#### Question

A non-conducting sheet of large surface area and thickness d contains a uniform charge distribution of density ρ. Find the electric field at a point P inside the plate, at a distance x from the central plane. Draw a qualitative graph of E against x for 0 < x < d.

#### Solution

Given:

Thickness of the sheet = d

Let the surface area of the sheet be s.

Volume of the sheet = sd

Volume charge density of the sheet, ρ = `"Q"/"sd"`

Charge on the sheet = Q

Consider an imaginary plane at a distance x from the central plane of surface area s.

Charge enclosed by this sheet, q =ρsx

For this Guassian surface, using Gauss's Law,we get:

`oint "E"."ds" = "q"/∈_0`

`"E"."s" = (ρ "sx")/∈_0`

`"E" =( ρ "x")/∈_0`

The electric field outside the sheet will be constant and will be:

`"E" =(ρ"d")/∈_0 `