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"Veritasium" (YT) - "The Big Misconception About Electricity" ?

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adx:

--- Quote from: bdunham7 on January 21, 2022, 10:41:51 pm ---
--- Quote from: SilverSolder on January 21, 2022, 10:35:54 pm ---
Let's take a step back, maybe I'm missing the point completely.

Are the fields that carry the energy outside the conductors normal electric and magnetic fields that we can measure if we want to?

--- End quote ---

Yes.  The 'S-field' vector at any point is the cross product of the E and H field vectors at that point.

--- End quote ---

Except for this:
https://en.wikipedia.org/wiki/Aharonov–Bohm_effect
 :o

adx:

--- Quote from: SilverSolder on January 21, 2022, 10:08:17 pm ---So you are saying the thinner we make the insulator, the stronger the magnetic and electric fields will become (to carry the same amount of energy as before)?

--- End quote ---

The stronger the electric field becomes, the voltage difference is the same, it is where the energy comes from (the potential energy).

The magnetic field does not change, except for where it is cancelled by current flowing the other way in the shield. For example in your shielding box, if it were made of copper, the magnetic field wouldn't be altered by its presence or size of holes.

adx:
I was thinking of something yesterday, long those lines. Said before but might be worth repeating in clearer form as a kind of alternate 'Poynting equivalence describer'.

Sredni's "orange parallel resistors circuit" (source: https://www2.oberlin.edu/physics/dstyer/CircuitSurveyor/help.html):


It is infinitely deep, so magnetic field in each loop is the same everywhere and zero outside the circuit. Thus it exactly represents the current flowing in each loop per KCL (completely independent of shape).

Voltage simply divides across the 'gaps', evenly if considering parallel wires (which are plates in this example), so increasing their spacing reduces the calculated electric field. The electric field exactly represents the voltage between the wires divided out over space.

Circuit theory requires that power is calculated from the voltage between wires, so considering power to be spread between the wires as a density is as reasonable as anything else. Therefore multiplying the magnetic and electric fields doesn't just give the same result as circuit theory, but is directly equivalent.

For 3D, consider replacing the front and back of the circuit with empty space, so it ends up as a slice say with square wires. Then consider the "vacuum contribution" to power flow - it should be zero. The fields spill around the wires because it is a 2D circuit in 3D land. The resulting mess is from adding vacuum and the complex topology, not because of any fundamental change to the way the circuit or its fields operate. (This last paragraph a slightly circular argument because we already know it works, but its purpose is to guide intuition, not prove anything.)

This isn't what I was getting at over the past couple of pages, but might be a useful stopgap.

SilverSolder:
Do electrons still actually flow in the wires, under the influence of the fields?

adx:

--- Quote from: SilverSolder on January 22, 2022, 01:00:12 pm ---Do electrons still actually flow in the wires, under the influence of the fields?

--- End quote ---

Yep. I think the argument (whatever it is) is over what they carry, being little springs with long range and peculiar behaviors. More spring force = more energy (even if the spring never moves and only contributes to the stationary mass of an object). Voltage is that force for electrons, so the arguments over where the energy is might go on forever.

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