A non-conducting ring of radius 0.5,m carries a total charge of 1.11 × {10^{

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2. Electric Potential and Capacitance

medium

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 an electric field $\vec E$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} {\, - \overrightarrow E .\overrightarrow {dl} } \,(l = 0$ being centre of the ring) in volt is

$2$

$-1$

$-2$

$0$

(IIT-1997)

Solution

(a) $\int_{\, – \infty }^{\,0} { – \overrightarrow E \, \cdot \overrightarrow {dl} } $ $=$ 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\,volt$

Standard 12

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Solution

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