First slide

Capacitance

Question

Initial charge on conducting sphere of radius r is Q₀. If S is closed at t = 0 then charge on the sphere at any time t is

Moderate

A

$Q_{0} e^{- t / 4 R}$
B

$Q_{0} e^{\frac{- t}{4 π ε_{0} R}}$
C

$Q_{0} e^{- \frac{t}{4 π ε_{0} R r}}$
D

none of these

Solution

This is simply discharging of a capacitor.
$∴ q = Q_{0} e^{- t / CR} where C = 4 π ε_{0} r$

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