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*From*: "Zani, Gerald" <gerald_zani@brown.edu>*Date*: Tue, 30 Nov 2021 11:23:06 -0500

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.

Feynman's Lecture II-27 is very good on this.

https://www.feynmanlectures.caltech.edu/II_27.html

The video is comical. But it is also confusing and annoying and is produced

with a "strange-mystery-hyped-tone" to gather social media hits.

Poynting's 1884 Paper;

On the Transfer of Energy in the Electromagnetic Field (1884)

https://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_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

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