Here, B = βe 2 0 /4πε w ε 0 is the Bjerrum length in water and cos γ kt = cos ϑ k cos ϑ t + sin ϑ k sin ϑ t cos(ϕ k -ϕ t ) is the cosine of the spherical distance on the sphere. Note that the magnitude of ξ ik is determined by the ratio of κ B and κR. The charges in the linearized CR approximation that follow from Eq. ( ) are then obtained by solving a linear system of equations k