surface integral of over any closed surface is independent of the free currents and picks out the "magnetic charges" within that closed surface: which does not depend on the free currents. The -field, therefore, can be separated into two independent parts: where is the applied magnetic field due only to the free currents and is the demagnetizing field due only to the bound currents. The magnetic -field, therefore, re-factors the bound current in terms of "magnetic charges". The field lines loop only around "free current" and, unlike the magnetic field, begins and ends near magnetic poles as well. Magnetism Most materials respond to an applied -field by producing their own magnetization and therefore their own -fields. Typically, the response is weak and exists only when the magnetic field is applied. The term magnetism describes how materials respond on the microscopic level to an applied magnetic field and is used to categorize the magnetic phase of a material. Materials are divided into groups based upon their magnetic behavior: Diamagnetic materials produce a magnetization that opposes the magnetic field. Paramagnetic materials produce a magnetization in the same direction as the applied magnetic field. Ferromagnetic materials and the closely related ferrimagnetic materials and antiferromagnetic materials can have a magnetization independent of an applied B-field with a complex relationship between the two fields. Superconductors (and ferromagnetic superconductors) are materials that are characterized by perfect conductivity below a critical temperature and magnetic field. They also are highly magnetic and can be perfect diamagnets below a lower critical magnetic field. Superconductors often have a broad range of temperatures and magnetic fields (the so-named mixed state) under which they exhibit a complex hysteretic dependence of on . In the case of paramagnetism and diamagnetism, the magnetization is often proportional to the applied magnetic field such that: where is a material dependent parameter called the permeability. In some cases the permeability may be a second rank tensor so that may not point in the same direction as . These relations between and are examples of constitutive equations. However, superconductors and ferromagnets have a more complex -to- relation; see magnetic hysteresis. Stored energy Energy is needed to generate a magnetic field both to work against the electric field that a changing magnetic field creates and to change the magnetization of any material within the magnetic field. For non-dispersive materials, this same energy is released when the magnetic field is