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So I know that emf is directly proportional to the rate of change of magnetic flux linkage.

And Lenz's law is that the emf opposes the change producing it.

I am assuming the coil already has a magnetic flux (even though I don't know why but it just seems to make sense).

When the magnet is moved towards the coil, the coil's magnetic flux repels the magnet in order for work to be done against the magnetic field. As the magnet moves closer to the coil, the work done is transferred into electrical energy; thus producing an emf in the coil.

When the magnet is in the coil, the resultant magnetic flux from the coil and magnet are 0, and so the emf when the magnet is in the coil is 0.

When the magnet moves away from the coil, the coil's magnetic flux attracts the magnet in order for work to be done again against the magnetic field. As the magnet moves further away from the coil's magnetic field, work is done against the magnetic field and so this work done is converted into electrical energy once again, producing an emf.

I think this is correct but I don't understand why the coil has a magnetic field in the first place. I.e this is was the case, wouldn't a chair repel a magnet if it comes close to it and an emf would be induced in the chair?

Oh, I think I might understand whilst writing this. As the coil is a conductor, it has a high number density (a lot of delocalised electrons) and so this when the magnet is close to it, the magnet causes the coil to be magnetised? Then we the magnet moves away, the coil becomes demagnetised and so the coil no longer has a magnetic field?

Thanks for any help, I am just trying to make sense of it all.

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The coil inherently does not have any magnetic flux. It has a flux linked with it due the presence of the magnet near by. The magnetic field of the magnet gives the coil flux (since the coil has a finite area). Apart from that, when the magnet is moved towards the coil, the changing magnetic field creates an electric field which "curls" around the direction of change in magnetic field at the coil and around it. This electric field is oriented in such a way that the current induced would create a magnetic field that opposes the change in the magnetic field. This begs the question of why the electric field is in this direction to which I don't know the answer.

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  • $\begingroup$ When you say the 'flux linked' does that mean that it basically produces a magnet field because it's near a magnet? Like a paperclip $\endgroup$
    – Phoooebe
    Sep 20, 2020 at 15:38
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    $\begingroup$ Faraday’s law of induction shows that the coil will have a voltage induced in it if/when the total flux linking the coil is changing w.r.t. time. This can be done by changing the B, or the area, or by moving the coil (any of these has the result of producing a time rate of change of the total flux linking the coil). If you don’t have this change w.r.t. time then no voltage will be induced in the coil. If you do have a voltage induced in the coil, a current will flow. This current will produce its own magnetic flux that opposes the flux that created it in the first place. $\endgroup$
    – relayman357
    Sep 20, 2020 at 17:30
  • $\begingroup$ Okay I think I understand now: the coil does not have a magnetic field. When the magnet moves towards the coil, there is a change of the coil's area within the magnetic field, and this change causes an emf to be induced within the coil. The current then flows in a direction that opposes the change that produced it; which was the coil's area moving in the magnetic field of the magnet. So the coil will repel the magnet. Is this correct? $\endgroup$
    – Phoooebe
    Sep 20, 2020 at 18:17
  • $\begingroup$ The average magnetic field in the area of the coil changes not the coil's area in the field( the fields extend to infinity). The rest of your understanding is correct. $\endgroup$
    – Janga Pardhu
    Sep 21, 2020 at 16:28

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