Q108 / 180 · JIPMER 2017 · Physics
A non-conducting ring of radius 0.5 m carries a total charge of $1.11 \times 10^{-10} \mathrm{C}$ distributed non-uniformly on its circumference producing on its circumference on electric field $\mathbf{E}$, everywhere in space.
The value of the line integral $\int_{l=\infty}^{l=0}(-\mathbf{E} \cdot \mathbf{d l})$ $(l=0$ being centre of ring) in volts is
- Correct answerA$+2$
- B$-1$
- C$-2$
- DZero
Solution
From definition of potential difference $\int_{l=\infty}^{l=0} \mathbf{E} \cdot \mathbf{d l}=$ potential difference at infinity and at centre of ring $=V_{\text {centre }}-V_{\text {infinity }}$
But by convention $V_{\text {infinity }}=0$ and $V_{\text {centre }}=\frac{1}{4 \pi \varepsilon_0} \frac{q}{R}$ $=9 \times 10^9 \times \frac{1 \cdot 11 \times 10^{-10}}{0.5}=2 \mathrm{volt}$ $\therefore \int_{l=\infty}^{l=0}(-\mathbf{E} \cdot \mathbf{d l})=2$ volt -0 volt $=2$ volt
Hence, the correct answer is option: 'A'.