I spoke with a Faculty today about the video.
Here is what I have. This is a compilation of his thoughts:
The key is to realize that we teach about simple resistor circuits
classically, without any field and only in terms of electron particle flow
and forces. Our traditional view of an electron as a particle moving in a
wire and bouncing around to make heat energy works well.
However, Poynting, influenced by Maxwell’s equations and by Faraday’s field
concept, scrapped the ideas of forces and particles and instead applied
field theory. This gave us a new interpretation for the energy and the
momentum when the flow of energy in a wire and a field is defined in all
space everywhere, not just inside the wire but also outside.
To get P=IV for a wire from a Poynting vector argument, think about it this
way:
The electric field along a wire of length L is simply E = V / L (from E =
- del V, Stokes theorem outcome).
The magnetic field goes around the surface of the wire, and it is B = mu_0
I / 2 pi r0 where r0 is the radius of the wire.
The poynting vector is the energy flow per time per unit area is,
S = ExB / mu_0,
and knowing that E and B are orthogonal,
S is V I / 2 pi r0 L,
and points inwards (minus r hat direction).
Now integrate S over the circumferential area of the wire (2 pi r0 L)
you get: Int[S . da] = I V, which is the power, P=IV.
So bottom line, the whole weirdness comes from thinking of energy in terms
of the fields. The energy is not treated with the classically familiar
treatment of an electron particle experiencing a force.
There are many other similar problems where people were on the verge of
establishing a new use for field theory, Paul Dirac messed around a lot
pushing electrodynamics to its limits in a classical way (particles,
forces), before field theory was established.
In circuits the simple explanation of current moving in a wire by being
pushed by the battery is a classical mechanical way that makes sense and is
a necessary and useful explanation.
But the fundamental question for a theoretical physicist is,
"What does the field theory approach say?"
Weird?
Yes.
Everything is even weirder if you quantize the electric and magnetic field.
A conceptual, cartoon treatment using pictures;
In a simple circuit,where does the energy flow?
A Collection of Diagrams
By William Beaty http://amasci.com/elect/poynt/poynt.html
I hope others enjoy this post.
- Jerry
--
Gerald Zani
Senior Engineering Technician
Brown University School of Engineering
(401) 863-9571