Conversely, if the radius ρ ρ of the observation point is less than the radius ρ ρ ′ of the line charge, we may factor out ( ρ ρ ′ ) 2 and expand the logarithms in powers of ( ρ ρ / ρ ρ ′ ) < 1 Φ Φ ( ρ ρ , θ θ ) = − − λ λ 2 π π ϵ ϵ { ln ⁡ ⁡ ρ ρ ′ − − ∑ ∑ k = 1 ∞ ∞ ( 1 k ) ( ρ ρ ρ ρ ′ ) k [ cos ⁡ ⁡ k θ θ cos ⁡ ⁡ k θ θ ′ + sin ⁡ ⁡ k θ θ sin ⁡ ⁡ k θ θ ′ ] } which may be written as Φ Φ ( ρ ρ , θ θ ) = − − Q 2 π π ϵ ϵ ln ⁡ ⁡ ρ ρ ′ + 1 2 π π ϵ ϵ ∑ ∑ k = 1 ∞ ∞ ρ ρ k [ I k cos ⁡ ⁡ k θ θ + J k sin ⁡ ⁡ k θ θ ] where the interior multipole moments are defined as Q = λ λ , I k = λ λ k cos ⁡ ⁡ k θ θ ′ ( ρ ρ ′ ) k , J k = λ λ k sin ⁡ ⁡ k θ θ ′ ( ρ ρ ′ ) k .