Classical Electrodynamics · Problem 1.11

Boundary-Value Problems in Electrostatics: I — John David Jackson

Physics — E&M · normal-derivative-electric-field-conductor

Problem

Use Gauss's theorem to prove that at the surface of a curved charged conductor, the normal derivative of the electric field is given by

\frac{1}{E}\frac{\partial E}{\partial n} = -\left(\frac{1}{R_1} + \frac{1}{R_2}\right)

where

R_1

and

R_2

are the principal radii of curvature of the surface.