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Q.

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

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a

+2

b

-1

c

-2

d

zero

answer is A.

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Detailed Solution

$\large \int_{l = \infty }^{l = 0} {\, - \overrightarrow E .\overrightarrow {dl} } \,(l = 0$ =potential at centre of non-conducting ring
$\large = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{q}{r} = \frac{{9 \times {{10}^9} \times 1.11 \times {{10}^{ - 10}}}}{{0.5}} = 2\,volt$

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