Current flow through a metal plate

[xrunner]

Suppose you had a plate of copper, such that it's dimensions were 1' thick, 3 feet x 3 foot square.

Suppose further that you attached a wire at the end of the plate, in the middle both vertically and horizontally, at each end of the plate (not at the corners but in the middle between each end at 1.5 feet). Now we pass a DC current of 1A through the plate. It has to flow through the plate to the other electrode.

How would the electrons flow to the other connector?

Would it be a tiny "path" or flow that would be in a straight line from one electrode to the other?
, assuming that one - and only one - path would be the lowest resistance path of any possible path?

Or, would it be a statistical sort of "spread" going through all kinds of paths that were equivalent lowest resistances?

Honestly I have no idea - I just thought this up. 

[Rufus]

How would the electrons flow to the other connector?

They will spread with current in each of the millions of notional paths being inversely proportional to the resistance of that path.

There is probably some magnetic effect as well which makes my head hurt thinking about it. 

[robrenz]

I am no authority on this but I have experimented with a copper sheet about 4" square and using my Micro ohm meter just as you described. I connected the source leads in the positions you described then took the sense leads with probe tips on them and just started probing around with the probes spaced about a half an inch apart. You can see where the current flows and where it is lower or does not flow at all.  You could do the same thing just using a power supply for you current source and probe around with your volt meter and you will start to see the shape of the main current path.

[xrunner]

Thanks.

I have been thinking about this for a few minutes. I suppose that one would model it as an infinite number of an infinite set of values of resistances all in parallel. Low as they all would be (in copper) it would produce some sort of weird field of electron flow, throughout the metal plate?

 

[EEVblog]

Or, would it be a statistical sort of "spread" going through all kinds of paths that were equivalent lowest resistances?

Yep, that one. Except that it's not statistical in any way. You can break it down into finite paths and look at the problem that way.
The total value of all paths in parallel will obey the usual formula, and ohms law will come out in the wash.

[EEVblog]

http://youtu.be/kmCvrGVtC0M?t=35m29s

[xrunner]

http://youtu.be/kmCvrGVtC0M?t=35m29s

I'm going to make sure I devote the time to watch the whole video and not cheat my way through it. I'll get back when I've watched it from beginning to end.

Thanks. 

[Psi]

Recently i saw a 110V UPS battery bank short out through some PCB tracks. The smallest track section just vaporized but you could see on the thicker track that the most of the current had taken the shortest path around due to the inner track edge being discolored.

eg,  # =  looks normal   1 = discolored area

##########
##########
##1111111##
##1         1##
##1         1##
A                B 

[EEVblog]

I'm going to make sure I devote the time to watch the whole video and not cheat my way through it. I'll get back when I've watched it from beginning to end.

The 35min mark linked above shows the ground plane test, so has some relevance here.

[robrenz]

You could do a square lattice of a few hundred equal value resistors in spice and source your current to a single node on each side of the lattice and then look at the current thru individual resistors and see the gradient.

[free_electron]

It depends on the frequency , and where the return pathway is...

If you place two plates on top of each other with 1/4mm of isolator inbetween.
You drill a hole vertically in the middle but 50cm from the right.
You solder a wire on top , horizontally center but 50 cm from the left.
You solder anothe wire at the bottom at the same spot of the one on the top

In the hole you solder a stub of wire.

If you now trace electrons you will still see the 'channel'. For dc the channel may be an inch wide. Center has most of the current and the edges are 1/2 inch away ( point where tou cant detect electron flow.
Bump up the frequency and the channel will contract...

[The Electrician]

The paths the electrons take are spread out all across the plate.  This kind of problem is solved using Laplace's equation.  For a simple case like this a conformal mapping will give the solution.

Have a look at the images here:

http://www.bing.com/images/search?q=conformal+mapping+flow&qpvt=conformal+mapping+flow&FORM=IGREx

Amongst all that are a few images showing flow paths (streamlines) around corners, around obstacles, etc.

[xrunner]

That was a very, very interesting video. Really one of the most interesting I've seen here. I had never seen a probe like that. That thing could occupy me for hours, just following the current flow through different things I might manage to connect to my power supply. 

Super Coolio. 

[robrenz]

You can see the same thing as far as general current magnitude and direction in various places using the power supply and voltmeter probes method I mentioned in post #2