 a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the dimensions of the source are reduced to zero while keeping the magnetic moment constant. it is a magnetic analogue of the electric dipole, but the analogy is not complete. in particular, a magnetic monopole, the magnetic analogue of an electric charge, has never been observed. moreover, one form of magnetic dipole moment is associated with a fundamental quantum propertyâthe spin of elementary particles. the magnetic field around any magnetic source looks increasingly like the field of a magnetic dipole as the distance from the source increases. == external magnetic field produced by a magnetic dipole moment == thumb|200px|upright|an electrostatic analogue for a magnetic moment: two opposing charges separated by a finite distance. each arrow represents the direction of the field vector at that point. thumbnail|200px|right|the magnetic field of a current loop. the ring represents the current loop, which goes into the page at the x and comes out at the dot. in classical physics, the magnetic field of a dipole is calculated as the limit of either a current loop or a pair of charges as the source shrinks to a point while keeping the magnetic moment  constant. for the current loop, this limit is most easily derived for the vector potential. outside of the source region, this potential is (in si units)  : {\mathbf{a}}({\mathbf{r}})=\frac{\mu_{0}}{4\pi r^{2}}\frac{{\mathbf{m}}\times{\mathbf{r}}}{r}=\frac{\mu_{0}}{4\pi}\frac{{\mathbf{m}}\times{\mathbf{r}}}{r^{3}}, with 4&pi; r2 being the surface of a sphere of radius r; and the magnetic flux density (strength of the b-field) in teslas is : \mathbf{b}({\mathbf{r}})=\nabla\times{\mathbf{a}}=\frac{\mu_{0}}{4\pi}\left(\frac{3\mathbf{r}(\mathbf{m}\cdot\mathbf{r})}{r^{5}}-\frac{{\mathbf{m}}}{r^{3}}\right). alternatively one can obtain the scalar potential first from the magnetic pole limit, :\psi({\mathbf{r}})=\frac{{\mathbf{m}}\cdot{\mathbf{r}}}{4\pi r^{3}}, and hence the magnetic field strength (or strength of the h-fi
Electric_and_magnetic_fields_in_matter Magnetism Magnetostatics