Spherical capacitor (inner radius a, outer radius b): C = 4piepsilon_0ab/(b-a). As b -> infinity (isolated sphere): C = 4piepsilon_0a. As (b-a) -> 0 with b ~ a ~ R: C ~ 4piepsilon_0R^2/(b-a) = epsilon_0A/d (reduces to parallel plate, since A = 4piR^2 and d = b-a). Cylindrical capacitor (inner a, outer b, length L): C = 2piepsilon_0L/ln(b/a). For (b-a) << a, this also reduces to the parallel plate formula with A = 2piaL. These are derived by finding V from E (using Gauss's law) and applying C = Q/V. JEE problems may involve concentric spherical or coaxial cylindrical configurations with multiple dielectric layers.
Part of JES-02 — Electrostatic Potential, Capacitance & Energy
Capacitor Geometries — Spherical and Cylindrical
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