# 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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