If the potential Φ Φ arises from a set of charges of magnitude q i at positions ( r i , θ θ i , ϕ ϕ i ) , then the image potential will be the result of a series of charges of magnitude R q i / r i at positions ( R 2 / r i , θ θ i , ϕ ϕ i ) . It follows that if the potential Φ Φ arises from a charge density ρ ρ ( r , θ θ , ϕ ϕ ) , then the image potential will be the result of a charge density ρ ρ ′ ( r , θ θ , ϕ ϕ ) = ( R / r ) ρ ρ ( R 2 / r , θ θ , ϕ ϕ ) .