Re: [Phys-L] standard dc circuits

[John Denker <jsd@av8n.com>]

On 11/22/2013 04:31 PM, Paul Lulai wrote:
> Starting at the node prior to the 2 parallel resistors. A charge q
> is present in the node. I would think the field it creates to move 
> charges in each of the upcoming parallel braches would be the same
> as the field if there were only one wire leaving that node.

Well, it's true that same q means same fields ... but that's a
red herring, because if the resistors were different the q would 
be different.

It's analogous to the force and deflection you get if you pile
bricks on a trampoline.  You cannot assume a_priori what the
force will be, and you cannot assume a_priori what the deflection
will be.  The deflection adjusts itself so as to bring about a 
force that equilibrates with the bricks.  If you change the 
number of bricks, the force and deflection will change.  After 
some complicated transient, the situation will settle into a 
new equilibrium.

> If the majority of the field is due to the charges closest to the
> charge to be moved,

Majority?  You can easily set up a situation where roughly
105% of the field acting on the resistor is due to local
charges, and negative 5% is due to fields coming directly
from the battery.  Hint:  flip the wires:
          _____      ______________
         |     |    |              |
         |     |    |              |
         |     |    |              |
       -----   |    |              Z
        ---    |    |              Z
       -----   |    |              Z
        ---    |    |              |
         |     |    |              |
         |     |    |      ________|________  <--- X
         |      \  /      |                 |
         |       \/       |                 |
         |       /\       |                 |
         |      /  \      Z                 Z
         |     |    |     Z                 Z
         |     |    |     Z                 Z
         |     |    |     |                 |
         |     |    |     |                 |
         |_____|    |_____|_________________|


I still say that for 99% of electrical engineering and 99.99%
of life in general, the macroscopic lumped-circuit approach
works just fine, and worrying about the microscopic charges
and fields is not a good use of time and effort.  It is fine
to discuss it amongst ourselves, but I'm not at all convinced 
we should inflict it on students in the introductory course.