# Why doesn't a magnetically levitating conductor oscillate?

• chandrahas
In summary: I meant that during the first half of the AC cycle, it is divided into 2 parts. One where the field is increasing, and...The attractive force is the force that tries to keep the plate in the air. The levitation force is the force that tries to keep the plate moving.
chandrahas

I was watching this video of veritasium today and was wondering why the aluminum plate doesn't oscillate when there is a changing magnetic flux. When the flux is increasing, the induced magnetic field (by the induced current) is against the magnetic field of the coil and this acts like 2 north or south poles facing each other, and hence they repel. But if the flux was decreasing, the induced magnetic field would be in the direction of the larger or main magnetic field. In this case, shouldn't they attract each other? acting like a north and a south pole? Since the drive current is sinusoidal, it should have equal amounts of each​

I understand that as the plate gets closer to the main coil, the change in flux increases and there would be more repulsion than attraction on average, but the plate should still be oscillating right?.

Is it because the plate doesn't have enough time to respond?

It is oscillating at 120 Hz. They talk about it in the video, but they call it vibration. Vibration is a kind of oscillation.

But they also said that it was about twice the frequency of the drive current I think, and is my hypothesis right then? and would the attractive and repulsive force be equal if the magnetic field was uniform along an axis and the strength varied with time. So this would mean that the conductor would only oscillate and not move right?

By the way, the demonstration in that video uses 800 amps of current, and it heats that plate enough to burn. There are serious safety problems. This is not the kind of thing to attempt to do at home.

I know, I would not try this home. I am just interested in this phenomenon.

chandrahas said:
But they also said that it was about twice the frequency of the drive current I think, and is my hypothesis right then? and would the attractive and repulsive force be equal if the magnetic field was uniform along an axis and the strength varied with time. So this would mean that the conductor would only oscillate and not move right?

When the direction of the magnetic field reverses, so do the direction of induced currents in the plate reverse. So you get repel/repel not attract/repel. Lenz's Law applies to both halves of the cycle. https://en.wikipedia.org/wiki/Lenz's_law

But you asked about the increasing/decreasing portions of each half cycle. To analyze that, you need to study the time dependent penetration of eddy currents from the surface to the interior of the plate. That is quite difficult.

However, it would be reasonable to expect the magnitude of the vibrations (oscillations) to increase as frequency is decreased. So at very low frequencies you may be correct. I'm not the best expert on those calculations.

Oh ok, thanks, I think I understand the vibration part. But another question that I was thinking about was this:
I used comsol (multiphysics software) to run a simulation of a conductor in a varying magnetic field and it seems that the levitation force is stronger than the attractive one even during the half cycles (even when the conductor is not vibrating). I don't understand why we have this asymmetry.

chandrahas said:
Oh ok, thanks, I think I understand the vibration part. But another question that I was thinking about was this:
I used comsol (multiphysics software) to run a simulation of a conductor in a varying magnetic field and it seems that the levitation force is stronger than the attractive one even during the half cycles (even when the conductor is not vibrating). I don't understand why we have this asymmetry.
I would suspect the simulation - as I always do.

Alright I'll check the simulation then, I might have gone wrong somewhere.

chandrahas said:
Alright I'll check the simulation then, I might have gone wrong somewhere.
But what "attractive' force are you referring to? The induced current is always in a direction to cause repulsion in maglev.

If I've understood correctly then during one half cycle the fields are N to N and in the other half cycle S to S. Eg they repel during both phases of the AC input. The only issue is that during the zero crossing there is a much reduced or zero field so it briefly falls.

CWatters said:
so it briefly falls.
That's the lowest extremity of the vibration.

If you raise the frequency is it likely that the 'oscillation ' becomes less noticeable?

I meant that during the first half of the AC cycle, it is divided into 2 parts. One where the field is increasing, and the other where the field is decreasing.

Here, in the first half of the picture, The field is increasing and hence the induced currents oppose the magnetic field repelling them, while when the field is decreasing, the induced currents produce a magnetic field in the direction of the external field. So, I thought the field interaction for the entire AC cycle would be:
external-induced
N-N , N-S ,S-S ,S-N

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chandrahas said:
I meant that during the first half of the AC cycle, it is divided into 2 parts. One where the field is increasing, and the other where the field is decreasing.
View attachment 216932

Here, in the first half of the picture, The field is increasing and hence the induced currents oppose the magnetic field repelling them, while when the field is decreasing, the induced currents produce a magnetic field in the direction of the external field. So, I thought the field interaction for the entire AC cycle would be:
external-induced
N-N , N-S ,S-S ,S-N
This is not correct. Lenz's law tells you that the induced magnetisation is always in a direction opposing its cause; you will only get repulsion.

Oh, didn't know that. I thought a decreasing field would be analogous to a bar magnet moving away, so a field opposing this motion is a field that attracts the moving magnet and make the magnet stationary. Wouldn't this correspond to an attractive field? I don't understand.

In the DC limit, Lenz' law tells us that the EMF goes to zero. At nonzero frequencies the induced EMF is proportional to (and opposing) the rate of flux change, so lower frequencies would require higher currents to maintain the same peak lifting force. However, with ordinary (non-superconducting) metals the induced currents are dissipated by resistive losses that cause the heating mentioned above. The conceptual cousin is magnetic hysteresis where, in permanent magnetic materials such as iron, the domains flip direction to counter the induced EMF and cause local heating as they do so.

chandrahas said:
I thought a decreasing field would be analogous to a bar magnet moving away,
The reducing field will induce a changing current that will induce a field that resists the change in the original field. You still get repulsion. Eventually, of course, the induced emf cannot drive sufficient eddy currents through the objects and the repulsive field drops.

## 1. Why doesn't a magnetically levitating conductor oscillate?

A magnetically levitating conductor does not oscillate because it is in a state of stable equilibrium. The conductor is suspended in mid-air by magnetic fields that are evenly distributed around it. This prevents the conductor from experiencing any net force that would cause it to oscillate.

## 2. How does the stability of a magnetically levitating conductor prevent oscillation?

The stability of a magnetically levitating conductor is achieved through the phenomenon of diamagnetism. This means that the conductor is repelled by the magnetic fields surrounding it, creating a stable equilibrium where the conductor remains suspended without any movement.

## 3. Can a magnetically levitating conductor ever oscillate?

In theory, a magnetically levitating conductor can oscillate if it is disturbed from its stable equilibrium. However, the magnetic fields surrounding the conductor are designed to be strong enough to maintain its stability, making it highly unlikely for it to oscillate in normal circumstances.

## 4. Are there any factors that can cause a magnetically levitating conductor to oscillate?

In rare cases, external factors such as strong vibrations or sudden changes in the surrounding magnetic fields can cause a magnetically levitating conductor to oscillate. However, these factors would have to be significantly strong to overcome the stable equilibrium and cause the conductor to oscillate.

## 5. Can changing the strength of the magnetic fields surrounding the conductor affect its stability and cause oscillation?

Yes, changing the strength of the magnetic fields can affect the stability of a magnetically levitating conductor. If the magnetic fields are weakened, it can disrupt the stable equilibrium and cause the conductor to oscillate. However, this would only happen if the magnetic fields are significantly weakened, as they are designed to maintain the stability of the conductor.

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