Question

A square metal plate of edge length 6.4 cm and negligible thickness has a total charge of 6.6 x 10-6 C. Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.71 mm from the center) by assuming that the charge is spread uniformly over the two faces of the plate. Express your answer in terms of N/C.

Answer 1

Answer:

$E=9.1\times 10^7 N/C$

Explanation:

We are given that

Length of side,l=6.4 cm=$6.4\times 10^{-2} m$

1 m=100 cm

Total charge,q=$6.6\times 10^{-6} C$

We have to find the magnitude E of the electric field just off the center of the plate.

Area charge density,$\sigma=\frac{q}{A}=\frac{q}{l^2}=\frac{6.6\times 10^{-6}}{(6.4\times 10^{-2})^2}$

$\sigma=16.1\times 10^{-4}C/m^2$

Electric field,$E=\frac{\sigma}{2\epsilon_0}$

Where $\epsilon_0=8.85\times 10^{-12}$

Substitute the values

$E=\frac{16.1\times 10^{-4}}{2\times 8.85\times 10^{-12}}$

$E=9.1\times 10^7 N/C$