A non-conducting ring of radius 0.5 m carries a total charge of 1.11 × 10^–10 C distributed non-uniformly on its circumference producing an electric field E everywhere integral $\int\limits_{l=\infty}^{l=0}-E . d l$ (l = 0 being center of the ring) in volt is :

+2

$-\int\limits_{l=\infty}^{l=0} \vec{E} . \vec{d l}=\int\limits_{l=\infty}^{l=0} dV$ = V (centre) - V (infinity) but V (infinity) = 0

∴ $-\int\limits_{l=\infty}^{l=0} \vec{E} . \vec{d l}$ corresponds to potential at centre of ring.

and V(centre) = $\frac{1}{4 \pi \varepsilon_0} . \frac{q}{R}$

$=\frac{\left(9 \times 10^9\right)\left(1.11 \times 10^{-10}\right)}{0.5} \approx$ 2 volt