A non-conducting ring of radius $0.5 \mathrm{~m}$ carries a total charge of $1.11 \times 10^{-10} \mathrm{C}$ distributed non-uniformly on its circumference producing an electric field $\vec{E}$ everywhere in space. The value of the line integral \(\int_{l=\infty}^{l=0}-\vec{E} \cdot…

Question

A non-conducting ring of radius $0.5 \mathrm{~m}$ carries a total charge of $1.11 \times 10^{-10} \mathrm{C}$ distributed non-uniformly on its circumference producing an electric field $\vec{E}$ everywhere in space. The value of the line integral $\int_{l=\infty}^{l=0}-\vec{E} \cdot \overrightarrow{d l}(l,=0$ being centre of the ring) in volt is

Aicharya · Accepted Answer

$\int_{-\infty}^{0}-\vec{E} \cdot \vec{d l}=$ potential at centre of non-conducting ring $=\frac{1}{4 \pi \varepsilon_{0}} \times \frac{q}{r}=\frac{9 \times 10^{9} \times 1.11 \times 10^{-10}}{0.5}=2$

A non-conducting ring of radius \(0.5 \mathrm{~m}\) carries a total charge of \(1.11 \times 10^{-10}…

Solution