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

Potential Due to Standard Configurations

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Point charge Q at distance r: V = kQr\frac{kQ}{r}. Uniformly charged ring (Q, radius R) on axis at distance x: V = kQsqrt\frac{kQ}{sqrt}(x2x^2 + R2R^2). Uniformly charged sphere outside (r >= R): V = kQr\frac{kQ}{r} (point charge behavior). Inside solid sphere (r < R): V = kQ3R2r2(2R3)\frac{3R^2 - r^2}{(2R^3)} — note V is maximum at center: VcenterV_{center} = 3kQ2R\frac{kQ}{2R} = \frac{3}{2}$$V_{surface}. Inside hollow sphere: V = kQR\frac{kQ}{R} (constant, equal to surface value). Electric dipole at far point (r, theta): V = kp*costhetar\frac{theta}{r}^2. Axial: V = kpr\frac{kp}{r}^2. Equatorial: V = 0 (the equatorial plane is at zero potential for a dipole). Key insight: V decreases as 1/r for point charge but as 1/r2r^2 for dipole — dipole potential falls off faster.

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