The insulation property of air breaks down when the electric field is $3 \times 10^{6} \mathrm{Vm}^{-1}$.…

The insulation property of air breaks down when the electric field is $3 \times 10^{6} \mathrm{Vm}^{-1}$. The maximum charge that can be given to a sphere of diameter $5 \mathrm{~m}$ is approximately
  1. $2 \times 10^{-2} \mathrm{C}$
  2. $2 \times 10^{-3} \mathrm{C}$
  3. $2 \times 10^{-4} \mathrm{C}$
  4. $2 \times 10^{-5} \mathrm{C}$

Solution

$\mathrm{E}=\frac{\mathrm{kQ}}{\mathrm{r}^{2}} \Rightarrow \mathrm{Q}=\frac{\mathrm{E} \times \mathrm{r}^{2}}{\mathrm{k}}=\frac{3 \times 10^{6} \times(2.5)^{2}}{9 \times 10^{9}}$
$=2 \times 10^{-3} \mathrm{C}$ /

Asked in: JEE Mains - Electrostatics - Test 2

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