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

Applications of Gauss's Law — Cylindrical and Planar

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Infinite line charge (lambda): Cylindrical Gaussian surface of radius r, length L. Flux = E(2pirL). Enclosed charge = lambdaL. Result: E = lambda2piepsilon0r\frac{lambda}{2*pi*epsilon_0*r}.

Infinite plane sheet (sigma): Pillbox Gaussian surface. Flux = 2EA (both flat faces). Enclosed charge = sigma*A. Result: E = sigma2epsilon0\frac{sigma}{2*epsilon_0}.

Two parallel infinite sheets: Same sigma: E = sigmaepsilon0\frac{sigma}{epsilon_0} outside both sides, E = 0 between them. Opposite sigma (+sigma and -sigma): E = sigmaepsilon0\frac{sigma}{epsilon_0} between them, E = 0 outside. This is the basis of a parallel plate capacitor's uniform field.

Infinite uniformly charged cylinder (rho, radius R): Inside (r < R): E = rho*r2epsilon0\frac{r}{2*epsilon_0}. Outside (r > R): E = lambda2piepsilon0r\frac{lambda}{2*pi*epsilon_0*r} where lambda = rhopiR2R^2.

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