# I Counterexample to the Poynting theorem

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1. Mar 13, 2018

### goran d

The counter-example is as follows: We have a rectangular toroid ferrite(ring ferrite), magnetized in a closed loop around the ring. We put capacitor plates on top and bottom surfaces, with suitable direction. Now the Poynting vector points inwards or outwards. We look at a cylindrical surface passing through the middle of the thickness of the ring. There is surface integral of the Poynting vector! But there is no free current, and electromagnetic energy is constant. Which seems to violate the Poynting theorem. Any exmplanation?

2. Mar 13, 2018

Very clever !! Just a guess=I'm no expert on the topic, is that the Poynting vector applies to electromagnetic wave propagation, and here there is no propagating wave.

3. Mar 13, 2018

### phyzguy

Feynman talks about just this case. See Figure 27-6 in the attached link. What you have is a circulating energy flow. I think you have no way to prove that electromagnetic energy is not circulating around the ferrite ring, so it is not really a counterexample.

4. Mar 13, 2018

### Staff: Mentor

That means either that your statement of the problem is wrong, or the analysis is wrong, or that you may misunderstand Poynting's Theorum.

Either post a link to your source, or show diagrams and your math coming to that conclusion. Otherwise, this thread may be deleted.

5. Mar 13, 2018

### goran d

Here is a diagram of what I mean by this description.

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6. Mar 13, 2018

Staff Emeritus
It can't be that! It's a paradox, I tell you! A paradox!

As drawn, the Poynting vector is zero. The E field in a conductor is zero and the B field, as drawn, does not leave the iron.

I fear the next step will be the Yeahbuts. I stipulate that had he asked a different question he would get a different answer. But for what he actually drew, S is zero.

7. Mar 13, 2018

### phyzguy

Ferrites are typically non-conductive, or at least very resistive. So I don't think you can conclude that E=0.

8. Mar 13, 2018

The case of a toroidal wound solenoid, without any core, carrying a DC current would follow the diagram of the OP, and would illustrate what the OP was trying to show.

9. Mar 13, 2018

Staff Emeritus
Our very first Yeahbut!

10. Mar 13, 2018

### Staff: Mentor

It appears that you have ignored what @phyzguy posted, and have not read his link... That's not conducive to a good discussion...

11. Mar 13, 2018

### Staff: Mentor

It is not possible for a source/field configuration to both satisfy Maxwell’s equations and violate Poynting’s theorem. However, I must admit that in this case it isn’t clear to me which is the problem.

@goran d can you show that your proposed configuration satisfies Maxwell’s equations?

12. Mar 13, 2018