Question

Intensity of electric field at a point close and outside a charged conducting cylinder is proportional to:

($r$ is the distance of a point from the axis of a cylinder)

• A. $\frac{1}{r}$
• B. $\frac{1}{r^2}$
• C. $\frac{1}{r^3}$
• D. $r^3$

Answer 1

Answer: (A)

$\frac{1}{r}$

Let the charge enclosed of the cylinder of length $L$ (a part of the cylinder) be $q$.

Considering a cylindrical gaussian surface of co-axial with the conducting cylinder,

$E\left(2\pi rL\right)=\frac{q}{{ϵ}_0}$

$⟹E=\frac{q}{2\pi {ϵ}_{0}Lr}\propto \frac{1}{r}$