Question

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

Uniform charge density = $\rho$

Let the area of the non conducting sheet be $A$.

Electric field at point $x$,

$E=\frac{\sigma }{2{\epsilon }_o}$ for $x>0;$ $E=\frac{-\sigma }{2{\epsilon }_o}$ for $x<0$

Electric field between the cross plane,

$E=\frac{\sigma }{2{\epsilon }_o}-\frac{(-\sigma )}{2{\epsilon }_o}=\frac{\sigma }{{\epsilon }_o}...\left(i\right)$

Charge at point x is,

$q=\rho \times volume=\rho Ax$

$\because \sigma =\frac{q}{A}=\frac{\rho Ax}{A}=\rho x$

Substituting $\sigma$ in eqn$\left(i\right)$,

We get,

$E=\frac{\rho x}{{\epsilon }_o}$