Physics of Magnetism

12

Permanent Magnets

12.1. INTRODUCTION

showing a broad hysteresis loop and a concomitant high coercivity. The remanence

determines the flux density that remains after removal of the magnetizing field and hence

is a measure of the strength of the magnet, whereas the coercivity

Permanent-magnetic materials are characterized by a field dependence of the magnetization

is a measure of the
resistance of the magnet against demagnetizing fields (see Fig. 8.2). The performance of a
magnet is usually specified by its energy product, defined as the product of the flux density
B and the corresponding opposing field H. If the hysteresis loop for a given magnet material
is available, the energy product of a particular magnet body made of this material can be
derived relatively easily. We illustrate this by means of Fig. 12.1.1, where we compare two
different types of magnet materials (A and B). In the left panels of the figures, the second
quadrants of the hysteresis loops of the two magnet materials are shown. In both cases,
these loops have been measured on samples of the magnet materials having the form of
long cylinders so that demagnetizing effects can be neglected see Table 8.1).
In the second quadrant, the direction of the external field is opposite to the flux density.
Each point on the B–H curve can be taken to represent the working point of a magnet
body subjected to its own demagnetizing field. Small demagnetizing fields and working
points close to the B axis apply in general to elongated or rod-shaped (the length of the rod
being large compared with its diameter) magnet bodies in their own demagnetizing field.
By contrast, the working points of a magnet body with a flat or disk-like shape correspond
to much larger demagnetizing fields and hence are located closer to the H axis. The energy
products B H for low or high demagnetizing fields, that apply to the two mentioned types of
magnet shapes, are relatively small as can be derived from the low values of the surface area
of the corresponding B H rectangles. The energy products (horizontal scale) corresponding
to all points of the B(H) curve are plotted as a function of the flux density (vertical scale)
in the right-hand parts of the figure. The largest possible value of the energy product for
each magnetic material is indicated by The corresponding working points are
indicated on the B(H) curves of both magnet materials as a filled and an open circle.

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