Question

The insulation property of air breaks down at $E=3\times 10^6$ $V/m$. The maximum charge that can be given to a sphere of diameter $5m$ is approximately (in coulombs)

• A. $2\times 10^{-2}$
• B. $2\times 10^{-3}$
• C. $2\times 10^{-4}$
• D. $2\times 10^{-5}$

Answer 1

Answer: (B)

$E=\frac{1}{4\pi {\epsilon }_0}\times \frac{q}{r^2}=9\times 10^9\times \frac{q}{r^2}$
$\therefore q=\frac{E\times r^2}{9\times 10^9}=\frac{3\times 10^6\times (2.5{)}^2}{9\times 10^9}=2.0833\times 10^{-3}$
$a$ should be less than $2.0833\times 10^{-3}$. In the given set of options $2\times 10^{-3}$ is the maximum charge which is smaller than $2.0833\times 10^{-3}$.