 3: Source simplifies to Vₐ = (σ/ε₀)(a − b + c), Vᵦ = (σ/ε₀)(a²/b − b + c), V𝒸 = (σ/ε₀)(a² − b² + c²)/c. Step 4: Compare with a < b < c and source values to select printed ordering.

Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ, −σ and σ, respectively. If Vₐ, Vᵦ and V𝒸 denote potentials of respective shells, the correct relation is: [Diagram: Image]