Charge density in a conducting medium

It is well-known that no permanent distribution of free charge can exist in a conductor. A common development of a "relaxation time" concludes that a charge distribution imposed in a conductor will decay exponentially with a time constant ε/σ. This development utilizes Ohm\´s law, J = σE, with σ constant, which is inappropriate for a variable charge density. The resulting relaxation time implies charge decay in a time which is too short by orders of magnitude.