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 on its circumference on electric field E, everywhere in space. The value of the line integral ${\int }_{l=\infty }^{l=0}(-E\cdot dl)$ ($l=0$ being centre of ring) in volts is?

• A. $+2$
• B. $-1$
• C. $-2$
• D. Zero

Answer 1

The correct option is A $+2$

From definition of potential difference
${\int }_{i=\infty }^{i=0}E\cdot dl=$ potential difference at infinity and at centre of ring $=V_{centre}-V_{infinity}$
But by convention $V_{infinity}=0$ and $V_{centre}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{R}$
$=9\times {10}^9\times \frac{1.11times{10}^{-10}}{0.5}=2$volt
$\therefore {\int }_{i=\infty }^{i=0}(-E\cdot dl)=2$volt $-0$ volt$=2$ volt.