Electrostatics Question 340
Question: . The insulation property of air breaks down at $ E=3\times 10^{6} $ volt/metre. The maximum charge that can be given to a sphere of diameter $ 5m $ is approximately (in coulombs) [MP PMT 1990]
Options:
A) $ 2\times {{10}^{-2}} $
B) $ 2\times {{10}^{-3}} $
C) $ 2\times {{10}^{-4}} $
D) $ 2\times {{10}^{-5}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ E=\frac{1}{4\pi {\varepsilon _{0}}}\times \frac{q}{r^{2}}=9\times 10^{9}\times \frac{q}{r^{2}} $ $ q=\frac{E\times r^{2}}{9\times 10^{9}}=\frac{3\times 10^{6}\times {{(2.5)}^{2}}}{9\times 10^{9}}=2.0833\times {{10}^{-3}} $ q should be less than 2.0833 ${10^{-3}}$.
In the given set of options 2 ${10^{-3}}$ is the maximum charge which is smaller than 2.0833 ${10^{-3}}$.
