Part of JES-02 — Electrostatic Potential, Capacitance & Energy

Capacitor Geometries — Spherical and Cylindrical

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Spherical capacitor (inner radius a, outer radius b): C = 4piepsilon0epsilon_0abba\frac{ab}{b-a}. As b -> infinity (isolated sphere): C = 4pi*epsilon0epsilon_0a. As (b-a) -> 0 with b ~ a ~ R: C ~ 4pi*epsilon0epsilon_0R^2ba\frac{2}{b-a} = epsilon0epsilon_0A/d (reduces to parallel plate, since A = 4piR2R^2 and d = b-a). Cylindrical capacitor (inner a, outer b, length L): C = 2piepsilon0epsilon_0L/lnba\frac{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 = QV\frac{Q}{V}. JEE problems may involve concentric spherical or coaxial cylindrical configurations with multiple dielectric layers.

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