Electromagnetic Induction of a permanent megnet

In summary, ε will be zero if rotation does not change B, but there will be a variation in B if rotation does change B.
  • #1
markuz88
3
0
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 :tongue:). 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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  • #2
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 :tongue:). 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.
 
  • #3
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
 
  • #4
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.
 
  • #5
I think I see... dB/dt will not be zero.

Thanks for your help, marcusl.
 
  • #6
You are welcome.
 

1. What is electromagnetic induction?

Electromagnetic induction is the process of generating an electric current by using a magnetic field, or vice versa. This phenomenon was first discovered by Michael Faraday in 1831.

2. How does electromagnetic induction work?

Electromagnetic induction works on the principle that a changing magnetic field can induce an electric current in a conductor. When a permanent magnet is moved near a conductor, the magnetic field lines cut across the conductor, causing electrons to move and create an electric current.

3. What is a permanent magnet?

A permanent magnet is a material that has a magnetic field that remains constant over time. Unlike electromagnets, which require an electric current to produce a magnetic field, permanent magnets have their own magnetic field due to the alignment of their atoms.

4. How is electromagnetic induction used in everyday life?

Electromagnetic induction has many practical applications in everyday life. It is used in generators to produce electricity, in transformers to change the voltage of electric currents, and in induction cooktops to heat up cooking pots.

5. What are the benefits of using electromagnetic induction in technology?

One of the main benefits of using electromagnetic induction in technology is its efficiency. It allows for the transfer of energy without the need for physical contact, reducing wear and tear on machinery. It also produces clean energy, making it a more environmentally friendly option compared to other power sources.

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