Metallic Spheres

Consider a system of three concentric metallic spheres with radii \(R_{1}= 10 cm, R_{2}=30 cm\) and \(R_{3}=40 cm\). The inner (\(R_{1}\)) and the outer (\( R_{3} \)) spheres are grounded (they are connected to a large conductor at zero potential ). The relation between the charge Q of the middle sphere and its potential V is linear \[ Q= C_{self} V.\] The coefficient \( C_{self} \) is called self-capacitance. Determine \(C_{self}\) in Farads for the middle sphere.

Details and assumptions

\[ k=\frac{1}{4\pi \epsilon_{0}}= 9\times 10^{9} m/F\]

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