On March 27, 1997 Bob Sciamanda was trying to answer the previously asked
question. "Which laws would be violated if we allow a large fraction of
field lines (originating on the inner side of the Q=+90 nC disk) escape
"sidewise" rather than terminate on the inner surface of the opposite
plate (Q=-10 nC).
He said that this would impose the forbiden"crossing of the field lines".
Here is how I was originally thinking about lines, semi-quantitatively,
without imposing any line crossings. The center line is along the axis
but all lines originating at r=R/8, for example, bend and are captured
by the other plate at r=R/2. And lines originating at r=R/4 are captured
at r=0.9999*R. The remaining lines, those originating at r>R/4, are
"escaping". How many? It depends on radial distributions of charge
densities.
I now realize that this does not have to happen because of induction.
My simple picture would be an absolute necessity (Gauss's law) if there
were no mutual induction. You know this but induction was not on the list
of your semi-quantitative considerations. What is still not totally clear
to me, and I hope somebody will take Don's suggestion (to summarize main
points of our discussion) seriously, is the radial distribution of charge
densities on the plates facing each other.
Which laws are violated if we allow two non-uniform distributions of
charges be created as the result of mutual induction? The only thing to
consider, it seems to me, is minimization of potential energy. If a set
of non-uniform distributions results in a lower potential energy (as
compared with uniform distributions) then it will prevail. I plan to
focus on this during the weekend.