Nobody in this thread, including myself, has tried to explain how audio interconnects sound different by invoking the Poynting vector.
Indeed, the Poynting vector was never mentioned until you brought it into the discussion back in post #107!
Like you, the vector calculus has long faded from my memory - but one thing I'm sure of - the Poynting vector has 'hee haw'* to do with how a silver interconnect sounds!
*'hee haw' = Scottish slang for 'nothing'!
So we don't need the Poyinting vector to explain the energy transport in a DC circuit, that remains for AC (time dependent EM field) only. The static Poynting vector only creates a angular momentum over the circuit (that is, it tries to bend your PCB).
Sorry for not quoting your entire treatise, but thanks for clearing that up!
Yes. I seem to recall reading Feynman on Poynting and angular momentum.Waly said:
Given that Poynting is not needed for DC (and may create confusion when tried) I suspect it might not help for quasistatic either (i.e. almost anywhere where the circuit (low frequency) approximation can be used). Of course, when EM radiation is taking place the Poynting vector does tell us where the energy is flowing - at least in the radiation field, but maybe not in the induction field?
Yeah, I've just had to wade through to page 3 of the article to find a reference to the Poynting vector!
I'm not much the wiser, but do agree that energy is propagated along the cable!
Alas, he was.
I couldn't give two hoots that Hawksford has a PhD. Guess what: I happen to have one. One of the salient aspects of having a doctorate is that it doesn't render you above criticism. The reverse in fact. And 'bollocks' is what that article is, as other tenured specialists in EM (with zero interest in audio) have pointed out in essentially those terms. It is riddled with so many problems that a critical analysis of it is practically an article in itself.
I couldn't give two hoots that Hawksford has a PhD. Guess what: I happen to have one. One of the salient aspects of having a doctorate is that it doesn't render you above criticism. The reverse in fact. And 'bollocks' is what that article is, as other tenured specialists in EM (with zero interest in audio) have pointed out in essentially those terms. It is riddled with so many problems that a critical analysis of it is practically an article in itself.
I wasn't trying to big the man up - just making sure we had the right Hawksworth!
I would be interested to know where the poor man went wrong - but I would have to understand what he was talking about in the first place!
He calculated the prop velocity of a planar wave into copper, figured it was storing energy (residual), built a test measure but used a magnetic steel wire instead of copper, then when he saw the inductive kickback at the end of a truncated sine, assumed he spotted what his equations predicted.I wasn't trying to big the man up - just making sure we had the right Hawksworth!
I would be interested to know where the poor man went wrong - but I would have to understand what he was talking about in the first place!
Bad assumptions, bad test setup, wrong conclusions.
A twisted pair of copper will run 180 nH per foot. Using a magnetic steel wire increased the internal inductance of the wire fron 15nH per foot to 1.5 microhenries per foot times two conductors.
Jn
Ps. I hate using an IPhone for posting...
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Yes. There is much loose talk about energy being propagated in the fields, but this only applies to radiation situations which is certainly not the case for audio interconnects.Galu said:
Incidentally, he talks about integrating the Poynting vector over an area. This is incorrect. It has to be a closed surface. Integrating over an open surface just leads to confusion. It just happens to be the case that for a perfect coax cable the Poynting vector is zero everywhere outside the cable so his false idea just happens to give the right answer. Note that in science getting the right answer does not mean that the method is necessarily correct.
It is best to assume that anything published by Hawksford (and possibly his students too) may contain basic errors. For example, his 'fuzzy distortion' stuff showed that he didn't understand that shot noise occurs when discrete charge carriers (e.g. electrons) are uncorrelated - which is not the case in a wire.
I thought according to field theory, energy must enter the wire radially from outside air. The 'free flight of energy' comes from outside not through the conductor.
On this Feynman observed "So our crazy theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside" The Feynman Lectures on physics Vol 2 p27.8-27.9
On this Feynman observed "So our crazy theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside" The Feynman Lectures on physics Vol 2 p27.8-27.9
This could be one of those rare occasions when Feynman got something wrong. It is best to think of the Poynting vector not as the flow of energy but as a means to calculate where the energy ends up. As I said, in a simple DC circuit the energy is actually carried by the electrons as potential energy. It can't be carried twice, as that would double the dissipation.
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