Question

The insulation property of air breaks down at $3 × 10^6V/m$. The maximum charge that can be given to a sphere of diameter $5\, m$ is nearly

• A. $2 × 10^2C$
• B. $2 × 10^3C$
• C. $2 × 10^4C$
• D. $2 × 10^5C$

Answer 1

Answer: (B)

Maximum electric field, $E_{max}=\frac{1}{4\pi\varepsilon_{0}} \frac{Q_{max}}{R^{2}}$
$3\times10^{6}=\frac{9\times10^{9}\times Q_{max}}{2.5\times2.5}$
or $Q_{max}=\frac{3\times10^{6}\times2.5\times2.5}{9\times10^{9}}$
$=2\times10^{-3}\,C$