Question

A non-conducting sheet of large surface area and thickness d contains a uniform charge distribution of density $\mathrm{\rho }$. 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.

Answer 1

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, $\rho =\frac{Q}{sd}$
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 = $\rho sx$
For this Guassian surface, using Gauss's Law,we get:
$$\begin{gathered} \oint E.ds=\frac{q}{{\in }_0} \\ E.s=\frac{\rho sx}{{\in }_0} \\ E=\frac{\rho x}{{\in }_0} \end{gathered}$$

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

$E=\frac{\rho d}{{\in }_0}$