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Ohmic heating in a conductor

  1. Apr 14, 2010 #1
    question
    For a plane wave of the form E(z,t)=Ee^i(kz-wt) and B(z,t)=Ee^(-kz)*e^i(kz-wt) write down the time-averaged ohmic heating loss per unit volume for any z.


    2. Relevant equations
    J=[tex]\sigma[/tex]E
    Maxwell's equations for linear media


    3. The attempt at a solution
    not sure where to start, i need a nudge
     
  2. jcsd
  3. Apr 15, 2010 #2

    phyzguy

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    You know E, and you gave us the equation for J, so you know J. Do you know how to find the Ohmic heating, given J and E?
     
  4. Apr 15, 2010 #3
    yea i figured it out. you take the dot product of J and E.
     
  5. Apr 16, 2010 #4
    ok now i have Re([tex]\sigma[/tex]) ((Ee^(-kz)e^i(kz-[tex]\omega[/tex]t))^2)/2

    is this right? do i need to simplify if im going to integrate with respect to z?
     
  6. Apr 16, 2010 #5

    phyzguy

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    Careful with the Re(). Remember Re(A) Re(B) is not equal to Re(AB) since there are cross terms. Here it looks like you assumed Re(E^2) = (Re(E))^2, which it's not.
     
  7. Apr 16, 2010 #6
    so is what i have already wrong?
     
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