This is probably a question with a very simple answer, but I want to make sure before I write too much.
I'm doing an investigation on Electromagnetic fields, in particular eddy currents and how they decelerate magnets, by sliding a magnet down an incline, recording the time taken and changing the thickness of the aluminium foil that the magnet is running over the top of. My results clearly show that the thicker the foil is the longer the magnet takes to travel down the incline, but I am having a hard time finding theory to back the results up with. So far all I've been able to find so far is the equation below on Wikipedia, despite my best efforts not to rely on it:
which finds power dissipation, where
P is the power lost per unit mass (W/kg),
Bp is the peak magnetic field (T),
d is the thickness of the sheet or diameter of the wire (m),
f is the frequency (Hz),
k is a constant equal to 1 for a thin sheet and 2 for a thin wire,
ρ is the resistivity of the material (Ω m), and
D is the density of the material (kg/m3).
My question is whether this is the function I'm looking for, as thickness is the only one of these variables I'm changing and the rest I can measure, and P=F x V when force is constant, in which case higher thickness=more power lost=decreased velocity – theoretically supporting my results. I'm just not sure though, as I haven't been able to find anywhere saying that this power lost has any relation to what I'm measuring and I don't want to write a few thousand words to be told I had the wrong equation.
Thanks, sorry for the wordy post, and if you know any sites that will help me with this other than Wikipedia I'd appreciate it.
Best Answer
I doubt this is your answer: what is the frequency $f$ doing, in the problem of a magnet sliding down an incline?
What you should ask yourself is: how is changing the thickness of the aluminum foil going to modify the time down the incline?
Increasing the thickness of the aluminum foil increases/decreases/leaves unaltered the foil's resistance (you pick one);
A larger resistance increases/decreases/leaves unaltered the power dissipated by eddy currents.
A larger/smaller power dissipated by eddy currents reduces/increases/leaves unaltered the kinetic energy of the magnet at the end of its run.
At some point, you will have to decide which formula for the power dissipated it is best to use, $I^2R$ or $V^2/R$. Try to decide whether $I$ or $V$ can be considered identical between two experiments...
Good luck with your homework.