My issue with the analogy (and any so far) is not with space or momentum, it's a simple logicistic calculation that if I have 100 electrons on one side of a battery and to discharge that battery I need to physically move those 100 electrons to the other side... and that they only move at 1cm/s through the conductor... the battery and conductor are able to complete this operation is a time far shorter than 1 cm/s physically permits.
They don't move individually at circa 0.1 cm/s, they each individually move randomly 100 million times faster. The 0.1 cm/s is just the
net drift velocity of the
whole electron cloud
as a whole. The drift is caused by an electric field, which propagates at the speed of light in that medium, so the effect of the electric field is felt at the far end of the wire mere nanoseconds after the potential difference is applied.
The pipe, marble analogy seems to suggest that the wire is full of electrons and so when you pop one in one end a displacement travels the length of the copper and one pops out the other end. That's fine, but if you think it through and instead of 100 electrons over a few minutes you want to run trillions and trillions of electrons down the same conductor for 10 years. There simply are not enough electrons in the conductor, so the electrons you add at one end, need to make it all the way to the other end. So the maximum physical transit of electrons is still 1 cm/s.
Put another way, you are still putting electrons in one end and getting them out the other, you surely have to see that if you run that experiement for long enough the first electron you put in, must have made it to the other end. Not unless electrons are simply bunching up at the near end and being fabricated at the far end so they can catch up at 1 cm/s. Run it for years, that just doesn't make sense.
So if it is 1 cm/s then it cannot be physical particle electrons "flowing" from on side of the battery to the other, something else must be happening.
I can't see where you're having a problem (other than perhaps with scale). If you use a hosepipe, do you expect the water you put in to appear immediately at the other end? No, you expect the water that is already in the hose to pour out first. The net drift of the cloud of water molecules down the pipe takes a few seconds, perhaps minutes, however the individual water molecules are moving much faster (Brownian motion remember), several orders of magnitude faster. Just the same as with an electron cloud in a wire.
The only significant difference is of scale, in copper the charge carrier density (number of conductance electrons per volume) is about 8.5 × 10
28 m
-3. So a 1m long, 1mm
2 cross section wire (~ 17 AWG wire) has 8.5 x 10
22 = 85,000,000,000,000,000,000,000 conductance electrons to play with. One amp of electricity requires the flow of 6.24 x 10
18 = 6,240,000,000,000,000,000 electrons per second. So that 1m x 1mm
2 wire already contains 13,620 amp seconds worth of conductance electrons before you've started. It's a very big pipe, they are very small marbles, they are vibrating very fast and very violently.
Also did Maxwell not describe everything as universal fields that are present everywhere and his work does not even mention the electron. I might be wrong but did Maxwell's work not pre-date the discovery of the electron?
So? Many correct scientific theories have predicted the behaviour of things that hadn't yet been discovered at the time. Maxwell's equations describe the world of electromagnetism. What is electron transport if it isn't an electromagnetic phenomenon?
The thing that moves the electrons is not electrons being inserted into the wire a la marbles, but electric fields. To understand electric fields and how charge gives rise to electric potential which gives rise to fields you need Maxwell - it is not simple and even when
well explained (don't expect that from me, I
just about understand it) some people will never 'get' it. Without a mentioning Maxwell, merely stating that it's the electric field from the voltage that makes it all move feels a bit to much like hand waving - so Maxwell gets a mention.
I can fully understand the effect of an EM field transiting the conductor via the electrons but I'm still stuck at the battery problem as it seems to suggest physical electrons are removed from negative ions at the - terminal and transported to the + terminal.
Yes,
eventually they are physically moved, via a conductor from one terminal to the other, dragged/pushed along by the electric field. You may be waiting some time for an electron that has left the -ve terminal to eventually reach the +ve terminal.