Question

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

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

Answer 1

The correct option is B $2\times {10}^{-3}$

Maximum Electric field , $E=\frac{1}{4\pi {ϵ}_0}\frac{Q}{r^2}=3\times {10}^6$
$r=\frac{5}{2}=2.5$
$\therefore Q=4\pi {ϵ}_0{r}^{2}E=\frac{3\times {10}^6\times 6.25}{9\times {10}^9}=2\times {10}^{-3}C$