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. $\rho \frac{x}{\varepsilon_{0}}$
• B. $\rho \frac{x}{2 k \varepsilon_{0}}$
• C. $\rho \frac{x^{2}}{2 a \varepsilon_{0}}$
• D. $\rho \frac{x^{2}}{2 k}$

Answer 1

Answer: (B)

Using Gauss's Law
$E(2 \pi x l)=\frac{\rho\left(\pi x^{2} l\right)}{k \varepsilon_{0}}$
$\therefore E=\frac{\rho x}{2 k \varepsilon_{0}}$