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I've been thinking about the shape of the voltage waveform induced by a magnet falling through a coil. I know (both intuitively and from empirical experience) that the voltage should become increasingly positive as the magnet approaches the coil, then it should decrease rapidly (intersecting the x-axis as it passes through the coil), finally becoming less and less negative as the magnet falls away from the coil. Of course, "positive" and "negative" could just as easily be reversed, depending on the magnet's orientation.

All this in mind, I've derived an equation for the induced voltage (as a function of time) starting from Faraday's and Lenz's laws. The full derivation is attached.

My question is as follows: why does the graph of the voltage function I end up with (see here) intersect the x-axis at t=0 (the instant that the magnet is dropped) rather than at the instant the magnet passes through the coil (about t=0.45 if dropped from a height of 1 meter)? In other words, why is the positive section of the voltage graph to theleftof the y-axis?

Thanks very much!

xenolalia

P.S. I was expecting the graph to more or less resemble this:

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# Magnetic Induction: EMF Function of Time

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