Question

The dielectric strength of air is $3.0\times {10}^{6}N{C}^{-1}$. The largest charge that a 0.30 cm radius metal sphere can hold without sparking is :

• A. 9 nC
• B. 8.2 nC
• C. 6 nC
• D. 3 nC

Answer 1

Answer: (D)

3 nC

Dielectric strength is the maximum electric field that a pure material can withstand under ideal conditions without breaking down.
Here $E=\frac{Q}{4\pi {ϵ}_0{R}^2}$
$\Rightarrow Q=E.4\pi {ϵ}_0{R}^2=3\times {10}^6.(4\pi \times 8.85\times {10}^{-12}\times {0.30}^2\times {10}^{-4})=3\times {10}^{-9}C=3nC$