Question

A very long charged solid cylinder of radius '$a$' contains a uniform charge density $\rho$. Dielectric constant of the material of the cylinder is k. What will be the magnitude of electric field at a radial distance '$x$' ($x$ < $a$) from the axis of the cylinder?

• A. $\rho \frac{x}{{ϵ}_0}$
• B. $\rho \frac{x}{2k{ϵ}_0}$
• C. $\rho \frac{x^2}{2a{ϵ}_0}$
• D. $\rho \frac{x}{2k}$

Answer 1

The correct option is B $\rho \frac{x}{2k{ϵ}_0}$

Applying gauss law
$E2\pi xl=\frac{\rho \pi x^{2}l}{k{ϵ}_0}\Rightarrow E=\frac{\rho x}{2k{ϵ}_0}$