Displacememnt current and Free current

[iontail]

1. The problem statement, all variables and given/known data

Find the angular frequency, w, at which the displacement current is equal to the free current in a conductor.

2. Relevant equations

jd(dislacement current) = ee_0(dE/dt)

where e = permiability of material and e_0 is the permitivity of free space
E=electric field
also
j=sE (s=constant of proportionality) j = free current

3. The attempt at a solution

from the question

ee_0(dE/dt) = sE

assuming that E=E0exp(i(wt-kz)) (plane wave) so therefore dE/dt = iwE

ee_0*i*w*E=sE

or (ee_0*i*w)(-ee_0*i*w)=s^2 (taking complex conjugate)
or w=(s^2/(ee_0)^2)^1/2 =s/(ee_0)


so the frequecy at which displacement current equals free current is s/(ee_0).

Is this derivation correct.