Question

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

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

Answer 1

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

For maximum charge, the given field should be the field at the surface of the sphere.

so $3\times {10}^6=\frac{1}{4\pi {ϵ}_0}\frac{Q}{R^2}$

or $3\times {10}^6=9\times {10}^9\times \frac{Q}{(5/2{)}^2}$

or $Q=2.08\times {10}^{-3}C\sim 2\times {10}^{-3}C$