Electrostatics Question 237
Question: A non-conducting ring of radius $ 0.5m $ 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 Cancelled]
Options:
A) 0
B) $ \frac{q}{8\pi {\varepsilon _{0}}x _{0}\ln 2} $
C) $ \infty $
D) $ \frac{q\ln 2}{4\pi {\varepsilon _{0}}x _{0}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ V=\frac{q}{4\pi {\varepsilon _{0}}x _{0}}[ 1+\frac{1}{3}+\frac{1}{5}+… ]-\frac{q}{4\pi {\varepsilon _{0}}x _{0}}[ \frac{1}{2}+\frac{1}{4}+\frac{1}{6}+… ] $
$ =\frac{q}{4\pi {\varepsilon _{0}}x _{0}}[ 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+…. ]=\frac{q}{4\pi {\varepsilon _{0}}x _{0}}{\log _{e}}2 $
