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] [2] 1 MGOe is equivalent to .[3]
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).[4] 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.
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):
(BH)\rm\equiv\operatorname{max}(-B ⋅ H).
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 is that the volume of magnet necessary for any given application tends to be inversely proportional to . This is illustrated by considering a simple magnetic circuit containing a permanent magnet of volume and an air gap of volume, connected to each other by a magnetic core. Suppose the goal is to reach a certain field strength in the gap. In such a situation, the total magnetic energy in the gap (volume-integrated magnetic energy density) is directly equal to half the volume-integrated in the magnet:[5]
E\rm=
| 1 | |
| 2\mu0 |
(B\rm)2{\rmVol}\rm=-
| 1 | |
| 2 |
B\rmH\rm{\rmVol}\rm=-E\rm,