I have a circuit where at least some of the capacitance is coming from large, non-radiating, spherical conductors. I would like to model it in SPICE to better understand its operation-- is such a thing possible? The capacitors I have available are all two terminal devices...
I know that the capacitance of my sphere is \$C=4\pi\epsilon_0 r\$, where \$r\$ is the radius of the sphere. I'm trying to figure out how to represent that in a SPICE circuit.
Updated to address points made in comments and answers:
Here is what I originally meant by "not coupled":
The self capacitance of a sphere is \$4\pi\epsilon r\$, where \$r\$ is the radius of the sphere.
If I have two spheres of equal radius the capacitance is:
\$2\pi\epsilon r \sum_{n=1}^\infty \frac{\sinh\left(\ln\left(\frac{d}{2r}+\sqrt{\left(\frac{d}{2r}\right)^2-1}\right)\right)}{\sinh\left(n\cdot\ln\left(\frac{d}{2r}+\sqrt{\left(\frac{d}{2r}\right)^2-1}\right)\right)}\$, where \$d\$ is the distance between sphere centers.
The summation limits to 1 as \$d\$ goes to infinity, and the remaining terms can probably be interpreted as the self capacitance of each sphere in series. So the total capacitance is the self capacitance of each in series, plus, what I will call a "mutual capacitance" caused by interaction of the electric fields and which is a function of distance.
By “not coupled”, I’d meant that this distance dependent mutual capacitance term is arbitrarily small, leaving only the self capacitance. Probably the wrong choice of language. The capacitance value is not dependent upon anything else in the circuit, but obviously Gauss’ Law still holds.
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