Halliday, Resnick & Walker — Gauss' Law: Problem 53

53 A square metal plate of edge length 12 cm and negligible thickness has a total charge of \(2.0 \times 10^{-6}\text{ C}\). (a) Estimate the magnitude \(E\) of the electric field just off the center of the plate (at, say, a distance of 0.50 mm from the center) by assuming that the charge is spread uniformly over the two faces of the plate. (b) Estimate \(E\) at a distance of 30 m (large relative to the plate size) by assuming that the plate is a charged particle.