Part of JES-01 — Electrostatics: Coulomb's Law, Field & Gauss's Law

Electric Dipole — Moment, Field, and Torque

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Dipole: two equal and opposite charges +q, -q separated by 2a. Dipole moment: p = q(2a), directed from -q to +q. SI unit: C m. For r >> a: Axial point (on the dipole axis): EaxialE_{axial} = 2kp/r3r^3 (along p). Equatorial point (perpendicular bisector): EeqE_{eq} = kpr\frac{kp}{r}^3 (opposite to p). General point at angle theta from axis: E = (kp/r3r^3)sqrt(1 + 3cos2cos^2(theta)). In a uniform external field E: Torque tau = p x E, |tau| = pEsin(theta). Potential energy U = -p.E = -pE*cos(theta). Stable equilibrium: theta = 0 (p parallel to E, U = -pE minimum). Unstable equilibrium: theta = pi (U = +pE maximum). Work to rotate from theta1theta_1 to theta2theta_2: W = pE(cos(theta1theta_1) - cos(theta2theta_2)).

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