A spherical conducting shell centered at the origin has radius R₁ and is maintained at potential V₁. A second spherical conducting shell maintained at potential V₂ has radius R₂ > R₁ but is centered at the point s ˆz where s 1.

(a) To lowest order in s, show that the charge density induced on the surface of the inner shell is

(b) To lowest order in s, show that the force exerted on the inner shell is

(c) Integrate the force in (b) to find the capacitance of this structure to second order in s.

o(0) = 0 R R(V - V) R - R - VD [R 3s R R R cose]. COS