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 $5\, m$ 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)

$E=\frac{1}{4 \pi \varepsilon_{0}} \times \frac{q}{r^{2}}=9 \times 10^{9} \times \frac{q}{r^{2}}$
$\therefore q=\frac{E \times r^{2}}{9 \times 10^{9}}=\frac{3 \times 10^{6} \times(2.5)^{2}}{9 \times 10^{9}}=2.0833 \times 10^{-3}$
$a$ 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 $2.0833 \times 10^{-3}$.