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Another puzzle



This is one of my favorites; not because of it's beauty or elegance or
subtlety, but because it brought the questions to a stop at my qualifying
exam. I apologize if it is trivial to some, but I suspect at least a few
will be bothered by it like the members of my committee were.

In my talk I had described an experimental apparatus which included a
capillary tube of glass used as a dielectric wave guide for a laser beam.
The beam was to travel along the hydrogen-filled capillary. One of my
transparencies illustrated several possible modes, and each one had E-field
lines terminating on the inner surface of the glass.

After the talk when the questioning began in earnest, one of the committee
members asked how the E-field lines could terminate on this non-conducting
surface without violating Gauss' Law. I thought for a moment (discounting
the possibility that the field could induce enough surface charge density
to save the situation) and then pointed out that apparently a
linearly-polarized, gaussian-shaded laser beam travelling through a vacuum
suffered the same deficiency.

At that point I was left a spectator to the ensuing arguments, and the
questions stopped.

Much later I came to the conclusion that I knew a qualitative answer, but
I've never pursued it beyond that.

Chip