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

Potential of Concentric Shell Systems

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For concentric conducting shells, the potential at any point = sum of contributions from all shell charges. At the inner shell (radius a, charge Q1) with outer shell (radius b, charge Q2): VaV_a = kQ1a\frac{kQ1}{a} + kQ2/b. VbV_b = kQ1b\frac{kQ1}{b} + kQ2/b. If outer shell is grounded (VbV_b = 0): Q2 = -Q1b/b... actually kQ1/b + kQ2/b = 0 gives Q2 = -Q1. If inner shell is grounded: kQ1/a + kQ2/b = 0, so Q1 = -aQ2/b. Grounding changes the charge distribution. The capacitance of the system: C = QVaVb\frac{Q}{V_a - V_b} = 4pi*epsilon0epsilon_0*abba\frac{ab}{b-a}. These problems require careful bookkeeping of which shell has what charge and how grounding modifies charges.

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