Simple Nature - Light and Matter

extended to the case where the charge is not along any axis of thecube, 11 and based on additivity we then have a proof that the fluxdue to an outside charge is always zero.No charge on the interior of a conductor example 35I asserted on p. 523 that for a perfect conductor in equilibrium, excesscharge is found only at the surface, never in the interior. Thiscan be proved using Gauss’s theorem. Suppose that a charge qexisted at some point in the interior, and it was in stable equilibrium.For concreteness, let’s say q is positive. If its equilibriumis to be stable, then we need an electric field everywhere aroundit that points inward like a pincushion, so that if the charge wereto be perturbed slightly, the field would bring it back to its equilibriumposition. Since Newton’s third law forbids objects frommaking forces on themselves, this field would have to be the fieldcontributed by all the other charges, not by q itself. But this is impossible,because this kind of inward-pointing pincushion patternwould have a nonzero (negative) flux through the pincushion, butGauss’s theorem says we can’t have flux from outside charges.11 The math gets messy for the off-axis case. This part of the proof can becompleted more easily and transparently using the techniques of section 10.7,and that is exactly we’ll do in example 37 on page 631.Section 10.6 Fields by Gauss’ Law 623