A simple formula for the interaction energy of cylindrical multipoles (charge density 1) with a second charge density can be derived. Let f ( r ′ ′ ) be the second charge density, and define λ λ ( ρ ρ , θ θ ) as its integral over z λ λ ( ρ ρ , θ θ ) = ∫ ∫ d z f ( ρ ρ , θ θ , z )