Question

A long cylinder contains uniformly distributed charge density $\rho$. The electric field at a point $P$ inside the cylinder at a distance $x$ from the axis is :

• A. $\frac{\rho x}{2{\epsilon }_0}$
• B. $\frac{\rho x}{3{\epsilon }_0}$
• C. $\frac{\rho x}{4{\epsilon }_0}$
• D. none of these

Answer 1

The correct option is A $\frac{\rho x}{2{\epsilon }_0}$

Consider a Gaussian cylinder of radius $x$ and length $l$.

By Gauss's law the field inside cylinder , $E.2\pi xl=\frac{Q_{en}}{{ϵ}_0}=\frac{\rho .\pi x^{2}l}{{ϵ}_0}$

$\Rightarrow E=\frac{\rho x}{2{ϵ}_0}$