Question

A non-conducting ring of radius $0.5m$ carries a total charge of $1.11\times 10^{-10}C$ distributed non-uniformly on its circumference producing an electric field E everywhere in space. The value of the integral $\underset{l=\infty }{\overset{l=0}{\int }}-E.dl$ ($l=0$ being centre of the ring) in volt is

• A. +2
• B. 1
• C. -2
• D. zero

Answer 1

Answer: (A)

$\underset{l=\infty }{\overset{l=0}{\int }}E.dl=\underset{l=\infty }{\overset{l=0}{\int }}dV=V$ (Centre) - $V$ (infinity)
but $V$ (infinity) = $0$
$\therefore \underset{l=\infty }{\overset{l=0}{\int }}E.dl$ corresponds to potential at centre of ring.
and $V$ (centre) $=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{R}$
$=\frac{(9\times 10^9)(1.11\times 10^{-10})}{0.5}=+2V$