A spherical metallic conductor of radius 6.0 cm is held in air. The maximum charge it can hold if dielectric strength of air is 20 kV/cm will be:
(Take $\frac{1}{4 \pi \epsilon_0} = 9 × 10^9 Nm^2C^{-2}$)
Answer & explanation
Correct answer: option 1
Electric Field near the surface $E = \frac{1}{4\pi \epsilon_0} \frac{Q}{R^2} =20\times 10^5V/m$
$ 9\times 10^9 \times \frac{Q}{36\times 10^{-4}} = 20\times 10^5$
$\Rightarrow Q = \frac{20\times 10^5 \times 36\times 10^{-4}}{9\times 10^9} = 0.8 \mu C$