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Re: AC electricity



I would like to thank David Bowman for a very good
summary. The energy, according to this description, is
carried toward a load outside of wires (of negligible
resistance) while the current is flowing inside if them.
I have two questions:

1) Poyting vector is not discussed in many
introductory physics courses. Is this a serious
omission and a source of misconceptions?

2) Consider a purely ohmic load which is heated.
It is clear that energy must enter somehow into the
load. It arrives through the space surrounding wires
and goes into the load. How does this happen?

Suppose the load is a high R wire perpendicular to
the energy-guiding wires (see below). Near that
load the Poyting vector is directed everywhere into
the load. The energy of the field "enters the metal"
and is dissipated in it. Is this a correct explanation?
Ludwik Kowalski

David Bowman wrote:

Consider two long parallel wires going out horizontally away from you
in the direction in which you are facing. Assume one wire is situated to
the right of the other one. Suppose these two wires each carry a current
such that the current in each wire is the negative of the current in
the other wire. Maybe there is an energy source connected to your end
of the wires and there is some resistive load connected across the wires
at the distant end. Let's analyze the direction of energy flow along the
wires.

Case 1. The right hand wire (from your point of view) carries current
(using the usual positive convention for current) down the wire away
from you, and the left hand wire carries a return current back up the
wire toward you. Also, the right hand wire is assumed to have a
positive voltage relative to the left hand wire.

In this situation the magnetic field is relatively strong in the region
between the wires. The direction of the magnetic field there is
predominantly upward as the magnetic field lines converge below the
wires, go up between the wires, and split above them with half of them
looping back (rightward and down) around the right wire, and half of them
looping back (leftward and down) around the left wire. This magnetic
field pattern is determined by the assumed direction of the currents in
the wires via application of Ampere's law using the right hand rule for
each wire and superposing the results. Since the right side wire is
positive w.r.t. the left wire there is an electric field which is also
relatively strong in the region between the wires and this field points
to the left from the positive right side wire to the negative left side
wire in that intermediate region.

The energy current vector (EM energy transported per unit time per
unit area perpendicular to the direction of the flow) for this situation
is
given by the Poynting vector which is proportional to the cross product
of the electric and magnetic fields (E x H). Since in the region where
the fields are relatively strong H points up and E points to the left, we
see (via the right hand rule) that the cross product points down along
the wires away from you. Thus, we understand that the wires guide the
transport of EM energy down along the wires away from you.

Case 2. *Both* the direction of the current flow in the wires and the
electric polarity of the wires is reversed from that of case 1. Since
the currents are reversed the magnetic field is also reversed. And since
the electric polarity is reversed the electric field is reversed as well.
But (-E) x (-H) = E x H so we see that the Poynting vector, i.e. the
energy current *still* points down along the wire away from you, and EM
energy is still being transported down the wire to the supposed load at
the far end. ...