Calculating Ohmic Heating Loss in a Conductor

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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=\sigmaE
Maxwell's equations for linear media


The Attempt at a Solution


not sure where to start, i need a nudge
 
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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?
 
yea i figured it out. you take the dot product of J and E.
 
ok now i have Re(\sigma) ((Ee^(-kz)e^i(kz-\omegat))^2)/2

is this right? do i need to simplify if I am going to integrate with respect to z?
 
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.
 
so is what i have already wrong?
 
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