Magnets exert forces and torques on each other due to the rules of electromagnetism. The forces of attraction field of magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles (such as electrons) that make up the material. Both of these are modeled quite well as tiny loops of current called magnetic dipoles that produce their own magnetic field and are affected by external magnetic fields. The most elementary force between magnets is the magnetic dipole–dipole interaction. If all of the magnetic dipoles that make up two magnets are known then the net force on both magnets can be determined by summing up all these interactions between the dipoles of the first magnet and that of the second. It is often more convenient to model the force between two magnets as being due to forces between magnetic poles having magnetic charges spread over them. Positive and negative magnetic charge is always connected by a string of magnetized material; isolated magnetic charge does not exist. This model works well in predicting the forces between simple magnets where good models of how the magnetic charge is distributed are available. Magnetic poles vs. atomic currents The field of a magnet is the sum of fields from all magnetized volume elements, which consist of small magnetic dipoles on an atomic level. The direct summation of all those dipole fields would require three-dimensional integration just to obtain the field of one magnet, which may be intricate. In case of a homogeneous magnetization, the problem can be simplified at least in two different ways, using Stokes' theorem. Upon integration along the direction of magnetization, all dipoles along the line of integration cancel each other, except at the magnet's end surface. The field then emerges only from those (mathematical) magnetic charges spread over the magnet's end facets. On the contrary, when integrating over a magnetized area orthogonal to the direction of magnetization, the dipoles within this area cancel each other, except at the magnet's outer surface, where they (mathematically) sum up to a ring current. This is called Ampère model. In both models, only two-dimensional distributions over the magnet's surface have to be considered, which is simpler than the original three-dimensional problem. Magnetic-charge model: In the magnetic-charge model, the pole surfaces of a permanent magnet are imagined to be covered with so-called magnetic charge, north pole particles on