Exchange spring magnet
The magnetostatic energy is the energy stored in the field generated by a material's magnetic moments. The magnet's field reaches its maximum intensity if all the magnetic moments orient in one direction; this is what occurs in a hard magnet. In order to prevent building up the magnetic field, sometimes magnetic moments tend to form loops. That way, the energy stored in the magnetic field can be constrained; this is what occurs in a soft magnet. What determines whether a magnet is hard or soft is the dominant term of its magnetic energy. For hard magnets, the anisotropy constant is relatively large, making the magnetic moments align with easy axis. The opposite case applies to soft magnets, in which the magnetostatic energy is dominant.
Magnetic field
Like all vector fields, a magnetic field has two important mathematical properties that relates it to its "sources". (For the "sources" are currents and changing electric fields.) These two properties, along with the two corresponding properties of the electric field, make up "Maxwell's Equations". Maxwell's Equations together with the Lorentz force law form a complete description of classical electrodynamics including both electricity and magnetism.