Re: [Phys-l] Capacitance problem

[mrmeyer@mtu.edu]

> If you want some more hints (including the solution), see:
>   http://www.av8n.com/physics/capacitive-divider.htm
I showed the author of the problem (who asserted its unsolvability) your
solution.  This is his response:

The assumption that the voltage across C1 does not change when
the switch is opened is flawed.  While it is true that
no current flows, the charge can redistribute and the
electric field due to that unbalanced charge across C1,
is no longer solely confined between the plates of the
capacitor.  Hence the voltage can change and the electric
field external to the capacitor can interact with the room
giving a very "environmentally sensitive" result.

The problem is that the two capacitance values given
are insufficient to describe the electromagnetic
situation -- one relevant discussion I found is in Berkeley
Physics series, Volume II, "Electricity and Magnetism"
by Purcell (near page 100).  There are three conducting
objects here: the infinite ground, the upper plate of C2 connected
to the lower plate of C1, and the upper plate of C1 (and any
wire attached).  There will be three coefficients relating
charge on those objects to their potentials.  Only two
coefficients are given.  I contend this problem cannot
be solved (correctly) because there is insufficient data given.

There may be cases where making an assumption about that
third value is a good approximation.  Explicitly adding a
capacitor C3 from node V1 to ground (modeling the third value
needed) leads to a (correct) solution, but the value of C3
needs to be known to get an answer and/or a limit taken if
one wants to assume it is "small."

Putting in resistors is a good idea.

- BHS