Q. 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 $\overrightarrow{E}$ everywhere in space. The value of the line integral $\int_{l = \infty}^{l = 0}{- \overrightarrow{E}.\overrightarrow{dl}}(l = 0$ being centre of the ring) in volt is
A) $+ 2$
B) $- 1$
C) $- 2$
D) Zero
Explanation
(a) $\int_{- \infty}^{0}{- \overrightarrow{E}.\overrightarrow{d}l} =$ potential at centre of non-$conducting\ ring$
$= \frac{1}{4\pi\varepsilon_{0}} \times \frac{q}{r} = \frac{9 \times 10^{9} \times 1.11 \times 10^{- 10}}{0.5} = 2\ volt$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.