# ABOUT MAGNETS   >   Terms in magnetism

## Basic terminology

### Magnetically hard material

Materials used for permanent magnets are referred to as a whole as "magnetically hard materials". Their basic magnetic property is an ability to retain a significant magnetic polarisation J even after the termination of the effect of an external magnetic field. The overall magnetic induction B in a material is given by the equation

B = mo . H + J
(1)

 where: H is magnetic field intensity [ A/m ] B is magnetic induction [ T ] J is magnetic polarisation [ T ] mo is vacuum permeability (4p. 10-7 Tm/A)

The magnitude of polarisation is proportionate to the magnitude of the magnetic field:

J = mo . (mr - 1) . H
(2)

where mr is the relative permeability

Equation (1) can alternatively be written in the form

B = mo . mr . H
(3)

### Hysteresis curve

The relationships J (H) or B (H) according to equations (2) or (3) characterise a magnetically hard material. The complete relationship curve from -Hmax to +Hmax and back is called the hysteresis loop. It is a reflection of the changes in the arrangement of the magnetic domains (Weiss domains) in a material. Basically, we distinguish two kinds of change: shifting of domain walls and rotation of magnetisation vectors. While the first mechanism is applied mainly in the area of lower fields, the second is important in the area of saturation. Fig.1 shows examples of both types of hysteresis curve. They differ by the additive component mo.H from equation (1). The relationship B(H) is more frequently used in technical practice, while the relationship J(H) is more useful in the field of material research.

### Characteristic parameters of a magnet

A permanent magnet is usually characterised by the following basic parameters: coercivity Hc remanence Bra maximum product (BH)max.

Coercivity Hc [ A/m ] is the magnetic field intensity that acts against the direction of spontaneous magnetisation until it reaches the overall material induction B = 0. The parameter Hc is a degree of the resistance of a magnet against demagnetisation (external field and the demagnetisation proper). Remanence Br [ T ] is the value of magnetic induction which will settle after magnetisation in the closed circuit of a magnet without the action of the external magnetic field. Fig. 1 shows that while the parameter Br is identical for both curve types B(H), J(H), the same does not apply to the parameter Hc. We therefore distinguish between coercivity HcJ and coercivity HcB. The maximum product (BH)max [  kJ/m3 ] (sometimes also termed the maximum energy product) is proportionate to the magnetic energy stored in a magnet having an optimum shape. The parameter (BH)max corresponds to the interactive force of a magnet against other ferromagnetic objects (mainly iron).

 Quantity Unit Conversion SI cgs Mag. field intensity H A/m Oersted (Oe) 1 A/m = 12,57.10E-3 Oe1 kA/m = 12,57 Oe Magnetic induction B Tesla (T) Gauss (G) 1 T = 1 Vs/m2 = 10E4 G1 mT = 10 G Magnetic polarisation J Tesla (T) Gauss (G) 1 T = 10E4 G1 mT = 10 G Magnetic flux F Weber (Wb) Maxwell (Mx) 1 Wb = 1 Vs = 10E8 Mx1 mWb = 10E 5 Mx Mag. energy density w J/m3 G.Oe 1 J/m3 = 1 Vs/m2.1 A/m = 1 T.A/m1 J/m3 = 0,1257.E3 GOe1 kJ/m3 = 0,1257.E6 GOe Vacuum permeability m0 T / (A/m) G / Oe m0 = 1,257.E-6 T / (A/m)      = 1,257.E-6 Vs / (Am)      = 1 G/Oe

## Magnetic circuit

A permanent magnet is often used in a magnetic circuit consisting of the magnet and pole shoes from a magnetically soft material, most frequently iron. This will ensure the optimum shaping of the poles and the air gap.

The calculation of a combined magnetic circuit is quite complicated. It is based on the application of the Biot-Savart principle and the magnetic flux conservation law. In the case of the circuit in Fig.3 the above-mentioned principles can be formulated as the equation

Hm . lm = g . Hg .lg
(4)

Bm . Am = s . Bg .Ag
(5)

 where: Hm, Bm field intensity or magnet induction lm, Am magnet length or cross-section Hg, Bg field intensity or gap induction lg, Ag gap length or cross-section g reluctance coefficient s escape coefficient

The coefficient g expresses the magnetic resistance of all magnetically soft and non-magnetic parts of the circuit (e.g. contact surfaces). In a high-quality circuit its value approaches 1. The coefficient s, which expresses the degree of escape of the magnetic flux from the gap, cannot be precisely determined due to a lack of suitable analytical calculation methods. In general, the procedure involves numerical methods during which the circuit is divided into a number of areas with different working points.

## Demagnetisation

As the term suggests, it is a process during which the overall magnetic polarisation in a magnet decreases. This can be the result of the effect of an external magnetic field in an opposite direction to the direction of polarisation. The process is called demagnetisation. In addition, every magnet is subject to the action of inner demagnetisation Hd, the origin of which is related to the principle of decreasing inner energy. The magnitude of Hd is given by the equation:

Hd = - Kd . J / mo
(3)

where Kd is the demagnetisation factor

The factor Kd depends on the shape of the magnet and the direction of magnetisation and its precise calculation is, in general, complicated. A simple formula is valid only for a rotational ellipsoid which, however, does not occur in practice. It is therefore determined using table values or various mathematical approximations. The general rule is that the greater the ratio of the dimension of the magnet in the direction of magnetisation and its perpendicular dimensions (sometimes called the magnet slenderness ratio), the lower is its demagnetisation factor. The relationship has the form of a hyperbole, i.e. decreasing the ratio to a half, for example, may well mean reducing Kd by a tenth or tenfold.

## Magnetisation methods

For a permanent magnet to perform its function, it is necessary to magnetise it after manufacture. The magnetic field intensity should reach at least three times the coercivity of the given material. Materials with a lower Hc value can only be magnetised after assembling the whole circuit. This can ensure the optimisation of the working point of the magnet.

Magnets with great coercivity are easier to magnetise separately, as there is no need to build special fixtures and eliminate forces generated during magnetisation.

The magnetisation of permanent magnets is mainly carried out using special magnetisers working on the principle of an electromagnet, the coils of which are supplied by pulse current of great magnitude, obtained by discharging condenser batteries or from a specially designed pulse source.

Sometimes it is required that all the magnets in a series have an identically set working point. This is achieved by repeated action of an increasing magnetic field of opposite polarity to the magnetic field after magnetisation. The magnitude of this demagnetisation field depends on the actually measured position of the working point in the pauses during demagnetisation.

## Temperature and time characteristics

### Curie temperature

With increasing temperature the magnetisation of all ferromagnetic materials decreases towards zero, the same also applies to permanent magnets. The temperature relationship is characterised by the so-called Curie temperature Tc, which is the intersection of the tangent of the descending section of the curve with the temperature axis (Fig. 4). When using permanent magnets it is necessary to ensure that the working temperature does not approach Tc, the safe distance is approx. up to 0.4 times Tc.

### Temperature compensating alloys

The relationship of magnet parameters with temperature cannot be avoided. When working with combined magnetic circuits this undesirable property can be eliminated by using a temperature compensating magnetic shunt, placed in parallel with the air gap of the magnet. Temperature compensating alloys have a steeply descending characteristic J (T). With increasing temperature the magnetic flux is driven by the shunt to the air gap as compensation for the loss in the flux due to the temperature characteristic of the magnet proper.

### Irreversible changes

Temperature and time changes of magnetisation are partly reversible and partly irreversible. The irreversible changes have their origin in the microstructure and the mechanism of magnetising the material. The action of time and temperature triggers off relaxation processes which lead to an increase in the inner energy. Macroscopically, the changes are manifested in reduced magnetisation, and possibly a reduction in other magnet parameters. However, the decrease is mostly insignificant. Where there is a requirement for an extended stability of properties over time, the magnet is subjected to artificial ageing, or alternatively thermal stabilisation (alternating temperatures). Before final magnetisation the magnet is exposed to the effects of an alternating magnetic field with a decreasing amplitude.

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