Re: [Phys-L] standard dc circuits

[John Denker <jsd@av8n.com>]

On 11/22/2013 02:21 PM, Paul Lulai wrote:
> The last line of Bob's statement is what I am trying to clean up for
> myself. - because the fields are half as strong. Why is it that the
> fields are half as strong at that location?  Why does the
> cross-sectional area of the wire affect the field produced by the
> batteries?


1) Rule #1:  Draw the circuit diagram.

         __________________________
         |                         |
         |                         |
         |                         |
        ---                        Z
       -----                       Z
        ---                        Z
       -----                       |
         |                         |
         |                 ________|________  <--- X
         |                |                 |
         |                |                 |
         |                |                 |
         |                Z                 Z
         |                Z                 Z
         |                Z                 Z
         |                |                 |
         |                |                 |
         |________________|_________________|



2) The field is produced by /all/ the charges, not just by the
 battery.  A small charge up close can have a bigger effect
 than a large charge far away.

 A battery can be modeled as a capacitor with eeeenormous
 capacitance.  It stores eeeeeenormous charge.

3) Kirchhoff's so-called laws are not valid here.  Some
 charge *must* accumulate on node "X" so as to enforce
 Ohm's laws.

 The capacitance of node X is very small, so the amount of
 charge needed to create the proper voltage is small, in
 accordance with the usual law: V = Q/C.

 This charge is so small that for "almost" all purposes it
 is negligible ... but it is just enough to establish the
 correct voltage on node X.

4) During the startup transient, or in any other situation
 where node X is not at the right voltage to uphold Ohm's
 law, unbalanced current flows into (or out of) node X.
 Charge accumulates on node X.

5) In some sense there is no such thing as a "DC circuit"
 because there is always going to be a startup transient.
 We can talk about the *behavior* of the circuit in the
 *DC limit* ... but that cannot possibly be the entire
 behavior.

 The macroscopic behavior can be understood in terms of
 macroscopic Ohm's law, but if you want to understand the
 microscopic physics you need to look at the startup
 transient and the little non-Kirchhoff steering charges.