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Power dissipated in a cylindrical cavity due to a current carrying filament

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data

    A cylindrical cavity oriented along z axis with length of 2 m has a filament in it upon which a current of 10 A is impressed. Cavity is perfectly conducting whereas it is filled with lossy dielectric. Electric field on the cavity is given as: E=-z(i+j). One has to calculate the power dissipated in the cavity. BTW, the frequency is 5 kHz.
    2. Relevant equations

    [tex]\nabla[/tex][tex]\times[/tex][tex]\vec{E}[/tex]=-del(B)/del(t)
    [tex]\nabla[/tex][tex]\times[/tex][tex]\vec{H}[/tex]=del(D)/del(t)+J
    S=\vec{E}[/tex]\times[/tex][tex]\vec{H}[/tex]

    3. The attempt at a solution

    It has to do with the Poynting vector. I tried to find the mangetic field from the current but without any value for the permeability and permittivity for the lossy material how can I find the power loss. Is the fact that question provides the electric field is in some way helpful.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2009 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    I assume you mean that the wall of the cavity is perfectly conducting while the cavity itself is filled with a dielectric?

    Is [itex]\textbf{E}=-z(\textbf{i}+\textbf{j})[/itex] the field on the cavity's wall, or throughout the cavity's interior?
     
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