Maximum energy product

In magnetics, the maximum energy product is an important figure-of-merit for the strength of a permanent magnet material. It is often denoted and is typically given in units of either (kilojoules per cubic meter, in SI electromagnetism) or (mega-gauss-oersted, in gaussian electromagnetism). 1 MGOe is equivalent to .
During the 20th century, the maximum energy product of commercially available magnetic materials rose from around 1 MGOe (e.g. in KS Steel) to over 50 MGOe (in neodymium magnets). Other important permanent magnet properties include the remanence () and coercivity (); these quantities are also determined from the saturation loop and are related to the maximum energy product, though not directly.
Definition and significance.
The maximum energy product is defined based on the magnetic hysteresis saturation loop (- curve), in the demagnetizing portion where the and fields are in opposition. It is defined as the maximal value of the product of and along this curve (actually, the maximum of the negative of the product, , since they have opposing signs):
Equivalently, it can be graphically defined as the area of the largest rectangle that can be drawn between the origin and the saturation demagnetization B-H curve (see figure).
The significance of can be illustrated by considering a simple magnetic circuit containing a permanent magnet of volume and an air gap of volume . The total magnetic energy in the gap (volume-integrated magnetic energy density) is then directly related to the volume-integrated in the magnet:
thus in order to achieve a particular magnetic field in the gap, the required volume of magnet can be minimized by maximizing in the magnet (by choosing a material with high , and operating it at the point by matching the magnet geometry to the circuit's reluctance).