Question

A system consists of two thin concentric metal shells of radii R₁ and R₂ with corresponding charges q₁ and q₂. Find the selfenergy values W₁ and W₂ of each shell, the interaction energy of the shells W₁₂, and the total electric energy of the system.

Answer 1

Self energy of each shell is given by qφ/2 where φ is the potential of the shell, created only by the charge q, on it. 

Hence, self energy of the shells 1 and 2 are :

The interaction energy between the charged shells equals charge q of one shell, multiplied by the potential φ, created by other shell, at the point of location of charge q.