Treacherous Cylinder

A cylindrical capacitor of length \( l \) has \(2\) plates, an inner plate of radius \( a \) and outer plate of radius \( b \). The portion of volume between the two plates of the capacitor is filled with a material of dielectric constant \(k\) and resistivity \(\rho \). Initially, the inner plate has a charge \(Q_0\). Assuming that the capacitance of the system is \(C\), the charge fl​own from the inner plate of the capacitor at time \(t=\rho k \epsilon_0 \) is \( S Q_0 \). Find \(S\).

Bonus: Find the charge on the inner plate of the capacitor as a function of time.

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