Oh... so close. For a moment I thought John Mallinckrodt did it... showed
that E outside the capacitor had to be zero. But then Bob's sharp eyes
noticed that John's equation 6 has a sign error. I think Bob is right. So
John's wonderfull approach has brought us right back where we started.
Gauss' Law can show that the fields on each outside region of the capacitor
have to be equal, but cannot show they have to be zero.
When I first read John's logic I made the same error that he probably made.
I said, of course, E3 has to be the negative of E1 for the surface with both
end caps outside. But that scenario requires that the FLUX into the surface
in reagion 3 be the negative of the flux into the end cap in region 1. And
in that geometry the fluxes are opposite when the fields point the same
direction.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817