Q. The electric intensity due to an infinite cylinder of radius $R$ and having charge $q$ per unit length at a distance $r(r > R)$ from its axis is
A) Directly proportional to $r^{2}$
B) Directly proportional to $r^{3}$
C) Inversely proportional to $r$
D) Inversely proportional to $r^{2}$
Explanation
(c) According to Gauss law $\oint_{}^{}{E.ds = \frac{ql}{\varepsilon_{0}}}$
$\oint_{}^{}{E.ds = 2\pi\ rl;}$ [$E$ is constant]
$\therefore E.2\pi\ rl = \frac{ql}{\varepsilon_{0}} \Rightarrow E = \frac{q}{2\pi\varepsilon_{0}r}\ \ i.e.\ E \propto \frac{1}{r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.