Question

A non-conducting ring of radius $0.5\, m$ 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 $\int\limits^{l=0}_{l=\infty}-E.dl$ ($l = 0$ being centre of the ring) in volt is

• A. +2
• B. 1
• C. -2
• D. zero

Answer 1

Answer: (A)

$\int\limits_{l=\infty}^{l=0}E.dl=\int\limits_{l=\infty}^{l=0}dV=V$ (Centre) - $V$ (infinity)
but $V$ (infinity) = $0$
$\therefore \int\limits_{l=\infty}^{l=0}E.dl$ corresponds to potential at centre of ring.
and $V$ (centre) $=\frac{1}{4 \pi\varepsilon_0}.\frac{q}{R}$
$=\frac{(9 \times10^9)(1.11 \times 10^{-10})}{0.5}= + 2 V$