Gene Fuller wrote:
Cecil Moore wrote:
Poynting vector = ExH = E*H*sin(A)
Incorrect. The Poynting vector is defined as E x H*. The vector
directions are critically important.
Those who don't remember what the cross product is,
please reference:
http://en.wikipedia.org/wiki/Cross_product
Another name for the cross product is the vector product.
Quoting "Fields and Waves ..." by Ramo & Whinnery:
Poynting vector = ExH These are, of course, vectors.
Quoting "Reference Data for Radio Engineers":
ExH is called the Poynting vector. Again, vectors.
The average Poynting vector is defined as
Re(E x H*)/2 in my references.
So your "Incorrect." assertion above is proven to
be incorrect.
The Poynting vector for a pure standing wave = 0.
Says who? Perhaps the time and space averages or "net", whatever that
means, but not the local instantaneous Poynting vector.
Let's deal with the average Poynting vector. The real
power in the fields is equal to the magnitude of the
average Poynting vector. There is zero real power in
the standing waves. Therefore, the average Poynting
vector is zero at every point on a line containing
pure standing waves.
So, using Occam's razor, here's the same question
for you stated in a different way.
If E and H* are both non-zero, how can the following equation
be equal to zero all up and down the line as we know it is for
standing waves?
Pav = Re(E x H*)/2 = 0 where E 0 H*
It is always zero even when both E and H are not zero.
Nonsense. It is E x H* at every point. If E or H is zero then the
Poynting vector is zero. Otherwise it will not be zero.
True for a uniform plane wave. But I have already proved
that a standing wave is not a uniform plane wave.
Pav = Re(E x H*)/2 = zero for a standing wave. I hope
you don't question that fact of physics.
The answer is that you have started with incorrect equations.
The answer is exactly what you have been missing. Please
solve the updated problem above.
It is obvious that if V*I*cos(A) = 0, then Re(E x H*)/2
must also be zero even when E and H* are not zero. How
do you explain that fact?
--
73, Cecil
http://www.w5dxp.com