Both of these potentials can be calculated for any arbitrary current distribution (for the amperian loop model) or magnetic charge distribution (for the magnetic charge model) provided that these are limited to a small enough region to give: A ( r , t ) = μ μ 0 4 π π ∫ ∫ j ( r ′ ) | r − − r ′ | d V ′ , ψ ψ ( r , t ) = 1 4 π π ∫ ∫ ρ ρ ( r ′ ) | r − − r ′ | d V ′ , where j is the current density in the amperian loop model, ρ ρ is the magnetic pole strength density in analogy to the electric charge density that leads to the electric potential, and the integrals are the volume (triple) integrals over the coordinates that make up r ′ . The denominators of these equation can be expanded using the multipole expansion to give a series of terms that have larger of power of distances in the denominator. The first nonzero term, therefore, will dominate for large distances. The first non-zero term for the vector potential is: A ( r ) = μ μ 0 4 π π m × × r | r | 3 , where m is: m = 1 2 ∭ ∭ V r × × j d V , where × is the vector cross product, r is the position vector, and j is the electric current density and the integral is a volume integral.