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When passing a bar magnet through a long solenoid why is it that the induced emf when the magnet is in the middle of the solenoid is zero? And if a spherical magnet is put inside the solenoid, will the emf produced have discontinuities because occasionally the magnetic field lines are parallel to the windings of the solenoid?

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[about a bar magnet inducing current in a solenoid as it passes through, axially]

The magnet both has a north pole, and a south pole. At the center of the solenoid, the symmetry of the situation means that the 'leading' north pole and the 'trailing' south pole give rise to equal and opposite EMF. So, it's zero for the sum.

Why would the shape of the magnet matter?

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No.There will not be zero emf. Induced current depend on the rate at which the magnetic flux through solenoid changes. If the magnet is just placed in the middle of the solenoid then induced current in the solenoid is ofcourse zero as no magnetic flux changing through the solenoid. But if the magnet is just momentarily is at the middle and is about to move then induced current will not be zero.

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  • $\begingroup$ I just went through leading a bunch of undergrads through a magnet drop lab and I can assure you that the EMF drops to zero in the middle of the solenoid. $\endgroup$ – Johnathan Gross Jul 23 '17 at 17:04
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Faraday's law gives that $$e = -\frac{\textrm{d}\phi}{\textrm{d}t}$$ With $\phi$ the flux of the magnetic field created by the magnet through the solenoid.

As one could not possibly get a higher flux than when the magnet is in the middle, $\phi$ reaches a maximum. Hence, the emf is zero when the magnet is in the middle.

I think the shape of the magnet doesn't matter.

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When the magnet, spherical or rectangular, is introduced very slowly (quasi-statically) anywhere inside the solenoid and kept there at rest then there will be no emf.. as a magnet has to move to induce emf.

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