Suppose that a collection of image point charges q₁, q₂, . . . , q_N is used to find the force on a point charge q at position r_q due to the presence of a conductor held at potential ϕ_C. Let U_A be the electrostatic potential energy between q and the conductor. Let U_B be the electrostatic energy of q in the presence of the image charges. Find the general relation between U_A and U_B and confirm that U_A = 1/2U_B when ϕ_C = 0.