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Homework Statement
Thin conducting disc, radius a, thickness b and resistivity p (assumed to be large enough induced currents produce no magnetic field). There is a uniform B field B0sin(wt) parallel to its axis.
I first had to find the electric field a distance r from the disc axis in the plane of the disc. I did this by equating the induced emf to the integral of E.dl around a closed circular loop which gave E=-a2B0wcoswt/2r. Then using J=E/p, I had to find the induced current density, giving J=-a2B0wcoswt/2pr. This may be wrong.
I now must find an expression for the time averaged power dissipated as heat over the disc.
Homework Equations
P=I2R
The Attempt at a Solution
I would like to find the resistance of the disc first, however I'm uneasy about this. The current flows in circles, so a thickness dr of the disc has resistance dR=2πrp/(bdr). I'm obviously going wrong there. I know how to find the resistance of a disc when the current flows radially outwards, but it should be different here right?
Once I have that, I guess I can just integrate out the current density to get the total current at an instance, find the instantaneous power from P=I2R and then time average it over a cycle.
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