SATHEE: Electrostatics Question 237

Electrostatics Question 237

Question: 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 $\int_{l = \infty}^{l = 0} - \vec{E} . \vec{d l} (l = 0$ being centre of the ring) in volt is [IIT 1997 Cancelled]

Options:

A) 0

B) $\frac{q}{8 π ε_{0} x_{0} \ln 2}$

C) $\infty$

D) $\frac{q \ln 2}{4 π ε_{0} x_{0}}$

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Answer:

Correct Answer: D

Solution:

$V = \frac{q}{4 π ε_{0} x_{0}} [1 + \frac{1}{3} + \frac{1}{5} + \dots] - \frac{q}{4 π ε_{0} x_{0}} [\frac{1}{2} + \frac{1}{4} + \frac{1}{6} + \dots]$

$= \frac{q}{4 π ε_{0} x_{0}} [1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots .] = \frac{q}{4 π ε_{0} x_{0}} \log_{e} 2$

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Electrostatics Question 237

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Answer:

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