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From: gjk@talcott.UUCP (John)
Newsgroups: net.physics
Subject: Re: Cancelling EM waves
Message-ID: <507@talcott.UUCP>
Date: Mon, 16-Sep-85 18:05:55 EDT
Article-I.D.: talcott.507
Posted: Mon Sep 16 18:05:55 1985
Date-Received: Thu, 19-Sep-85 06:40:33 EDT
References: <543@sri-arpa.ARPA>
Organization: Harvard
Lines: 33

In article <543@sri-arpa.ARPA>, DHowell.ES@Xerox.ARPA writes:
> Let's say I have a device that emits an electromagnetic wave...
> Now I set up another one of these, and place it exactly one wavelength
> away from the other.  I have them emit in the same direction so that the
> waves overlap and are in phase.  Now the output of this system is an
> electromagnetic wave with the same frequency and twice the amplitude.
> I'm putting twice as much energy in and getting twice as much energy
> out.
> 
> Here's the question...  If I place them half a wavelength apart so that
> they are 180 degrees out of phase, the waves will cancel...

First of all, the amount of energy in an electromagnetic wave is proportional
to the square of the amplitude, so if the devices are completely in phase, the
energy output will be four times as large.  So something is definitely amiss.

The answer is that the amount of work it takes to create an electromagnetic
wave (or any electromagnetic field, for that matter) depends on the
pre-existing electromagnetic field.  This is analogous to mechanical force and
energy:  If you apply a constant force to an object, the amount of energy
transferred to the object depends on its velocity.

We can also analyze your specific example.  Any device that emits light does
so because electrically-charged particles in it are vibrating.  It is not only
the case that a vibrating charged particle creates an electromagnetic wave,
but also an electromagnetic wave causes a charged particle to vibrate.
Anyway, the electromagnetic wave from the first device would cause those very
particles in the second device to vibrate, and would therefore change the
behaviour (either amount of output or the energy consumption) of the second
device in such a fashion that energy is conserved.
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