Re: Electric Field Lines

[brian whatcott <inet@INTELLISYS.NET>]

At 05:26 10/25/01 -0400, Ed Schweber wrote:
> Hi:
>
>    Yesterday I posed a question about the standard algorithm for
> constructing electric field lines, using a dipole as a paradigm.
>
>   " 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."
>
> Johm Denker peplied:
>  " That sentence is awfully hard to parse.  It has too many "ands" and not
>     enough punctuation."

....Since we did not explicitly take the density into consideration, why
> should the correct density suddenly appear.

>    I spoke of spheres, because I wanted to avoid some difficulties with
> point charges. But these spheres can be arbitrarily small compared to the
> distance between them. The E field just outside either sphere would be
> predominently effected by only that sphere and would be symmetrically
> distributed around it. My original question still remains.

> Ed Schweber


Ed,
I think you are looking for a geometrical feature of space that
has been mentioned before. It is particularly clear in the case
of a charged (or massive) sphere at infinite remove from other
objects, except a test charge (or object).

A fluence (which may be portrayed with fictitious equispaced
lines emanating from the sphere's surface) spreads into space
with a density proportional to the number of fictitious lines
cutting a spherical shell at some distance from the sphere's
center r. The total area of such a shell is of course
4 pi r squared and the "line" density is proportional to
 1/r squared at any distance r.
This is the geometric basis for the inverse
 square laws.   It is not so intuitive, when the objects of
interest are two spheres: the mythical lines are not then said
to emanate evenly from the spherical surfaces, are they?

You will recall the Excel demonstration of field computation
by relaxation methods (Also from John Denker) which demonstrates
a handy way to develop the form of the fluence, field or
 force effect around given shapes in these more difficult cases.


brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!