A battery maintains the potential difference V between the spheres of a spherical capacitor with capacitance C. Move the center of the inner sphere away from the center of the outer sphere by an amount Δ and call the new capacitance C'.

(a) Use a symmetry argument to show that C' = C to first order in Δ.
(b) Use a force/energy argument to show that C' = C to first order in Δ.