Q. A non-conducting ring of radius 0.5 m carries total charge of $1.11 \times 10^{- 10}$ C distributed non-uniformly on its circumference producting an electric field everywhere in space. The value of the line integral $\int_{l = \infty}^{l = 0}{- E.dl\ (l = 0}$ being centre of ring) in volt is
A) $+ 2$
B) $- 1$
C) $- 2$
D) Zero
Explanation
(a) By definition $\int_{l = \infty}^{l = 0}{- E.dl = V,\ \ }$ the potential at the centre of ring and $V = \frac{1}{4\pi\varepsilon_{0}}.\frac{Q}{R} = \frac{9 \times 10^{9} \times 1.11 \times 10^{- 10}}{0.5} = 2V$
Hence value of given line integral is 2 V.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.