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# Re: [Phys-L] standard dc circuits

• From: John Denker <jsd@av8n.com>
• Date: Fri, 22 Nov 2013 14:53:08 -0700

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.