Re: sphere within a sphere

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: Mddeming-at-aol-dot-com
 >
 > Hi All,
 > I don't immediately see how it makes an improvement, but it brings up some
 > interesting questions. As I understand it, the two spheres are insulated
 > from each other, so that he has created a spherical capacitor with the
 > inner plate connected to the top of the TC. The outer sphere presents a
 > larger C(top) w/r to ground than the small one, but the two spheres are a
 > capacitor in series with C(top), which reduces net C(top)? (net change in
 > resonance??). What is the potential/polarity of outer sphere w/r to inner
 > one? w/r to ground?? These are going to require a lot more coffee (and
 > aspirin) for a Sunday morning than I have available right now. Any gurus of
 > simulation want to play with this?

Consider the simple case where the outer sphere has twice the radius of
the inner sphere. The model of the system in this case reduces to two
identical capacitances, one between the spheres and another from the
outer sphere to ground. Both capacitances are equal to the free-space
capacitance of the outer sphere. The terminal capacitance at low
voltage is then one half of the capacitance of the outer sphere, and
the potential at the outer sphere is one half of the potential at
the inner sphere (it is insulated). But as soon as the voltage grows
enough (even with the system detuned) and a spark connects the two
spheres, the terminal capacitance corresponds to the outer sphere
capacitance.
My Inca program can calculate the capacitances in this system, but what
it calculates is the capacitance matrix:
C11 C12
C12 C22
This corresponds to a model that has Ca and Cb between the spheres
and the ground and Cc between then, so:
Ca+Cc=C11
Cb+Cc=C22
Cc=-C12
Or: Ca=C11+C12, Cb=C22+C12, Cc=-C12
In the example, C11=C, C22=2*C, and C12=-C, and so Ca=0 and Cb=Cc=C.

Antonio Carlos M. de Queiroz