= Charge relaxation in an isolated conducting cylinder
{title2=$\rho(t)=\rho_0e^{-\sigma t/\epsilon_0}$}
A uniform cylindrical volume charge relaxes exponentially under <Ohm's law> and the <continuity equation for electric charge>. In a cylinder of radius $R$ initially carrying no surface charge, the radial conduction current deposits $\rho_s(t)=R\rho_0(1-e^{-\sigma t/\epsilon_0})/2$ on its surface. Total charge per unit length remains $\pi R^2\rho_0$, so the exterior radial <electric field> is time independent even though the interior field decays. Neglecting the deposited surface charge violates charge conservation.
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