Point charge Q at distance r: V = kQ/r. Uniformly charged ring (Q, radius R) on axis at distance x: V = kQ/sqrt(x^2 + R^2). Uniformly charged sphere outside (r >= R): V = kQ/r (point charge behavior). Inside solid sphere (r < R): V = kQ(3R^2 - r^2)/(2R^3) — note V is maximum at center: V_center = 3kQ/(2R) = (3/2)V_surface. Inside hollow sphere: V = kQ/R (constant, equal to surface value). Electric dipole at far point (r, theta): V = kp*cos(theta)/r^2. Axial: V = 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/r^2 for dipole — dipole potential falls off faster.
Part of JES-02 — Electrostatic Potential, Capacitance & Energy
Potential Due to Standard Configurations
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