Electromagnetic Induction of a permanent megnet

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Discussion Overview

The discussion revolves around electromagnetic induction involving a rotating permanent magnet and its interaction with a surrounding coil. Participants explore various configurations of the magnet (axially and radially polarized) and the implications for induced voltage under different conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Marcus presents a scenario with an axially polarized rotating magnet and a surrounding coil, suggesting that induced voltage is zero due to no change in magnetic flux (dB/dt = 0).
  • In a second scenario with a radially polarized magnet, Marcus argues that the induced voltage remains zero, citing that the angle θ = 90° results in zero flux linkage (ψ = 0).
  • Marcus proposes a third case where the coil partially surrounds the magnet (covering 270°), asserting that induced voltage is still zero due to θ = 90°, although he acknowledges a variation in B.
  • A participant challenges Marcus's geometry in the third case, suggesting that the rotation of the magnet would introduce a significant flux change as the poles pass the coil.
  • Marcus clarifies that the magnets in question are round and seeks further understanding of induced voltage when the magnet is polarized along different axes.
  • Another participant encourages Marcus to visualize the magnetic field lines to better understand the induction process.
  • Marcus acknowledges a potential oversight regarding the change in magnetic field (dB/dt) not being zero in certain configurations.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which induced voltage occurs, particularly regarding the effects of magnet rotation and the geometry of the setup. The discussion remains unresolved with multiple competing perspectives on the scenarios presented.

Contextual Notes

Participants note the importance of geometry and the orientation of the magnetic field in determining induced voltage, with some assumptions about the uniformity of the magnetic field and its effects on the coil's flux linkage remaining unexamined.

markuz88
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Hello everyone,

How are you doing?

I have a doubt about electromagnetic induction, in three particular cases. I need to confirm that I have the right concepts, so I ask for your help.

The main problem:

Imagine that you have a permanent magnet, axially polarized and rotating on its axis with a constant angular speed. Surrounding this magnet, a coil (constant area section pointing in the same direction of magnet polarization). The main question is: will there be induced voltage?

This is what I think:

1) We know that, for a constant Area, flux linkage ψ = B*A*cos θ.
In this case θ = 0°, so ψ = B*A.
And the induced voltage is ε = -N*dψ/dt = -N*A*dB/dt.

In this main case, I think that there will be no variation in B, because the rotation does not change it at all. So dB/dt = 0, thus ε = 0.

2) Let's suppose the magnet is now radially polarized, but keeping the surrounding coil. In this case, can I affirm that rotation still doesn't change B at all (actually it does change B, but if we consider the whole thing it does not)? And not only because of this ε is zero, but θ = 90°, which implies ψ = 0.

3) Now suppose the coil doesn't fully surround the magnet. Let's say it covers only 270° of it (a little abstraction is needed, I know :-p). In this case of non-symmetry, there will be a variation in B, but ε is still zero because θ = 90°.

Am I correct? Did I miss something?

Thank you,

Marcus
 
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markuz88 said:
Hello everyone,

How are you doing?

I have a doubt about electromagnetic induction, in three particular cases. I need to confirm that I have the right concepts, so I ask for your help.

The main problem:

Imagine that you have a permanent magnet, axially polarized and rotating on its axis with a constant angular speed. Surrounding this magnet, a coil (constant area section pointing in the same direction of magnet polarization). The main question is: will there be induced voltage?

This is what I think:

1) We know that, for a constant Area, flux linkage ψ = B*A*cos θ.
In this case θ = 0°, so ψ = B*A.
And the induced voltage is ε = -N*dψ/dt = -N*A*dB/dt.

In this main case, I think that there will be no variation in B, because the rotation does not change it at all. So dB/dt = 0, thus ε = 0.
Correct.

markuz88 said:
2) Let's suppose the magnet is now radially polarized, but keeping the surrounding coil. In this case, can I affirm that rotation still doesn't change B at all (actually it does change B, but if we consider the whole thing it does not)? And not only because of this ε is zero, but θ = 90°, which implies ψ = 0.
Correct.

markuz88 said:
3) Now suppose the coil doesn't fully surround the magnet. Let's say it covers only 270° of it (a little abstraction is needed, I know :-p). In this case of non-symmetry, there will be a variation in B, but ε is still zero because θ = 90°.
I don't understand your geometry. The classic case is a bar magnet magnetized along its axis z, near a coil parallel to the x-y plane that is located a small distance away along the z axis. Now spin the magnet around the x-axis (at the magnet midline). Each time the pole swings past the coil, it introduces a large flux in the coil.
 
Ah, first, I forgot to tell that these permanent magnets are round magnets.

But the third case is a bit more complicated... well, you have just described a "common" generator, right?

And thank you for your reply! If you let me, I want to ask you other geometry. This is going to help me understand a bit more. I drew it to make it easier to see the problem. The red/blue part of magnet is only north/south pole division (ie, in the picture, it is polarized along axis X).

aEZLQ.png


If this magnet rotates around axis X with a constant speed ω, as the coil remain still, should I expect induced voltage? I guess not, because, again, θ = 90°. But what I can't see is: what if the magnet is polarized in Z axis? Notice that this is very similar to case (2) I described before, but the coil is in front of the magnet, not surrounding it.

Thanks again,

Marcus
 
First part--you are right. Second part--what do you think? Draw your magnet as a dipole, for example, and draw a few field lines around it to see what happens.
 
I think I see... dB/dt will not be zero.

Thanks for your help, marcusl.
 
You are welcome.
 

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