- #1

th5418

- 27

- 0

## Homework Statement

We know that free charges inside a conductor will eventually move to the conductor surface. Consider a free charge initially placed inside a conductor at t=0. Show that the free charge density [tex]\rho_f[/tex] will dissolve exponentially with time. Express the characteristic time needed to dissolve the charge in terms of the conductor's dielectric constant [tex]\epsilon[/tex] and the conductivity [tex]\sigma[/tex].

## Homework Equations

I think I should use charge conservation. I'm not sure...

[tex]delJ + \frac{d\rho}{dt} = 0[/tex]

## The Attempt at a Solution

I know what the solution should be..

[tex]\rho (t) = \rho_0 e^{t} [/tex]

where [tex]t=\frac{\epsilon}{\sigma}[/tex]