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Displacememnt current and Free current

  1. Aug 14, 2009 #1
    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.
     
  2. jcsd
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