Re: [Phys-l] Poynting Vector

[chuck britton <britton@ncssm.edu>]

Many thanks, Tom, for this insight.

At the risk of running this vector into the ground, I'd like to offer  
an example from Feynmann. It's not his exact setup - but I believe it  
does successfully show that SOMETHING with physical significance is  
flowing

Consider a short, superconducting solenoid in free space.
Short, because we must make use of the non-zero field outside the  
solenoid.

Put a (charged) coaxial  capacitor around the solenoid and coaxial  
with it.

Everything is at rest (except for the charges flowing in the solenoid  
- which could be positive OR negative with no difference in outcome).

At a given time, the solenoid 'goes normal' with negligible external  
interference.

Once the current is zero - the setup is seen to be rotating in space  
with a calculable angular velocity.

Question - since there is evidently some angular momentum in the  
initial picture - can it be equal to the angular momentum of the  
energy flow associated with the Poynting Vector which existed between  
the capacitor plates?


		This is not intended to reproduce Feynmann's example - but I am  
(perhaps incorrectly) assuming the same phenomena are involved.


On Jun 30, 2008, at Jun 30(Mon) 9:52 , Tom Sandin wrote:

> In SI, the Poynting vector is defined to be the vector product E
> cross H (where H equals B/musubzero in the nonmagnetic dielectric of
> the capacitor). The Poynting vector has unit W/m^2 and so some
> incorrectly believe that it always gives the em power transferred per
> perpendicular area.
>
> To quote Reitz and Milford (2nd ed), "It is tempting to interpret E
> cross H itself as the energy flow per unit time per unit area. The
> latter interpretation, however, leads to certain inconsistencies; the
> only interpretation which survives careful scrutiny is that the
> integral of E cross H over a CLOSED surface represents the rate at
> which electromagnetic energy crosses the CLOSED surface." (my
> emphasis).
>
> I use the example of crossed static E and B fields to show the
> fallacy of assuming the Poynting vector always gives the em power
> transferred per perpendicular area.
>
> Tom Sandin