Re: Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)
- From: "FrediFizzx" <fredifizzx@xxxxxxxxxxx>
- Date: Tue, 27 Dec 2005 11:39:46 -0800
"nym" <neverwillreply@xxxxxxxxx> wrote in message
news:1135695525.426597.115060@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| >>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.
| So you have to assume this? This sounds like assuming that Coulomb's
| Law holds. However, I am trying to derive Coulomb's Law from Gauss's
| Law (like on
|
http://people.bu.edu/wwildman/WeirdWildWeb/courses/sl/resources/physics/em/em01.htm
| ) This to me is assuming what I am trying to prove. What's the
| difference between Coulomb's Law and space being uniform and
isotropic?
I don't think it is quite the same. There is nothing in Coulomb's law
about the "direction" part of this assumption.
| > 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.
| 1. I am trying to find the assumptions for classical electromagnetism,
| so would I also need an assumption about the magnetic field?
| 2. The derivations of Gauss's Law I've seen derive it for an electric
| field from a static charge. However, Gauss's Law is used where the
| electric field is not static, such as in the derivation of the speed
of
| an electromagnetic wave. Would these proofs hold in situations such as
| these where the electric field is not static such as in an
| electromagnetic wave? I don't really see how.
I do believe all four Maxwell's equations are required for the
derivation of the speed of an EM wave.
| I've found another page
|
http://www.ieee-virtual-museum.org/collection/tech.php?id=2345877&lid=1
| that says that Maxwell's equations are "first principles", where they
| are not derived from other equations. I imagine it means these are
just
| first principles for classical electromagnetism. If this is the case
| (which is the point I am trying to argue) then I should be able to
| derive Coulomb's Law from these.
It is possible to derive Maxwell's equations from Coulomb's law and
Special Relativity. So you should be able to get Coulomb's law by the
reverse procedure. Then I guess the assumptions would be those of SR?
| > 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.
| No - but I have just checked - it is in the library here so I will
take
| a look. I've been looking at Bleaney and also at Duffin.
OK, good. Hope it helps.
FrediFizzx
.
- References:
- Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)
- From: nym
- Re: Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)
- From: FrediFizzx
- Re: Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)
- From: nym
- Re: Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)
- From: FrediFizzx
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