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Electromagnets and an induced magnetic field in aluminuium plates

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I am trying to conduct an investigation based on the set up of a set of copper coils with AC ran through them to make them an electromagnet. Held above them inplace is an aluminium plate. I know that the changing magnetic field induces a current in the aluminium plate, which induces a voltage and then a magnetic field which is out of phase with the electromagnet, and so an oposing force is made. I am measuring the force by having a sensitive set of scales under the coil which measures the change in force on the coil.

However i am trying to investigate the effects of changing the electromagnet

I have already tried
-different diameter of wire.
-Differnt radius of the coils
-Different number of coils.
-Changing the current through the coils.

I have already discovered (i think) that it is a squared relationship for increasing the current and force.

However is there an equation for this?


Also, what kind of relationship should i expect with the other factors and why?

How exactly would i calculate the force that results in the copper coils being pushed in to the scales? Measuring the change in weight only really gives me a sort of qualatative answer.


any help would be much appreciated.
Thanks
 

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