Thursday 24 January 2019

electromagnetism - How eddy current brakes function


Take the following example:


here


where a rectangular sheet of metal is entering a constant magnetic field at $v \dfrac{m}{s}$. Due to Faraday's law of induction + Lenz's law, we can state that an eddy current will be generated to oppose the increase of magnetic flux through the sheet of metal, so as to produce a magnetic field coming out of the page (represented by the red dots). Intuitively, I believe that this induced magnetic field should act as a 'brake' on the metal plate, as Lenz's law implies that the induced current should always in some way act against the motion, but I don't see how to calculate this 'retarding' force that would act to reduce the plate's speed?



Answer



I had a fundamental misunderstanding of eddy currents. I believed that eddy currents were formed simply in the part of the metal that was already submerged in the magnetic field, but in reality it is actually something like


here
(source: boredofstudies.org)


this, where only half the eddy current is actually in the field. If this is the case, then you can just use $F = qv*B = IL*B$, probably with some integration, and you can find the force. So the retarding force is just a variation on the lorentz force.



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