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A square metal plate of edge length 8.4 cm and negligible thickness has a total charge of \(6.4 \times 10^{-6}\) C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.39 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 33 m (large relative to the plate size) by assuming that the plate is a point charge. Give your answers in N/C.
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