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A non-conducting ring of radius {0.5}{m} carries a total charg

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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 E everywhere is space. The value of the integral $\int_{l = \infty}^{l = 0} - E . d I (l = 0$ being centre of the ring) in volt is

+ 2

- 1

- 2

zero

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Noah Discussed

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 E everywhere is space. The value of the integral

\int_{l = \infty}^{l = 0} - E . d I (l = 0

being centre of the ring) in volt is

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Text solutionVerified

Answer: ASolution:

- \int_{l = \infty}^{l = 0} E . d I = \int_{l = \infty}^{l = 0} d V = V (centre) - V (infinity)

but

V (infinity) = 0

∴ - \int_{l = \infty}^{l = 0} E . d l

corresponds to potential at centre of ring
and

V (centre) = \frac{1}{4 π ϵ _{0}} . \frac{q}{R} = \frac{( 9 \times 10 ^{9} ) ( 1.11 \times 10 ^{- 10} )}{0.5} \approx 2 V

Therefore the correct answer is a.

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Question Text	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 E everywhere is space. The value of the integral $\int_{l = \infty}^{l = 0} - E . d I (l = 0$ being centre of the ring) in volt is
Answer Type	Text solution:1
Upvotes	150