I'm trying to figure out a relation for eddy current braking. Specifically, I'm attempting to derive an equation that would relate an electromagnet's principles (magnetic field B, current I, and power P) to the induced eddy currents/resulting force.
So far I have the current derivation:
For a given aluminum plate with a magnetic field moving horizontally, acting on a L x L cross section.
F = I x LB [I = Induced eddy current, L = vertical length of plate, B = Mag field]
Voltage = emf (experienced by changing mag flux) = d/dt = B*dA/dt = B*L*dx/dt = B*L*v*dt/dt = BLv
[L = vertical length held constant, A = cross sectional area, v = horizontal velocity of moving magnetic field]
so, I = V/R = emf/R = BLv/R
Plugging into F = ILB = B2*L2*v/R
Okay, now that I have this force equation, I realize this all pertains to the eddy currents in an aluminum plate. The part I can't figure out is the R value, the resistance experienced by the eddy currents is a property of the material itself but I'm not sure how to figure that out.
I've found that R = rho*L/A yeah?