Question

A non-conducting sheet of large surface area and thickness $d$ contains uniform charge density $\rho$. The electric field at a point $P$ inside the plane at a distance $x$ from the central plane $0<x<d$ is :

• A. $\frac{\rho }{2{\epsilon }_0}$
• B. $\frac{\rho d}{2{\epsilon }_0}$
• C. $\frac{\rho x}{{\epsilon }_0}$
• D. $\frac{\rho x}{2{\epsilon }_0}$

Answer 1

Answer: (C)

$\frac{\rho x}{{\epsilon }_0}$

We electric field due to the charge sheet at a certain distance x from sheet is $E=\frac{\sigma }{2{ϵ}_0}$ for $x>0$ and $-\frac{\sigma }{2{ϵ}_0}$ for $x<0$ where $\sigma =$ surface charge density.

The electric field in between the cross plane is $E=\frac{\sigma }{2{ϵ}_0}-(-\frac{\sigma }{2{ϵ}_0})=\frac{\sigma }{{ϵ}_0}$

here, charge of plane at x is $q=\rho \left(volume\right)=\rho \left(Ax\right)$ also $\sigma =q/A=\frac{\rho \left(Ax\right)}{A}=\rho x$

Thus, the required filed is $E=\frac{\rho x}{{ϵ}_0}$