Question

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 $r^2$

Answer 1

The correct option is C Inversely proportional to r

According to Gauss law $\oint E.ds=\frac{ql}{{ϵ}_0}$
$\oint E.ds=2\pi rl$; (E is constant)
$\therefore E.2\pi rl=\frac{ql}{{ϵ}_0}\Rightarrow E=\frac{q}{2\pi {ϵ}_{0}r}$ i.e. $E\infty \frac{1}{r}$