Maximum energy product

[4] Other important permanent magnet properties include the remanence (Br) and coercivity (Hc); 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 (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): 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).

Suppose the goal is to reach a certain field strength Bgap in the gap.

By choosing a magnetic material with a high (BH)max, and also choosing the aspect ratio of the magnet so that its −BH is equal to (BH)max, the required volume of magnet to achieve a target flux density in the air gap is minimized.