Re: Derivation of Coulomb's Law frorm Maxwell's Equations (Gauss's Law)

>>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 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'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.

> 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.

Nym

.

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