A metal wire is bent in the shape of a circle of 10 cm radius. It is given a charge of 200 μC which spreads on it uniformly. The electric potential at its center is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 18 × 106 V
Potential is a scalar, so the contributions of all the small charges on the ring simply add. Every element of the ring is at the same distance R from the centre, so the whole charge acts as if it were at distance R.
\( q = 200\,\mu\mathrm{C} = 2\times10^{-4}\,\mathrm{C} \)
\( R = 10\,\mathrm{cm} = 0.1\,\mathrm{m} \)
\( \displaystyle V = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{R} \)
\( \displaystyle V = \frac{9\times10^{9} \times 2\times10^{-4}}{0.1}\,\mathrm{V} \)
\( \displaystyle V = 1.8\times10^{7}\,\mathrm{V} = 18\times10^{6}\,\mathrm{V} \)