Re: Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)
- From: "FrediFizzx" <fredifizzx@xxxxxxxxxxx>
- Date: Mon, 26 Dec 2005 13:29:25 -0800
"nym" <neverwillreply@xxxxxxxxx> wrote in message
news:1135545077.885565.149650@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > No. I suppose this is due to the assumption that space is uniform
and
| > isotropic.
| I'm not sure what it means for space to be uniform and isotropic.
Could
| you elaborate on this?
Basically just that the electric field strength will fall off
proportional to 1/distance^2 in any direction from the point source.
IOW, the inverse square law holds true no matter what direction you are
from the point source.
| Is there an assumption on a point charge that it produces a field that
| is symmetric?
Spherically symmetric? Yes, for classical electrodynamics due to the
inverse square law. Now for quantum electrodynamics, we have to realize
that a point-like charge would have to be an electron, muon, etc. Does
a "free" electron or muon have a spherically symmetric divergent E
field? I think we assume that they do. But do they really?
| Also, could it be something to do with Faraday's Law of induction? If
| there is no changing magnetic field, then the curl of E is 0. Thus
| somehow the electric field can't "spiral" (sorry for the vague
| description).
For a given "system" all of Maxwell's equations must hold true
classically.
| To elaborate further as the the point of my post: I would like to
| understand exactly what assumptions are made in current
electromagnetic
| theory, and to understand how everything else is derived from them.
|
| What seemed to be true is that the assumptions are Maxwell's equations
| (current version) + the Lorentz Force. However, is there another
| assumption that space is uniform and isotropic? Is there a reference
| available that very clearly states *all* the assuptions and derives
the
| other results from them - in that order. I am unable to find one. I
| know this may not be how it was found historically, but it is what I
| think will be useful to me.
|
| For example, the books I've looked at have started with Coulomb's Law,
| and used it to "derive" Gauss's Law. However, they then go on and use
| Gauss's Law for any electric field that is not constant, - it is used
| in the derivation of the speed of an electromagnetic wave. Thus
they've
| made an assumption that Gauss's Law applies in other than
electrostatic
| situations. Thus is looks like Gauss's Law is fundamental, and (as
I've
| read on
|
http://people.bu.edu/wwildman/WeirdWildWeb/courses/sl/resources/physics/em/em01.htm
| ) Coulomb's Law should be able to be derived from it - and not the
| other way around. Hence my orginal post and subsequent request for a
| reference that does it the "assumptions" -> "derivations" way.
I think you can just use the assumption that the inverse square law
holds true for classical electrodynamics is all you need. Oops... I
think there is also the "principle of superposition" that must be
assumed. Have you read and studied Griffiths' "Introduction to
Electrodynamics"? I think you need the principle of superposition to
get the static E field part of the Lorenz force law. Griffiths starts
his "Electrostatics" chapter with the principle of superposition.
FrediFizzx
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps
http://www.vacuum-physics.com
.
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