I remember I have seen someone written an essay on the effect of Shaking an electromagnetic coil between magnets, now what I want to do is to fill it with Mathematics, and raise some questions. The issue I had with that article is that it has ignore that the way we move the electromagnetic coil relative to the Magnet would affect how it respond to the change of the magnetic field it experienced. Thus effectively should be how does my way of moving an electromagnetic coil between magnets affect the voltages and currents formed in the coil. To be more precise, the way we shake the electromagnetic coil would affect how the voltage generated in each element of the electromagnetic coil.
Consider the simplest case, the electromagnetic coil is just moving back and fro linearly from a Permanent magnet. Now, as the electromagnetic coil is approaching the magnet, the rate of change of magnetic flux is greatest for those electromagnetic coil element that is closer to the magnet than the those who are further away from the magnet. Thus, within the same electromagnetic coil, there are difference in the voltages between different elements. Those who are closest has greater voltage compare to those who are further from the magnet. Since the electromagnetic coil can only have one voltage an current throughout itself, therefore I suspect an average of all voltage is what we measured for the whole electromagnetic coil. Moreover, for the electrical current, assuming that the electrical resistance is about the same throughout the electromagnetic coil, then we have the current is given by the average voltage/average electrical resistance.
Could anyone in the world verify my hypothesis?
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