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Two
errors, made by everyone for more than a century, have combined together to
cause dreadful problems in electromagnetic theory. The first is confusion over
the sign of time. When I walk three miles across town to catch the train, I
lose one hour. Thus, my velocity is (+3 miles)/(-one hour), or -3mph.
Similarly, when a TEM Wave travels in a vacuum down a transmission line, it
gains 300,000 miles for the loss of one second. Thus, its velocity is
–(300,000)/1 or
-c. The change of voltage with distance compared with the
change in time is –c, where c = 1/√µ€ . Thus, if we have
a voltage ramp travelling along at the speed of light, dv/dx is negative
because in the forward direction we have a ramp sloping down. However,
dv/dt is positive because at any point, the voltage is rising. Thus, dv/dx
= -c dv/dt . See the diagram
.
Now the
truth is that when a signal travels down a transmission line, v/i = Zo = a
constant. Also dv/di = Zo = k√(µ/€),
where k is a constant relating to the geometry of the conductors forming
the transmission line. Thus, if we substitute di for dv on one or other
side of the above equation dv/dx = -c dv/dt, we can get Zo di/dx = -c dv/dt , or dv/dx = -c Zo di/dt . This is where Lenz’s
Law rears its ugly head. It is accepted by everyone that electricity
resists the change of magnetic field, and the minus signs above, which
really only derive from our slovenly way of saying we walk at +3mph rather
than -3mph, are thought to imply causality between v and i. The minus sign
is nothing of the sort, as we can see by looking at another equation we can
concoct in the say way. If we have a voltage ramp travelling at the speed
of light, c dv/dx = -dv/dt, because c=dx/dt. Thus, if the minus sign makes us think that v causes i, we can
equally well make the idiotic assertion that v causes v.
The
second confusion results from our misinterpratation of Faraday’s Law.
Faraday did not deliver electric current down the wires into the primary of
his transformer . Rather,
he delivered a TEM Wave travelling at the speed of light guided by the
wires, which had both an electric (voltage) dimension and a magnetic
dimension. Much of the signal was reflected at the entry into the
transformer, and the rest was reflected at the far end of the transformer.
Some of the TEM Wave crosstalked into the secondary coil, and some of this
was emitted towards his galvanometer. What left the transformer and
travelled to the galvonometer was not electric current. It was a TEM Wave.
At every stage in the process, there was the appropriate amount of magnetic
field associated with the electric field. There was no trasfer between
electric energy and magnetic energy.
Faraday’s
experiment led everyone to conclude that changing magnetic field caused
electric current. It did not
. At every stage in his historic experiment, there was ExH energy current,
and nothing else.
These
two confusions give plausibility to the idea that when a sinusoidal signal
travels down a transmission line, the changing electric field causes a
changing magnetic field, and vice versa. To sustain this delusion, it is
important to overlook the fact that the electric field and the magnetic
field are in phase, so that change in one could not cause the other. That
is why their relative phase is never discussed in text books, and rarely
even drawn.
What
were the causes of this confusion, lasting for more than a century? One of
the causes is the adulation bestowed on people like Einstein and Feynman. We
are unable to think of the possibility that such men were human, and
thought this kind of thing through in a muddled way. If any mere mortal had
said what they said, careful analysis would have exploded it.
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