Re: Physics of Wireless Transmission

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>


This business of wireless transmission never seems to get
resolved to everyone's (or even anyone's!) satisfaction.  One
constantly turns up references to it, and explanations of it.
It was even mentioned in the daily paper the other day!

Many of the explanations I come across vaguely attribute the
power transfer to the current flow rather than an EM wave,
which is fair enough - up to a point.  That point is reached
when the explanation suggests that the power is carried, in some
sense, 'mechanically' by the flow of electrons, something like
in hydraulics where a fluid is pumped through a pipe to do work
at the far end.   In reality, the electrons, by virtue of their
presence and their freedom of movement, serve only to place a
constraint - a boundary condition - on the EM field in the
vicinity of the wire - which sometimes has the effect of guiding
EM waves along the wire to give that thing we call 'electricity'.

I don't think many on the list will have trouble with that, and
the discussion might then move towards a slightly different area
of confusion.   We find for example, explanations which say
that the coupling is purely electrostatic, for example, in much
the same way as the coupling across a transformer is thought of
as purely magnetic.   But when you look closely at these two
'pure' situations, you inevitably discover that the complimentary
field component is at work too, and the power transfer across the
system is found to be the usual integral of the cross product of
the two field components.     This shouldn't be any surprise when
you think about it - it's the only mechanism that EM offers for
energy and momentum transfer.

Now the dedicated enthusiasts might want to argue whether or not
such a coupling is considered to involve an EM wave.  Well there's
an EM field and it waggles up and down, so in that trivial
sense it's a wave alright.   But it's not 'propagating' in the
way we normally picture a radio wave as doing - is it?  The
'transmitter' and 'receiver', whether they are the windings
of a transformer or the plates of a capacitor, are never more
than a tiny fraction of a wavelength apart.  Nevertheless, the
same set of EM equations suffice to describe the behaviour
of the field in both cases, polarisation is important in both,
and in both cases the power transfer is quantified by that
integral again.   Apart from the proximity of source and load,
and the (apparent) prevalence of one or other field component,
the basic coupling mechanism is still fundamentally the same.
I think the terminologies we use: 'electric', 'magnetic', and
'electromagnetic', tend to exaggerate the difference to the point
where they sound like separate mechanisms, or more seriously,
are invoked as separate 'independent' mechanisms.   They're all
based on the same simple set of underlying equations, although
the picture is muddied a little because we tend to classify the
solutions of those equations, applying such labels as near-field,
far-field, induction field, and so on.  And we make matters worse
by disguising the specialised applications of the EM equations by
giving them names like circuit theory, transformer theory,
scattering theory, etc.

Whatever you label the EM interaction with in a wireless power
scheme, it must be expected to satisfy the usual set of equations,
unless you're going to propose some unknown new force.  There's
no mechanism available to support 'current mechanics' (if we can
credit with a name the assorted bag of 'hydraulic' explanations).
If you think you have a mechanism which is just using current or
just using an E or H field, then look more closely at it - you must
inevitably find that all three are present and, importantly, none
are indispensable when analysing the power transfer behaviour.

Gerry wrote:
> any E field that varies with time (aka electric wave) involves
> movement of charge that in turn creates an H field. Time varying
> E fields are always accompanied by a time varying H field.

> Even a static E field in one frame of reference will be a time
> varying E field in another moving frame of reference.

Bob wrote:
> But a time varying field must radiate but apparently only in
> the moving frame  !!!!!

There is no inconsistency here, nor really a paradox.  An observer
moving through a *uniform* static E-field will measure a uniform and
constant H component too, and so a uniform non-zero Poynting vector.

If the movement is 'across' the field, ie in the plane perpendicular
to the E-field, he will see E, H and velocity all mutually perpendicular
ie he will see a constant uniform power flow all around him, which is
natural - he is, if you like, witnessing the energy density of the
field passing by him. Both observers will agree on the field energy
density E^2 + H^2 [1], each using their own measured values of E
and H.   Movement in any other plane will just be some transformation
of the above.  Neither the 'static' or the moving reference frame
has any absolute significance as far as EM theory is concerned,
either is equally valid.

Suppose the field is non-uniform, eg the observer moves through the
E-field from a stationary charged object.   The observed E-field
will rise to a maximum value, then decay away as the observer leaves
the charged object behind.  Naturally, this time-varying E-field has
an H component too, thus a non-zero, non-uniform, time-varying
Poynting vector.  But there is no radiation to infinity. The 'lines'
of the Poynting field emerge from the source, loop outwards and
return back to their source.  The observer sees what is called an
evanescent field.  It's a radio wave that never gets launched to
infinity, its intensity typically dies away exponentially with
distance from the source, and its power flow loops or bounces back
to the source.

If the observer carries a charged object (as he must if he's going
to measure E and H) that object will exchange some energy and momentum
with the field - some of those looping Poynting lines will be inter-
cepted and terminate on the moving charge.  In response the source
charge will experience some reaction by the same mechanism working
simultaneously in the other direction.  We have an EM interaction
between the relatively moving charges - a scattering event in which
the two charged bodies, one of which we considered static, have
exchanged some energy and momentum and will have changed their
velocities accordingly.[2]

One important point: don't take these explanations too literally,
I'm describing properties of the EM mathematics, not the physical
situation.  Beware especially the Poynting vector.  It is just
a mathematical device, not a real field.  Only its integral over
a closed surface has any physical significance.  For example,
different observers will draw completely different maps of the
Poynting 'field' (some will have zero Poynting everywhere).  But
everyone will still be able to agree on the resulting behaviour
of any system immersed in the field.

BTW, the above is automatically compatible with SR, since the EM
equations themselves inherently are, but you don't need to invoke
relativity here to get a feel for what's going on.

Back to Tesla.  Has anyone ever made a list of all the different
explanations and proposals that Tesla offered for power transmission?

[1] ignoring trivial factors for clarity.

--
Paul Nicholson
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