Re: [Phys-l] Poynting Vector

[chuck britton <cvbritton@embarqmail.com>]

but - - - - -

	The Poynting vector is non-zero only within the capacitor		nicht whar?

	But the space filling Vector  Potential (A?) doesn't give a hoot  
about the charged capacitor	(or does it??) (I'll wager it DOES)

	Would Feynmann's solenoid rotate if there were no charge in the  
picture?



(GAD - Corson & Lorain was a LOOOOOOONG time ago)


On Jun 30, 2008, at Jun 30(Mon) 1:12 , John Denker wrote:

> On 06/30/2008 09:47 AM, chuck britton wrote:
> > If I remember correctly, Feynmann related the angular momentum to the
> > 'Vector Potential' of the B field.
>
> It's *all* related.  You can't have a vector potential without
> having a B-field somewhere, and vice versa.  You can express the
> physics in terms of A or in terms of B;  the words are different
> but the physics is the same.
>
> > This makes it independent of the Poynting Vector??
>
> No, not independent.  It's *all* related.
>
> > I'm thinking it might be related to the 'flow' of energy in the
> > capacitor.
>
> Sure.  It's *all* related.
>
> In this case, the relationship can be understood in terms of the
> symmetry of the stress-energy tensor.  (See previous note.)  In
> particular,
>  a) the top row T(0,...) is the same as
>  b) the left column T(...,0).
>
> The point is that
>  a) the spacelike part of the left column represents the energy
>   flowing in the x,y,z directions.
>  b) the spacelike part of the top row represents momentum in the
>   x,y,z directions that doesn't flow anywhere in space;  it just
>   sits there in space.  (You can say it "flows" toward the future,
>   if you want to take a four-dimensional view of the situation).
>
> Bottom line:  Yes, the energy-flow is related to the momentum.
> "Related" as in "identical" (up to meaningless factors of c).
>
> Reference:  Electromagnetic stress-energy tensor:
>   http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor
>
> Reference:  Conservative flow in spacetime:
>   http://www.av8n.com/physics/conservative-flow.htm
>
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