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Ohmic heating in a conductor

by smcdan32
Tags: electrodynamics, ohmic, plane wave
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smcdan32
#1
Apr14-10, 08:31 PM
P: 4
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
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phyzguy
#2
Apr15-10, 07:38 PM
P: 2,179
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?
smcdan32
#3
Apr15-10, 10:09 PM
P: 4
yea i figured it out. you take the dot product of J and E.

smcdan32
#4
Apr16-10, 12:06 AM
P: 4
Ohmic heating in a conductor

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?
phyzguy
#5
Apr16-10, 06:06 AM
P: 2,179
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.
smcdan32
#6
Apr16-10, 08:10 PM
P: 4
so is what i have already wrong?


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