Q. 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, VB and VC denote the potentials of the three shells, then for c = a + b, we have:
A) VC = VB ≠ VA
B) VC ≠ VB ≠ VA
C) VC = VB = VA
D) VC = VA ≠ VB
Explanation
[Solution from source] VA = (σ/ε₀)(a − b + c) = 2aσ/ε₀ for c = a + b. VC = (σ/ε₀)(a² − b² + c²)/c = (σ/ε₀)(2a² + 2ab)/(a + b) = 2aσ/ε₀. VB = (σ/ε₀)(a²/b − b + c) = (σ/ε₀)(a²/b + a), which differs from 2aσ/ε₀ unless a = b, so VC = VA ≠ VB. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.