Re: Electric Field Lines

["John S. Denker" <jsd@MONMOUTH.COM>]

At 06:19 AM 10/24/01 -0400, Ed Schweber wrote:
> ... you should get the standard field line configuration for the dipole.
>
>     What has recently begun to perplex me is that we have only paid explicit
> attention to the direction of the field and the correct proportionality
> between the density of the field lines and the strength of the field seems
> to have appeared by magic.

That sentence is awfully hard to parse.  It has too many "ands" and not
enough punctuation.  If it means what I think it means, the answer is simple:

The magical solution does not give a fully-correct description of the field
surrounding two charged conducting spheres.
        (The original question didn't specify _conducting_, but I
        will assume that, since the question didn't specify otherwise.
        If the situation were otherwise, anything would be possible,
        and the question would be pointless.)

In particular, imagine two conducting spheres almost touching.  They will
look more like a parallel-plate capacitor than like an ideal dipole.  The
field lines will not be equally spaced around the sphere, not even close.

So the question should be, why is the magical "equal spacing" condition
even close to correct, for small, widely-spaced spheres?

Answer:  IF (big if) we are going to describe the field in terms of field
lines, the physics has numerous things to say about how the field lines behave.
  1) The field lines start and stop only on charges.
  2) There is tension in each line.
  3) There is repulsion between lines.

Item 3 appears to answer the question.

==================

Remember that field lines will never be more than a crude approximation to
the real physics, and trying to precisely quantify the behavior of the
lines is guaranteed to be a waste of effort.