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Re: Electric Field Lines



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."

An extra comma may have helped, but I don't think whk I was asking
is all that mysterious. The algoritm is based soley on the direction of the
field. However, the final result also has the correct density of field
lines. Since we did not explicitly take the density into consideration, why
should the correct density suddenly appear.

Johm Denker continues:
"The magical solution does not give a fully-correct description of the
field
surrounding two charged conducting spheres ... "The field lines will
not
be equally spaced around the sphere (note: a specification in my
original
algorithm), not even close."

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.

John Denker continues
"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."

The field lines in my algorithm are just a map of the field, not literal
things. They do not have a tension. And they no more repel each other than
the lines on a contour map are pulled down hill by gravity.

Quark confinement is sometimes explained in terms of the lines of the
gluon fielding attracting each other. But gluons carry color charge, photons
do not carry electric charge.

As I noted earlier, I used a dipole as a paradigm. But the same
question appliues to other charge configurations as well, say two charges
equal in both sign and magnitude So my question still remains. The algorithm
only takes the direction of the field into account, yet the proper
connection between the strength of the E field and the density of the lines
emerges as well. Why?

Ed Schweber