Ohmic heating in a conductor

  • Thread starter smcdan32
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  • #1
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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.


Homework Equations


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


The Attempt at a Solution


not sure where to start, i need a nudge
 

Answers and Replies

  • #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?
 
  • #3
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yea i figured it out. you take the dot product of J and E.
 
  • #4
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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?
 
  • #5
phyzguy
Science Advisor
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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.
 
  • #6
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so is what i have already wrong?
 

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