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From what I understand, if you have a magnet moving with a relative velocity towards a coil, Lenz's law states that the current flow induced in the coil will create a magnetic field that opposes the change that induced it. So it will essentially create a magnet with an opposing field to the magnet moving towards it.

In the picture below, disregarding magnet 2, if magnet 1 moves towards the coil it induces a magnetic field in the coil as shown, with the 'north pole' of the coil repelling the north pole of magnet 1. If you only look at magnet 2 now, moving away from the coil as shown, it creates a 'south pole' in the coil that attracts the north pole of magnet 2.

If I am correct until this point, would that mean that if the two magnets were in motion together, in the same direction but on opposite sides of the coil, the induced voltage in the coil would be doubled? Is there something that I am missing in this interaction? Thanks in advance for any clarification.

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What you are thinking is right. This is a perfect application of the famous superposition theorem. The individual effects of both the magnets are added together. In this case, since they are supporting each other, the induced EMFs are added together.
Consider what will happen when magnet 2 is going the other direction? The effects of both the magnets might cancel out and no emf might be induced in the coil!

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Yes, you are right. You are essentially doubling the magnetic flux and thus the derivative of the flux with respect to time also doubles, which is proportional to the induced emf which will thus also double.

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