Re: How many volts ?

[SCIAMANDA@edinboro.edu]

Ludwig wrote:

> . . .        Perhaps there is 
> a law which prevents lines from "bending and unbending" but I do not recall 
> it. In the same spirit I wander if Maxwell's laws can be used to demonstrate, 
> somehow, that each static line must be confined to a single plane. Call such 
> rules "Faraday's no-bending and no-twisting principle", if you wish. This 
> is not a call for a demonstration; only for an honest statement that it 
> exists, or can be performed.
                                              Ludwik Kowalski

Ludwig,
There is a restriction as to just how a field line can "bend and twist". 
Mathematicaly it requires that the "Curl of E" be zero, which physically 
means that it is a conservative field, and also leads to the existence of 
equipotential surfaces which have been mentioned. As suggested, try to 
construct these surfaces, everywhere perpendicular to E, and see what 
happens.

Certainly bending would take place in a field line after leaving the conducting 
surface if that surface were irregular in shape (eg. with hills and valleys).
Another case: this would happen if one plate were larger than the other 
(in the "overhang" region).
But your symmetrical, plane geometry just doesn't need such complications!

I certainly don't think this is a "nuisance".  I do not appreciate, and am 
curious about, your arguments from "induction" and "minimum energy".  I do 
understand what these ideas entail, but I guess I'm just not familiar with 
using them to quantitatively solve such boundary value problems.  Perhaps 
you could elaborate a bit, when time allows.

Bob Sciamanda           sciamanda@edinboro.edu
Dept of Physics
Edinboro Univ of PA     http://www.edinboro.edu/~sciamanda/home.html