A metal plate 8.0 cm on a side carries a total charge of . We will calculate in the infinite plate approximation (a) the electric field 0.50 mm above the surface of the plate near the plate’s centre; (b) the field at a distance of 30 m.

Solution:             Click For PDF Version

(a)

The area of the metal plate which is 8.0 cm on a side is

.

Total charge on the plate is .

On a metallic plate charge will be equally divided on its two sides, front and back. Therefore, the surface charge density on each side of the plate will be

In the infinite plate approximation the electric field at a distance of 0.50 mm above the surface and for that matter at any other distance from the plate will be given by

(b)

If we want to estimate the field at a distance of 30 m from the plate, we can assume that the total charge of is concentrated at a point and in this approximation the electric field will be