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)

2

Answer 2

$\int^{l=0}_{l=\infty}E.dl=\int^{l=0}_{l=\infty} dV=V$ (Centre) - V (infinity)
but V (infinity) = 0
$\therefore \int^{l=0}_{l=\infty}E.dl$ corresponds to potential at centre of ring.
and V (centre) $=\frac{1}{4 \pi\varepsilon_0}.\frac{q}{R}$
\hspace25mm =\frac{(9 \times10^9)(1.11 \times 10^{-10})}{0.5}= + 2 V