How induction works within a coil (nuances of it)

[FusionJim]

Please help me understand whether my understanding is correct. If I have a solenoid like coil with empty middle , and a magnet that goes through the coil, the coil is longer than the magnet, there is induction as the magnet approaches the coil until the moment when one of the magnet poles is fully immersed into the coil (the field lines have stopped increasing) then as the second pole of the magnet moves inwards the induction goes down to zero. This forms the first half period of a full sine wave, the second half cycle is formed as the magnet exits and the same thing happens as when it entered , so far so good right?

Now what is the reason why there is no induction when the magnet is moving through the part of the coil where both of it's poles are fully encircled by the coil?

1) Is it because equal and opposite field lines cut the same coil at the same time (because both poles of the same magnet are within the coil loop at the same time) ?
2) Or is it because due to both poles being within the coil there is no change in flux since both poles are of equal magnetic field strength ?

I ask this because the way it seems to me is that if the first is true then there is induction in the coil even when both magnet poles are within the coil but it is localized to each magnet pole and the total coil current sums to zero because the currents within the wire adjacent to each pole run in opposite directions, meanwhile if the second is true then there is no current induced (not even a localized one) when the magnet is fully inside the coil because there is no net change in flux.

It would seem to me the localized electrons in the part of coil that faces each magnet pole at each moment should feel the moving field lines from the pole which within the vicinity of each pole are always in one direction , so there should be localized current induced even if the total current is zero due to opposite currents cancelling within the whole coil?


Similarly if I think of the simple experiment where a cylindrical axially polarized magnet is dropped through a conducting pipe, I believe there are localized currents adjacent to each pole as the magnet falls, and each current adjacent to each pole runs opposite to the other current, so in total two counterrotating circular currents.




My last question is this, if in theory (because it doesn't seem to exist in practice) we had a magnetic monopole magnet and this monopole magnet was moving through a very long solenoid shaped coil, if the speed of the moving magnet was constant , would it produce pure DC voltage within the coil?
I would tend to thin - yes, because the field lines from the magnet (all in the same direction) would continually cut the wire inducing a steady current and voltage within the coil. Am I right?

 

[Baluncore]

The voltage induced in the coil is determined by the rate that the magnetic field lines cut the coil.

The current that flows in the coil is determined by the load connected to the coil terminals.

Try to understand single turn coils first, rather than long solenoids where both poles of the magnet are within the coil. Some turns of a long coil will be induced with one polarity, while another may be the opposite, partly cancelling the first.

This forms the first half period of a full sine wave, the second half cycle is formed as the magnet exits and the same thing happens as when it entered , so far so good right?

With a bar magnet sliding through a long solenoid, the waveform will not be a sinewave. To get a sinusoid you should spin a short magnet about its centre, inside the coil.

 

[marcusl]

#2 is correct--there is no induced EMF unless the flux within the coil is changing with time. The EMF will increase and then go to zero as you say, and will repeat with opposite polarity as the magnet nears and exits the far end of the coil, but the waveforms will not be sinusoidal. A numerical simulation is needed to find the actual waveform.
Your #1 is basically one of the reasons for #2 rather than a root cause. To answer your third question, consider about how the flux in the coil changes as the monopole enters, passes through, and exits the coil. I'll leave that as an exercise for you to think about.

 

[FusionJim]

Some turns of a long coil will be induced with one polarity, while another may be the opposite, partly cancelling the first.

Yep that is what I think too.

To answer your third question, consider about how the flux in the coil changes as the monopole enters, passes through, and exits the coil. I'll leave that as an exercise for you to think about.

Here is what I think , as the monopole would approach the solenoid coil the same thing would happen as with the regular two pole bar magnet up until the point where the forward facing pole of the bar magnet is fully inserted within the coil - that is you would see a rise in EMF and a peak at the moment the first pole is fully within the coil. Then for the bar magnet as the second pole starts to enter the coil the EMF drops down to zero where zero is when the second pole is also fully within the coil. As for the monopole , I would think that the EMF doesn't drop, since all field lines are in the same direction and the magnet keeps on moving, the field lines would then cut the individual turns of the coil as the magnet passes and cause continual induction with the same rate of change given the magnet physical speed is kept constant.
So for the monopole magnet there would be an initial increase in EMF as it approaches the coil and then constant EMF as long as it moves through the coil and then the same decrease in EMF as it exits the coil at the other end.


The reason I also believe this is because I built some time ago a test generator to test out various nuances of induction. I took a core of a toroidal transformer, and wound many closely spaced single turns around the core, each single turn was connected in parallel with the next one and each turn also had a mosfet transistor that I was controlling from a 8 bit flip flop logic. This allowed me to chose which turns at which point around the toroid will be ON at any given time. Then I made a two pole rotor. The rotor was made from two 180 degree wide metal sides. The metal side pieces were attached to flat rectangular neodymium magnets. Imagine a circle , cut it in half, leave the center empty and add two flat rectangular magnets with magnet flat sides facing each metal half. This gave me a rotor that had very wide pole surfaces (180 degrees) , as I rotated the rotor adjacent to the toroidal stator, I commutated the mosfets transistors in such a way that only the windings facing the flat rotating pole are ON and they follow the pole. Sure enough, I only got steady DC at the output.


My logic is this, because the rotor poles were as wide as possible (180 degrees is max) the individual single turns experiences a constant change of flux while each single pole was passing them by, In theory each individual turn on the toroid stator could not know that there was another pole to come by at a later time, all the electrons within the wire could experience is a long single pole passing by causing steady rate of change of flux causing steady EMF which manifested as DC at the output.


I hope I wrote this in an understandable way. So My guess is that with a magnetic monopole passing through a coil at a steady rate one could get pure DC within the coil. What do you think?

 

[renormalize]

So My guess is that with a magnetic monopole passing through a coil at a steady rate one could get pure DC within the coil. What do you think?

Yes, this has been discussed on PF before. See, for example:
https://www.physicsforums.com/threa...monopole-passing-through-a-wire-loop.1005625/
and also:
https://physics.stackexchange.com/q...ough-a-wire-loop-which-way-does-the-current-f

 

[Baluncore]

So My guess is that with a magnetic monopole passing through a coil at a steady rate one could get pure DC within the coil. What do you think?

In the real world.
https://en.wikipedia.org/wiki/Homopolar_generator