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At equilibrium, a conducting object will have no electric field, current or excess charge in its interior. There's a fairly simple derivation for how an initial (non-equilibrium) interior charge density d

d(x,y,z,t) = d

(I tried to include the derivation of the formula, but haven't mastered the math notation yet, so I gave up. The derivation makes use of the continuity equation, Ohm's law and Gauss' law and can be made in four lines.)

So far so good, the interior charge distribution falls exponentially to zero, with a known relaxation time epsilon/g (i.e. the permittivity divided by the conductivity).

Now a conductor hasn't necessarily reached equilibrium because it has no interior excess charge. We could have started with zero interior charge density, and had a non-equilibrium surface charge distribution instead. A non-equilibrium surface charge distribution will cause an interior electric field and current until equilibrium is reached.

Now to the questions:

Is there any easy way to calculate, or at least estimate, the time it takes for the internal electric field and current density, not just the interior charge distribution, to drop to zero?

Will the result, like for the interior charge density, be independent of the shape of the conductor?

_{0}falls to zero exponentially with time t when the conductor approaches equilibrium. For a homogeneous and isotropic conductor with conductivity g and permittivity epsilon the interior charge density d can be written asd(x,y,z,t) = d

_{0}(x,y,z)e^(-gt/epsilon)(I tried to include the derivation of the formula, but haven't mastered the math notation yet, so I gave up. The derivation makes use of the continuity equation, Ohm's law and Gauss' law and can be made in four lines.)

So far so good, the interior charge distribution falls exponentially to zero, with a known relaxation time epsilon/g (i.e. the permittivity divided by the conductivity).

Now a conductor hasn't necessarily reached equilibrium because it has no interior excess charge. We could have started with zero interior charge density, and had a non-equilibrium surface charge distribution instead. A non-equilibrium surface charge distribution will cause an interior electric field and current until equilibrium is reached.

Now to the questions:

Is there any easy way to calculate, or at least estimate, the time it takes for the internal electric field and current density, not just the interior charge distribution, to drop to zero?

Will the result, like for the interior charge density, be independent of the shape of the conductor?

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