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## Homework Statement

Show that any charge distribution in a conductor of conductivity σ and relative

permittivity κ vanishes in time as ρ = ρ0exp(−t/ζ) where ζ = κǫ0

σ

## Homework Equations

Maxwell's equation

∇ · D = ρfree

equation of continuity for a free charge density

∇ · Jfree = −∂(ρfree)/∂t

ohms law

J = σE

## The Attempt at a Solution

I can see that ρ will get smaller and smaller as time 't' increases according to

ρ = ρ0exp(−t/ζ) and clearly some sort of substitution is required of the equations but I can't see how substitution will result in a exponential appearing. Basically I don't know where to start so any help would be appreciated or a push in the right direction.

Thanks