Capacitance

Question

Initial charge on conducting sphere of radius r is Q_{0}. If S is closed at t = 0 then charge on the sphere at any time t is

Moderate

Solution

This is simply discharging of a capacitor.

$\therefore \phantom{\rule{1em}{0ex}}\mathrm{q}={\mathrm{Q}}_{0}{\mathrm{e}}^{-t/\mathrm{CR}}\text{where}\mathrm{C}=4\pi {\epsilon}_{0}\mathrm{r}$

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