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What is the maximum charge that can be given to a sphere of diameter $$10cm$$ if the breakdown voltage of air is $$2\times10^4 V/cm$$?

Discussion:

Dielectric breakdown is when current flows through an electrical insulator when the voltage applied across it exceeds the breakdown voltage. This results in the insulator becoming electrically conductive.

The breakdown voltage of air is $$2\times10^4 V/cm$$

For a sphere, $$V= \frac{q}{4\pi \epsilon_0 r}$$
We can find charge $$q= 4\pi \epsilon_0 r V$$ $$= \frac{(5)(2\times10^4)}{9\times10^9}$$ $$=1.11\times 10^{-5}$$