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Re: [Phys-l] phase and mplitude in E&M



On 09/20/2011 04:26 AM, chuck britton wrote:

Is it only for a traveling E&M wave in free space that the two waves
pass zero simultaneously?

Pretty much yes. For a pure traveling EM wave in free space,
it is absolutely guaranteed that E and B go together. They go
to zero together and do everything else together. Specifically,
we have either

E' = cB' [1a]
or
E' = -cB' [1b]

depending on which way the wave is traveling. Here E' is
pronounced "E prime" and denotes the total derivative of E
with respect to the scalar phase.

This applies to *any* running-wave waveform, including
arbitrary-shaped wave packets (not just sine waves).

We need the primes in equation [1]. That is, we can't just
write E = cB, because there could also be some stray static
field lying around that doesn't propagate. This is usually
not very interesting, but we might as well write the equation
properly, with the primes.

Well, no, I suppose a purely STANDING wave does too?

Nope.

For a standing wave, there are isolated places where E is
identically zero while B is oscillating (or vice versa), so
we can't even talk about phase at those points. Otherwise,
though, for the usual sinusoidal standing wave the E and B
are 90 degrees out of phase.

======

For more on all this, including the equations and even a
spacetime diagram, see:
http://www.av8n.com/physics/maxwell-ga.htm#sec-plane-waves