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Re: Confused by a derivation.



If the equal-opposite charged capacitor is the only thing around, and if the
plates are large but not infinite, then one can imagine field lines outside.
Some of the charge on each plate is on the outside, the field lines start on
the outside of the positive plate and wrap around to end on the outside of
the negative plate. Indeed this is true of lab-sized capacitors.

Of course this is precluded if we are literally thinking of the plates as
infinite sheets. I suppose we were thinking that. In that case I think I
like the argument that there can be no charge on the outside surfaces
because there is no way (in the infinite plate case) for the field lines
starting on the outside positive charges to get to and then end on the
outside negative charges.

An obvious transition then popped into my mind that for some reason hadn't
been there before. As we shrink the infinite plates smaller and smaller,
the field line pattern gradually changes from being straight/uniform/inside
to the curved/non-uniform/inside&outside field line pattern we draw for a
dipole. Our lab capacitor is between these extremes. Whether it is more
like the infinite sheets or more like the dipole depends on the relation
between plate size and plate separation. Right now I am saying to myself...
duh... but I actually had not pictured that transition before... especially
in the opposite direction... i.e., if we start with the dipole pattern and
then start expanding the charge points as conductive planes, the field
outside the planes diminishes and diminishes and must become zero as the
planes become infinite.


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