# Metallic Spheres

**Electricity and Magnetism**Level 3

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**

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