A square metal plate of edge length 12 cm and negligible thickness has a total charge of 5.6 × 10-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.49 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 29 m (large relative to the plate size) by assuming that the plate is a charged particle.

a) 2.2*10^7 N/C

b) 60 N/C

Explanation:

To start with, we say that the

Area charge of the plate, σ = q/2A

σ = 5.6*10^-6 / 2(12*10^-2)²

σ = 5.6*10^-6 / 0.0288

σ = 1.944*10^-4 C²/m

Next, we find the electric field

Electric field, E = σ/Eo

Electric field, E = 1.944*10^-4 / 8.85*10^-12

Electric field, E = 2.2*10^7 N/C

b)

E = kq/r²

E = [8.99*10^9 * 5.6*10^-6] / 29²

E = 50344 / 841

E = 60 N/C

This means that the E at a distance of 29 m is 60 N/C

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