Author Topic: Exception to Poynting theorem  (Read 1113 times)

Offline goran d

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Exception to Poynting theorem
« on: 07/17/2018 08:03 PM »
All right, this time i'll try to be less arrogant, please point to my error!
If we re-derrive the pointing theorem without assuming constant permeability, we get extra components - one electric and one magnetic. The magnetic is H^2 (d mu / d t). This component can be seen in electric motors.
For instance, if we pull a ferrite bar towards a coil, mu would grow where the field is stronger, but will reduce at the back when the field is weaker. So we lose electric energy, which gets converted to motion.
However, let's consider a synchronous motor, where the rotor is a ferrite rod, and the stator coils are pure wire, no core. The stator coils are much larger than the rotor, so that their field would appear uniform. This means that the "extra" component to the pointing theorem will give nothing, due to the uniform field, to the limit of infinite stator coils, while the mechanical energy we get is reduced to the one caused by the torque on the rotor. It seems like a way around the Poynting theorem, creation of energy compatible with it.

Offline 1

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Re: Exception to Poynting theorem
« Reply #1 on: 07/18/2018 11:53 PM »
I'm not sure I understand what you're asking, exactly, but I think it sounds like you're trying to account for a changing mu when it's not needed.

The purpose of the stator coils as a whole is to create a rotating (constantly reorienting) magnetic field. As such, the field from/in the coils are, at best, steady-state sinusoidal; never really uniform. The input from the power supply as well as the contribution from the rotor field mean that you always have a changing magnetic flux through the stator coils without any need for a changing permeability. As such, your extra terms would rightfully be expected to contribute nothing.

The easiest way to convince yourself of this is probably to realize that in lieu of a ferrite magnet in the rotor, you could use an electromagnetic coil instead; identical to that of one of the stator coils in DC operation. In this case, there is only one static value of mu in the entire system*. Once the magnetic field from the rotor is in place, the stator coils don't really know/care whether it's generated by an electromagnet or bar magnets, and we can expect the performance of the motor to be more or less identical.


*technically an oversimplification, but you get the idea. 

Offline goran d

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Re: Exception to Poynting theorem
« Reply #2 on: 07/21/2018 04:41 PM »
Okay, i can see your point. But what about direction dependent mu? We raise H in the big mu direction, then rotate it by 90 degrees, then lower H. On the way up, we get square curve, on the way down we get a line curve, so it must have gained energy. Thats assuming very large difference in mu depending on direction.

Offline meberbs

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Re: Exception to Poynting theorem
« Reply #3 on: 07/22/2018 04:10 AM »
Okay, i can see your point. But what about direction dependent mu? We raise H in the big mu direction, then rotate it by 90 degrees, then lower H. On the way up, we get square curve, on the way down we get a line curve, so it must have gained energy. Thats assuming very large difference in mu depending on direction.
Short version is that when you talk about EM energy and the Poynting vector in materials there are a couple different ways of doing the bookkeeping. The physical field is the B field, rather than the H field. The H field basically subtracts out the portion of the B field that is "locally" generated by the material. Different ways of bookkeeping basically can attribute some of the momentum of an em wave passing through a material to the photons or to fields generated by the material, and some is temporarily at least in actual motion of particles in the material.  You can see discussions of this if you research the Abraham-Minkowski controversy (note: many sources make it out to be a bigger deal than it is, and it is mostly fueled by misunderstandings and miscommunication.)

What really matter to you is this:
-Maxwell's equations in free space work in general (with caveats related to quantum mechanics)
-Modified Maxwell's equations for materials that use D or H instead of E and B build in assumptions about the materials, notably that they are linear.
- The D or H fields are used as a bulk approximation of what the charges do in the material (their detailed behavior is partially dictated by quantum, making individual modelling pointlessly difficult.)
- If you want do fancy non-linear materials, you are going to need a lot of care to get it right, even more than the care already needed for momentum balance in linear materials
-At the end of the day, everything is operating under fundamental rules (Maxwell's EM, and quantum mechanics) that are fundamentally conservative, so you won't be breaking any conservation laws with them.

Offline goran d

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Re: Exception to Poynting theorem
« Reply #4 on: 08/07/2018 06:32 PM »
This time I think I nailed it! If we have a rotating uniform field, and a permanent magnet lagging behind the angle, the d(Flux)/dt through the area of the magnet will be constantly reduced, because the angle is increasing relatively to stationary space where the magnet is. That means that E.j_b is not zero i.e. the E field is doing work on the bound current. But the bound current doesn't get affected by the work therefore there is net energy balance, direction dependent on relative direction of field and magnet. If it were a wire the rotor current would reduce, conserving energy. But the bound current doesn't.
« Last Edit: 08/07/2018 06:33 PM by goran d »

Offline meberbs

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Re: Exception to Poynting theorem
« Reply #5 on: 08/07/2018 10:32 PM »
More information is needed to understand what you are describing.
If we have a rotating uniform field,
What kind of field, electric or magnetic? What is generating this field? A common way people think they broke conservation laws in electrodynamics is to ignore back reactions on the sources of fields.

and a permanent magnet lagging behind the angle,
Is the magnet moving or not? How is it oriented relative to the field and relative to the changing direction of the field?

the d(Flux)/dt through the area of the magnet will be constantly reduced,
What do you mean "area of the magnet"? A simple model for a permanent magnet is an infinitesimal magnetic dipole. This has a dipole moment, but no area. (And this is not some non-physical model, fundamental particles like an electron have a dipole moment, but no area.)

That means that E.j_b is not zero i.e. the E field is doing work on the bound current. But the bound current doesn't get affected by the work therefore there is net energy balance, direction dependent on relative direction of field and magnet. If it were a wire the rotor current would reduce, conserving energy. But the bound current doesn't.
If the field is doing work on the current, then the current is affected. You have incorrect assumptions behind your statements, but due to the confusion of what your setup is, I can't tell what they are specifically.

Offline 1

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Re: Exception to Poynting theorem
« Reply #6 on: 08/07/2018 11:12 PM »
More information is needed to understand what you are describing.

I think goran's building on the example of the synchronous motor mentioned in the first post. Still, I have questions similar to yours; so I'll wait for his/her replies.

Offline goran d

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Re: Exception to Poynting theorem
« Reply #7 on: 08/08/2018 01:40 PM »
Yes, it is the synchronous motor with much larger coils. But it seems my mind gets confused by the fact that the Poynting theorem makes the work equal to E.J, without including the work done by the magnetic field when it creates an EMF. Since dB/dT passes through the poles rather than being at right angles, the idea was that work is being done on the bound current by the electric field. And that the magnet will not demagnetize as a result. This is due to the fact that Poynting theorem excludes the work done by magnetic field generated EMF. But maybe the magnet will simply get demagnetized? The magnet and B -field rotate at the same rate.
According to my calculation, the EMF from the E-field is:
ωBa2
And the average EMF from the B-field is:
2ωBab
provided a is a square magnet's side and b is its length.
So they don't always cancel out.
« Last Edit: 08/08/2018 03:12 PM by goran d »

Offline meberbs

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Re: Exception to Poynting theorem
« Reply #8 on: 08/08/2018 03:06 PM »
Yes, it is the synchronous motor with much larger coils. But it seems my mind gets confused by the fact that the Poynting theorem makes the work equal to E.J, without including the work done by the magnetic field when it creates an EMF.
Magnetic fields never do any work ever. By definition, they generate a force perpendicular to the velocity of the charge they are acting on. A force perpendicular to the velocity can't do work. When they create an EMF, they literally are creating an electric field, and that does the work. If you ignore the electric field generated by a changing magnetic field you obviously get the wrong answer. The Poynting theorem needs you to include all electric fields, not just some of them.

If you are not moving the source of the magnetic field, dB/dt is zero in your rest frame, but you have another force that you have ignored. There is a force acting on the object experiencing EMF to make it move in the first place. That is where the work comes from, and is not modeled as an electromagnetic force (it could be gravity) so it is not covered by Poynting's theorem. (In a practical experiment, it would be contact forces, which technically have an electromagnetic origin, but since atomic bonds are involved, this would be excessively complicated to calculate, so leaving out the details and treating it just as an arbitrary external force is easier.

Since dB/dT passes through the poles rather than being at right angles, the idea was that work is being done on the bound current by the electric field.
dB/dt is not a force generating field. It is proportional to the curl of the electric field. If you don't know what curl is, it would take me too long to accurately describe here, but basically the actual field is perpendicular to the direction of the curl.

And that the magnet will not demagnetize as a result.
This is an assumption. It is not true in general. Magnets can be demagnetized, and doing so involves work.

The magnet and B -field rotate at the same rate.
If this is true, then the fluxes don't change, so there is no EMF (but there are still electric fields generated by the changing magnetic fields, without doing the calculations, I expect this will result in some low frequency radiation). With this, your description of the setup is contradictory. Please clarify.

Offline goran d

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Re: Exception to Poynting theorem
« Reply #9 on: 08/08/2018 03:50 PM »
"dB/dt is not a force generating field. It is proportional to the curl of the electric field. If you don't know what curl is, it would take me too long to accurately describe here, but basically the actual field is perpendicular to the direction of the curl."
dB/dt passes through the middle of the magnet so the electric field generated by it will be either aligned or couner-aligned with the bound current. This is because it rotates around dB/dt.

Offline goran d

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Re: Exception to Poynting theorem
« Reply #10 on: 08/08/2018 04:27 PM »
Uh, maybe I really don't know what I was talking about.

Offline meberbs

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Re: Exception to Poynting theorem
« Reply #11 on: 08/08/2018 04:43 PM »
Uh, maybe I really don't know what I was talking about.
I recommend taking a course on electrodynamics, or at least picking up a good textbook. (I have Griffith's Introduction to Electrodynamics, Jackson's Classical Electrodynamics is also well known.)

Either one will be difficult to follow though if you don't have enough background in multivariable calculus. (Divergence, gradient and curl are essential concepts, as are some related theorems.) Griffith's book has a chapter covering these, but really they are enough to be part of a separate course, and the chapter is more for review.

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