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 $\stackrel{\rightharpoonup }{E}$ everywhere in space. The value of the line integral $-{\int }_{l-\infty }^{l=0}\stackrel{\rightharpoonup }{E}\stackrel{\rightharpoonup }{dl}$ (l=0 being centre of the ring) in volt is

• A. + 2
• B. - 1
• C. - 2
• D. Zero

Answer 1

The correct option is A + 2

V = $-{\int }_{-\infty }^0\stackrel{\rightharpoonup }{E}.\stackrel{\rightharpoonup }{dl}$
$=\frac{1}{4\pi {ϵ}_0}\times \frac{q}{r}=\frac{9\times {10}^9\times 1.11\times {10}^{-10}}{0.5}=2$ volt