# 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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