A non-conducting ring of radius 0.5 m carries a total charge of \( 1.11\times10^{-10}\,\mathrm{C} \) distributed non-uniformly on its circumference. The electric potential at the centre of the ring is (take \( \frac{1}{4\pi\varepsilon_0}=9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → +2 V
Electric potential is a scalar, so the potential of a group of charges is the algebraic sum of the potentials of its parts. Every charge element of the ring is at the same distance \( R \) from the centre. So each adds \( k\,dq/R \), however unevenly the charge is spread.
\( \begin{aligned} V &= \frac{kQ}{R} \\ &= \frac{9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}}\times1.11\times10^{-10}\,\mathrm{C}}{0.5\,\mathrm{m}} \\ &= \frac{0.999}{0.5}\,\mathrm{V} \\ &\approx +2\,\mathrm{V} \end{aligned} \)
The total charge is positive, so the potential at the centre is positive.