Capacitance of a system of 3 concentric spheres

[Anthony]

1. 3 conducting spheres of radius a, b, c (a<b<c) are held at a potential of 0, V, 0 respectively. What is the capacitance of the system?

2. Q=CV (which I assume extends to Q_i=C_ijV_j for multiple conductors).

3. I've calculated the fields in the two interesting regions, calculated the charge on each sphere - this gives Q_a+Q_b+Q_c=0.

I can't find many references to the "total capacitance" of a system of conductors and how it would relate to my C_ij. I might be missing the totally obvious, but that'll be down to my utter incompetence when it comes to physics!

Thanks for shedding any light on the matter. It shouldn't be too difficult, because the question comes from an undergraduate example sheet on introductory EM.

 

[member 553083]

The total capacitance of the system is equal to the sum of the individual capacitances of each sphere. The capacitance of a single isolated spherical conductor is given by C = 4πε0a,where a is the radius of the sphere and ε0 is the permittivity of free space. Therefore, the total capacitance of the system is given byCtotal = 4πε0(a + b + c).