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The maximum energy product is defined based on the magnetic hysteresis saturation loop (B-H curve), in the demagnetizing portion where the B and H fields are in opposition. It is defined as the maximal value of the product of B and H along this curve (actually, the maximum of the negative of the product, −BH, since they have opposing signs):
Cassette tape label with coercivity (a measure of the external magnetic flux required to magnetize the tape) measured in oersteds The oersted is defined as a dyne per unit pole . [ clarification needed ] [ 6 ] The oersted is 1000 / 4π (≈79.5775) amperes per meter, in terms of SI units .
is the maximum energy product in units of J/m 3 (Joules per cubic meter) is the normal distance between the two parallel faces of the magnets; is the distance between the magnetic dipole axes of the two magnets.
The saturation remanence and coercivity are figures of merit for hard magnets, although maximum energy product is also commonly quoted. The 1980s saw the development of rare-earth magnets with high energy products but undesirably low Curie temperatures. Since the 1990s new exchange spring hard magnets with high coercivities have been developed ...
The total energy in the space occupied by the system includes a component arising from the energy of a magnetic field in a vacuum. This component equals U v a c u u m = B e 2 V 2 μ 0 {\displaystyle U_{vacuum}={\frac {B_{e}^{2}V}{2\mu _{0}}}} , where μ 0 {\displaystyle \mu _{0}} is the permeability of free space , and isn't included as a part ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Alnico's remanence (B r) may exceed 12,000 G (1.2 T), its coercivity (H c) can be up to 1000 oersteds (80 kA/m), its maximum energy product ((BH) max) can be up to 5.5 MG·Oe (44 T·A/m). Therefore, alnico can produce a strong magnetic flux in closed magnetic circuits, but has relatively small resistance against demagnetization.
The maximal energy density B·H max is proportional to J s 2, so these materials have the potential for storing large amounts of magnetic energy. The magnetic energy product B·H max of neodymium magnets is about 18 times greater than "ordinary" magnets by volume. This allows rare-earth magnets to be smaller than other magnets with the same ...