Copper Block Energy Flow Riddle

[EEVblog]

Riddle: Where does the energy flow in this steady state DC circuit with a copper block?
And where do the Poynting vectors point?
Does any of the energy flow inside the copper block?

As a bonus, extend the size of the copper block to the size of the earth.

Existing Veritasium thread:  https://www.eevblog.com/forum/chat/veritasium-how-electricity-actually-works/msg6140149/#msg6140149

[RoGeorge]

My best guess (not a physicist, and no field simulator):

At first, during the (AC) transient regime, when you connect the wire to the battery, the current flows through the read wire, and through a thin (imaginary) return path, right underneath the read wire.  An imaginary "wire" that goes parallel with the red wire, right at the surface of the copper block, so, the return path is not through the entire cube.  Think of a voltage step traveling through a transmission line.

The energy flow is something different than the current flow, and the energy flow path is different from the electric current's path.

The energy flows through the empty space between the wire and the copper cube.  Energy is in the EM field, not in the wires.  Energy flows from the battery, through the empty space encircled by the direct and the return path of the current.  The path "chosen" (when multiple choices are available, like in this entire block of copper) is the path with the smallest area.

So in this case, am imaginary thin wire right at the surface of the cube, right underneath the red wire.  For example, if you shape the red wire like an S, the imaginary wire at the cube surface will also copy the same S shape, and the AC current will not go straight, the AC current will follow the S shape.  Yes, the AC current is that dumb. 

After the transient turn-on period has ended, once the stationary (DC) current is established, the return path is no longer a thin trace right under the red wire.  At DC, the return path is the entire cube.

I can't say about Poynting vectors because I've never used them in practice, only read the theoretical part some long time ago.

[iMo]

The energy is not transferred by electron flow (the "electron current") but by the "electric field" (created by the potential's diffs in the battery) which is spreading itself over the entire Universe (AC/DC regardless). The speed of electrons is a couple of millimeters per second in copper and the electrons are lightweight, so they do not carry "much of energy".
The "field's intensity" is the highest in the closest proximity to the copper's surfaces (of any conductor in your example), where the Poynting's vectors direct towards the inside the surface. Its angle of "penetration" into the surface depends on the resistivity of the conductors.
Disclaimer: I learned this 40 years ago, so it might be different these days..

[Marco]

The electric current spreads out through the bulk, then pulls back in on the other side. If there was a stack of high conductivity and low conductivity plates on either side to spread the current, it would evenly conduct through the bulk of the copper block.

The local energy transfer to heat is the volume integral of i^2*r. Energy flow is too ill defined in this context to comment on.

Real calculations get a bit complex :
https://iopscience.iop.org/article/10.1088/2399-6528/aa8ab6/pdf

[Electrodynamic]

The energy is transferred by the mobile free electron drift and the associated electric fields or simply charge carriers.

Logically, the electric field cannot change if the particles which carry the electric fields do not change. What throws many people off is that were dealing with a large electron cloud which only moves an extremely small amount. So in our block billions of free electrons shift a little in one direction however the electric field change appears much larger than the imperceptible physical change.

A.D.Moore explains this pretty well in his book on electrostatics. He explains how if we had a 1cm cube of aluminum and separated all the opposite charges 1m apart the forces pulling them together would be 10^14 or one hundred trillion tons. The voltage across the 1m space would be one quadrillion volts.

So we can begin to see how moving some charged particles an extremely small amount in one direction within a material can produce some pretty big forces as electric fields.

[golden_labels]

Are we back to my model of reality is more truer than your model of reality? I’m going to regret it, I’m going to regret replying, …

Without giving this much thought, I’ll just make an intuitive guess. Let’s see how that goes!

Inside a conductor electric field is 0. The field is going to be between cube surfaces and the wire. So the energy flow is along the battery, upper, and LED surfaces of the cube and the wire over it. From the battery side to the LED side.

I believe the complicated geometry of the battery and LED are not a part of the puzzle, so I assumed they are both infinitely small spherical cows.

So we can begin to see how moving some charged particles an extremely small amount in one direction within a material can produce some pretty big forces as electric fields.

Even more interesting: the sheer number of moving charges is big enough, that the almost-zero relativistic effects their ant-paced movement causes do get multiplied to observable scales.

[Marco]

Inside a conductor electric field is 0.

Only if there's no current or it's a superconductor.

[EEVblog]

At first, during the (AC) transient regime, when you connect the wire to the battery, the current flows through the read wire, and through a thin (imaginary) return path, right underneath the read wire.

Steady state DC discussion only.

[SiliconWizard]

Beyond figuring out an answer to this question, the really interesting part is devising a measurement setup able to actually prove that your answer is correct.

[Fungus]

I'm going with an Australian football shape across the middle of the cube with the two points of the ball where the LED and battery are.

Electron movement won't actually be zero anywhere in the cube but it'll be highly concentrated around the shortest line between the diode and the battery.

Reasoning

The resistance of copper isn't zero. The path of least resistance is across the center so that's the path most electrons will take.

A path around the outside of the cube is longer so it has higher resistance. Less electrons will go that way.

The size of the cube is big enough and the current is small enough to produce a measurable gradient in this example.

[golden_labels]

Only if there's no current or it's a superconductor.

At steady state DC?

[coppercone2]

I have seen some pretty strange things happen on my resistance heater press I made.

With a steel block you can see where it starts glowing first

[johansen]

I'm going with an Australian football shape across the middle of the cube with the two points of the ball where the LED and battery are.

its even more perfectly spread out than that, the distance along the perimeter of the cube is only twice the distance across the cube.

it wouldn't be hard to make a cube of 5x5x5 resistors on the order of 100 cm in length to make a 1 meter cube of about 800 resistors, so you can put an amp meter across any two points.

send 10 amps through any two points and enjoy the the arguments on your findings vs the simulations.

[Marco]

Only if there's no current or it's a superconductor.

At steady state DC?

If the entire block is at steady state DC voltage there is no internal electric field.

If the block has a voltage across it, there is by definition an electric field across it and DC doesn't have a skin effect to keep it out of the interior.

[Marco]

I think Poynting vectors aren't very illuminating when there is no or almost no dynamic EM interaction. We only need the E here.

The math works out even at DC and I'm sure smarter people than me can still see it as energy flow regardless, but for people more like me I think it's better to leave Poynting vectors to antennas.

[Nusa]

As a bonus, extend the size of the copper block to the size of the earth.

In which case the resistance of an earth-sized block of copper combined with the resistance of the 2x-earth-length red wire would be so high that the battery might as well not be connected at all.

[Berni]

Nothing really special about this.

The poynting vector would still be pointing towards the LED in the area between the two conductors. Just that one of the conductors happens to be a lot thicker so it is taking up more physical space.

I suppose the one thing that can make things confusing is that all the poynting vector explanations assume a thin wire where all the current is flowing along a infinitely thin line. Here that is no longer the case, but you could replace the copper cube with 1000 thin wires that follow the path the current is taking trough the copper cube (tho you would have to have some very conductive wires to compensate for the lack of conductor crossection area). This path would likely be mostly a sphere between the terminals but also curving some into the corners a little.

But as said above the E field inside the cube is very small (but not 0 as it is not a superconductor) so the poynting vectors in there would also be near 0. Yet the poynting vectors don't really point anything physical, so just because they point along one side of the cube doesn't mean anything more flows along that side.