Understanding the Poynting Vector Dilemma in Electrical Circuits

[cak942]

I was curious about how exactly energy was transferred in electrical circuits because all my texts were inadequate. After pouring through many sources ("electrical energy transfer" or anything similar yields crappy results through every search engine I tried) I finally found something I could buy: The energy is transferred through electromagnetic waves OUTSIDE of wires.

After researching Poynting's Theorem and vectors and trying to figure out exactly how the energy is sent and received, I ran across an issue with this theory.

A steady-state DC current has no accelerating charges (assuming the circuit has been closed for some time), no oscillating electric fields, and no oscillating magnetic fields. How can energy be transferred through electromagnetic waves if there is no reason those waves should be there?

And if the answer is that energy isn't, then how the heck is it transferred??

 

[jasonRF]

cak942,

What you read is right - Poynting's Theorem shows that the energy is carried in the fields outside the wire. Note that Poynting's theorem holds for DC as well as for AC. In fact, the DC case is a standard example in most EM textbooks. This is one topic for which the Feynman Lectures on Physics is hard to beat. I did a quick google search and found the following lecture notes that also may help (from a standard electrical engineering class).

http://inst.eecs.berkeley.edu/~ee117/sp09/lectures/lecture21.pdf

Charts 13-18 give the standard treatment, with not so many words, though.

Jason

 

[Bob S]

I had the same confusion you had, until I realized that in a microwave waveguide, ALL the power was actually contained between the waveguide walls, not in them. The power had to be in the E and H fields, and the Poynting vector calculation gave respectible answers. It took me a while to realize that the Poynting vector calclation also applied to the ac power flowing to this computer in the power cord. The H fields are primarily outside the conductors, and there is 120 volts ac between them. This becomes more obvious when you consider a 1000-MHz signal traveling between two wires, because the skin effect forces all the current to the surface of the wires, and all the E and H fields are between the conductors, not in them.

 

[cak942]

Thank you for the confirmation JasonRF and the great example Bob S. That gave me a reason to continue reading about Poynting's Theorem. I'm not quite that far in my classes to understand everything I've read relating to Poynting's Theorem (I'm just going into my Freshman year) but I understand the principles of the theorem and it makes circuit theory make sense to me at a much deeper level. I never really like memorizing how to do things, I prefer knowing how they work at the deepest level, because if I forget what I've memorized, it's a cinch to learn it again when you truly understand what's going on.

However, Poynting's Theorem proves that energy is transferred through E and M fields outside of conductors and flows into the conductors, but I haven't been able to locate a description of HOW or WHY. How does the energy flow? I thought energy traveled in electromagnetic waves, yet in this case it is not. And Why does energy flow into the wiring? I know that the math shows that it flows into the wire, bur what forces the energy to behave that way?

Again, thank you for your time and responses.