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# The Joy Of Poynting Vectors.

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• Subject: The Joy Of Poynting Vectors.
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• Date: Fri, 22 Apr 2005 07:59:19 -0600
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Original poster: "Steve Conner" <steve.conner@xxxxxxxxxxx>

Hi all

>http://www.itee.uq.edu.au/~aupec/aupec00/edwards00.pdf

That's a very interesting paper. If you're a real sucker for punishment you
can analyse the power flow in a Tesla coil just the same way. You can also
prove that electrical power- whether AC or DC- and no matter what the
frequency- does not travel in wires. Poynting vector analysis says there can
be no power flow unless both E and H fields are present, and there can be no
E field inside a conductor. So the electrical power must be flowing in space
around and between the wires of a circuit, just like Paul Nicholson says in
his piece on "non-Hertzian" waves. But I digress.

The Poynting vector is the cross product of the electric and magnetic
fields. It shows the direction that power is flowing in a system of EM
fields. It's the same as the "direction of propagation" of a radio wave that
you get taught in your ham radio licence classes.

If you're not keen on math, "cross product" just means the right hand rule
thing. If you drew some arrows on a piece of paper with the E field pointing
up and the H field pointing to the left, the Poynting vector would be
sticking out of the page at you. (disclaimer for US readers- don't sue me if
you poke yourself in the eye with it) The magnitude of it is equal to
(magnitude of E times magnitude of H times cosine of phase angle between
them) IIRC. It's a long time since the last math lecture I slept through.

Anyway back to Tesla coils. If you look at the fields at the surface of the
secondary winding, there is a H field normal to the wire (ie along the
length of the secondary) caused by the primary current, and an E field along
each turn of wire caused by the secondary voltage. If you wave your fingers
and thumb around for a bit you can see that the Poynting vector associated
with these fields points from the primary coil towards the secondary.

If the relative phase of one of the fields reverses (because the H field of
the secondary current overcomes the H field of the primary current or
whatever) then the Poynting vector turns round and points the other way.
This is what happens at the "notch" in primary current.

This is my interpretation of it anyway. Maybe someone who knows more about
these things- like Paul Nicholson- could comment?

Steve Conner