Re: Maxwell's equations

parbuckle@grapevine.net.au

drl wrote:

> Get a copy of Panofsky and Phillips and study chapter 1 until it is in
> your bones. They prove the following theorem:

> Give any vector field V (satisfying natural differentiability
> conditions) and let

> D = div V
> C = curl V

> Define

> phi(x,y,z) = (1/4pi) integral over all space ( D(X,Y,Z) / R ) dX dY dZ
> A(x,y,z) = (1/4pi) integral over all space ( C(X,Y,Z) / R ) dX dY dZ
> where R = sqrt ( (x - X)^2 + (y - Y)^2 + (z - Z)^2 ) and the integration
> is over X,Y,Z. Then

>V = -grad phi + curl A

> If s -> 0 and C -> 0 at infinity, then this resolution is unique. The
> import of this theorem is - if there are no sources at infinity, then a
> vector field is uniquely determined by its divergence and curl. One
> cannot overstate the importance of this result for a proper understanding
> of EM.
> Corollary - any non-uniqueness in the resolution of a vector
> field in terms of its sources must come from additional sources at
> infinity.

My question:

Does the theorem above apply to fields that depend on time or only to
static fields?