I have a mass of 1 kg in position P at 0 meters over sea level.
I take this mass 1000 meters away to drop it from a cliff into a hole deep 10 meters.
The potential energy of the mass is converted into kinetic energy and then this is uses to generate heat. Let's say I 'generated' 1 joule of energy.
Has this energy traveled along the 1000 meters path?
If we take the Poynting style conservation of energy argument, we know that energy is created in the volume of space around where you 'generated' it. Energy was 'dissipated' in the volume of space around where you dropped it. So we can say energy flowed through the space between. But we can't say exactly the path that the energy took.
Edit:
However, if we decide that the potential energy is located where the mass of the rock is located (like we do by saying that the fields have energy), then energy flowed along with the rock. How much potential energy the rock contains is a problem without knowing the baseline zero potential energy of the system.
I hate analogies. Water analogy, rock analogy, whatever.
If so: HOW MUCH ENERGY does travel along the path?
The fact that most of the system's energy is stored in the magnetic field around the wires, hints further that "energy flows outside the wires", but this is an interpretation, and one can take either point; they're equivalent, once everything's quiescent, i.e. you can solve from one given the other (and material properties, boundary conditions, all that).
One of the problems with analogies is that you have to have a deep understanding of model's (in this case hydraulic) system. Derek seems to have done his homework. He points out that unlike a hydraulic system (where the water from the pump to the load has high pressure and low velocity and the water in the return pipe has lower pressure and higher velocity),
What is making the electrons drift is not some kind of pressure. It is just a portion of the electric field generated by the battery that does not contribute to the transfer of energy from the battery to the load. So electrons in the wire are not being pushed by each other like in a fluid. They're just parading in response to an external cause (the electric field) exactly like in the load.
I posted this comment on Derek's video, slighly expanded:
Riddle me this, a new thought experiment: Let's go extreme and say you have a 100mm diameter copper conductor at pure steady state DC delivering a small amount of power to a pure resitive load, say 1W, but go as low as you want. No transients, no skin effect, no nothing, just pure steady state DC into a resistive load.
Is there NO energy WITHIN this comicly large wire? None? It's all on the OUTSIDE of the wire in the fields at DC? Really? REALLY?
The classicial field theory math might work at DC, but I just can't get over the feeling that it doesn't pass the sniff test at DC. I don't get The Vibe I get with AC and transients. Quantum Electrodynamics and probability theory in the electron fields within the wire better passes the sniff test at DC.
Can someone please convince me that there is no energy flow within this 100mm diameter wire at all, and that all the energy flows outside the wire at DC.
I have a mass of 1 kg in position P at 0 meters over sea level.
I take this mass 1000 meters away to drop it from a cliff into a hole deep 10 meters.
The potential energy of the mass is converted into kinetic energy and then this is uses to generate heat. Let's say I 'generated' 1 joule of energy.
Has this energy traveled along the 1000 meters path?
If we take the Poynting style conservation of energy argument, we know that energy is created in the volume of space around where you 'generated' it. Energy was 'dissipated' in the volume of space around where you dropped it. So we can say energy flowed through the space between. But we can't say exactly the path that the energy took.
Edit:
However, if we decide that the potential energy is located where the mass of the rock is located (like we do by saying that the fields have energy), then energy flowed along with the rock. How much potential energy the rock contains is a problem without knowing the baseline zero potential energy of the system.
I hate analogies. Water analogy, rock analogy, whatever.
It was not meant to be an analogy.
I am considering the mechanical system only.
In more detail: one perfectly flat frictionless path goes from point A (the source) to point B (the load). We can put the weight on the path and with an infinitesimal push we make it travel D meters to point B.
Now, at point B we have a cusps that leads to lets' say 20 different holes of different depths, from 1 to 20 meters. Chance determines what the final path will be. But once the weight falls into one of the holes, all of its gravitational potential energy from height 0m to the depth of the hole gets converted into heat (to simplify things).
At the bottom of each hole there is a path (horizontal and perfectly frictionless) that leads back to the source.
At the source the weight is lifted by a machine to sea level and the cycle repeats.
Not an analogy, I repeat. It is a mechanical system.
Does the energy travel through the one forward path at sea level?
If so: HOW MUCH ENERGY does travel along the path?
Remember, I do not know which hole the weight will fall into until the weight falls into it.
If we cannot get an agreement on this mechanical system, how can we get an agreement on the electromagnetic system where the depth of the hole is determined by the charges themselves (by creating a surface distribution that obeys the constitutive relation in the wires and resistor)?
Well, as I understand it, a medium is needed to hold charges, and if there are no charges, there's no field?
The question then is more about fields making charges move rather than charges moving creating fields. Or something.
Can we lock the other thread or something? This discussion is super confusing to read when we've got entire lines of thought being double-posted in both threads. It's super confusing to follow who is responding to what.
"Let's see - is this the BIG thread talking about how Veritasium is right but actually wrong or the LITTLE thread talking about how Veritasium is wrong but actually right?"
Why is it that, in the two capacitor paradox problem, the two capacitors are connected in parallel with each other and the switch connected in series as shown in the circuit below?
Source: Wikipedia en.wikipedia.org/wiki/Two_capacitor_paradox
If those two capacitors are identical (same capacity) the voltage after switch is closed will be 0.707 * Vi
That's not how physics works. You're implying that energy can be created out of nothing to buffer an energy deficit.
Using the water analogy, if you have two buckets of the same capacity to represent the two capacitors, then one bucket is filled and the other is empty. This is the initial condition. If you pour 70.7% of the water from the filled bucket into the empty bucket, then there will be 29.3% of the water remaing in the initially-filled bucket. How can there also be 70.7% water remaining in the initially-filled bucket when only 29.3% of the water remains in that bucket?
That is absurd and contradictory. That's the definition of a paradox.
Well, as I understand it, a medium is needed to hold charges, and if there are no charges, there's no field?
The question then is more about fields making charges move rather than charges moving creating fields. Or something.
In this example (Derek's setup) the charges are needed to create the field as the only electric field is inside the battery
There is no moving object in this experiment.
I'm not sure you got what I meant, nor that I got what you meant. And nobody talked about moving objects here.
That's not how physics works. You're implying that energy can be created out of nothing to buffer an energy deficit.
Using the water analogy, if you have two buckets of the same capacity to represent the two capacitors, then one bucket is filled and the other is empty. This is the initial condition. If you pour 70.7% of the water from the filled bucket into the empty bucket, then there will be 29.3% of the water remaing in the initially-filled bucket. How can there also be 70.7% water remaining in the initially-filled bucket when only 29.3% of the water remains in that bucket?
That is absurd and contradictory. That's the definition of a paradox.
What extra energy are you seeing ?
There is no extra energy. Half of the energy stored in the charged capacitor is transferred to the identical capacity discharged capacitor and that will result in 0.707 * Vi.
Voltage is not energy.
Really? This? Again? Charge is the conserved quantity. In a capacitor the voltage is proportional to the charge (due to the very definition of Capacitance) so in this case voltage is conserved too. Electrical energy does not have to be conserved in an electric circuit - it is often converted to some other form of non-electrical energy (heat. light, motion, radio waves and sometimes smoke).
You will never, never, never, never, never, never, never, ever get a stable state with 0.707 * Vi.
If you don't believe me take it up with this random internet guy from Princeton:
https://physics.princeton.edu/~mcdonald/examples/twocaps.pdf
"If there were no damping (dissipative) mechanism, the circuit would then oscillate forever"
"[if there is a damping (dissipative) mechanism] eventually a static charge distribution results, with charge Qi/2 and voltage Vi/2, on each capacitor."
You can test that by calculating the energy stored in now the 2F equivalent capacitor
0.5 * 2F * 2.1212 = 4.5Ws
Is the "ideal" system in a steady state (i.e. without oscillation?)
If so can you please tell me how much charge is in each of those ideal 1F capacitors, (or the ideal 2F combined one, if you like that better)? I am pretty sure the formula is Q = CV.
As we have no source of charges in this system (aside from the initial charged cap) if this is more than the initial charge, where these additional charges have appeared from? No charges are able to cross either capacitor, and we can't just magic up +s and -s out of nowhere.
And yes, I do understand why in all cases half the energy is lost. The 'ideal' case is not realizable, and your solution of 0.707 Vi is inconsistent, because the Lumped Element Model is just an approximation of reality.
You can test that by calculating the energy stored in now the 2F equivalent capacitor
0.5 * 2F * 2.1212 = 4.5WsYes, I do understand why in all cases half the energy is lost. The 'ideal' case is not realizable.
0.707 Vi is never a solution, even with ideal components. You can take a different path through the math of the system and end up with a different answer, which is 0.50 Vi. With ideal components the system is either in a constant state of change (oscillating) or cannot be solved to a consistent answer.
Edit: Sorry about the random edits
Please understand that energy conservation can not be broken.
You have the impression that charge is linear but you need more energy to push the second electron in compared to the first one.
EEVblog wrote:
Dereks's video at 21:10 Re. Rick Hartley about fields is 100% correct for high speed PCB design. But that does NOT apply at DC, not at all, not even one tiny bit.
Yes there is no oscillation.
You can get super close to ideal if you use an efficient DC-DC converter to transfer the energy from the charged capacitor to the discharged capacitor.
Oh; tut tut tut -- it can of course be done with a converter, but a converter is a nonlinear element! Indeed an ideal converter has a negative (and hyperbolic at that) resistance input characteristic (for nonzero power flow, fixed load resistance/power), a great many things are possible with that, which are not possible in a linear system.
I trust you didn't misspeak earlier, that you mean a nonlinear element is in fact necessary to perform this experiment, right?
Tim