Re: [Phys-l] Poynting Vector

[John Mallinckrodt <ajm@csupomona.edu>]

I wrote:

> It's coming from one side and going to the other.  ;-)

But I probably should have added that the fringing fields guide it in  
the other direction on the outside back around to the start so that  
it isn't really "coming from" or "going to" anywhere.

This would seem to be a special case of what I think must be a  
perfectly general statement about the flow of EM energy (and, thus,  
momentum) around a static charge distribution immersed in a uniform  
magnetic field.  In such a case, the magnitude of the integral of the  
Poynting flux over all space is proportional to the magnitude of the  
integral of the electric field vector over all space.  Since every  
infinitesimal charge produces a spherically symmetric electric field  
with a vanishing integral over all space, the superposition principle  
guarantees that the integral of any arbitrary electrostatic field  
over all space is also zero.

Thus, there can be no net energy or momentum flow in the case under  
consideration or any other involving an electrostatic E field in a  
uniform B field.

Of course, as Curtis and Brian have intimated, none of this  
necessarily applies to an electrodynamic situation.

John Mallinckrodt
Cal Poly Pomona

> On Jun 28, 2008, at 9:48 AM, Jeffrey Schnick wrote:
>
> > Consider a charged simple parallel plate capacitor in a static  
> > uniform
> > downward-directed magnetic field.  The capacitor is oriented so that
> > from our point of view, the electric field between the plates of the
> > capacitor is directed rightward.  Poynting tells us that between the
> > plates, energy is flowing away from us at a rate proportional to EB.
> > Where is that energy coming from and going to?