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
IIT 1997, Medium
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(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$
$ = \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$
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