Magnetic permeability

“ The coefficient of magnetic induction varies with the material of the
induced mass, and varies with the intensity of the magnetizing force.
This variation is due to the fact that as the induced magnetism in a
body increases, the magnetizing force required to maintain such
induction, increases in a more rapid ratio. The coefficient of magnetic
induction is the same as magnetic permeability, and in a certain sense
is the analogue of conductivity. It is also termed the multiplying power
of the body or core magnetized. ”

“ The permeability of a metal belonging to the ferromagnetic class—iron, nickel, cobalt and some of their alloys—is a function of the magnetic force, and also depends upon the previous magnetic history of the specimen. As the force increases from zero the permeability of a given specimen rises to a maximum, which may amount to several thousands, and then gradually falls off, tending to become unity when the force is increased without limit. Every other substance has a constant permeability, which differs from unity only by a very small fraction ”

“ For particular purposes it is necessary to obtain the highest possible magnetic permeability corresponding to a high, or the highest attainable flux density. This is generally the case in the electromagnets which are employed as the field magnets in dynamo machines. It may generally be said that whilst the best wrought iron, such as annealed Low Moor or Swedish iron, is more permeable for low flux densities than steel castings, the cast steel may surpass the wrought metal for high flux density. ”

“ The magnetic susceptibility κ expresses the numerical relation of the magnetization to the magnetizing force. From the equation κ = (μ − 1) /4π, it follows that the magnetic susceptibility of a vacuum (where μ = l) is 0, that of a diamagnetic substance (where μ < l) has a negative value, while the susceptibility of paramagnetic and ferromagnetic substances (for which μ > 1) is positive. No substance has yet been discovered having a negative susceptibility sufficiently great to render the permeability (= 1 + 4πκ) negative. ”

“ For the details of various forms of permeameter and hysteresis meter technical books must be consulted.3
An immense number of observations have been carried out on the magnetic permeability of different kinds of iron and steel, and in the following tables are given some typical results, mostly from experiments made by J.A. Ewing (see Proc. Inst. C.E., 1896, 126, p. 185) in which the ballistic method was employed to determine the flux density corresponding to various magnetizing forces acting upon samples of iron and steel in the form of rings. ”

“ Unfortunately the Committee did not take into account the fact that in the first case the force between the electric charges depends upon and varies inversely as the dielectric constant of the medium in which the experiment is made, and in the second case it depends upon the magnetic permeability of the medium in which the magnetic poles exist. ”

“ These expressions show that the thicker the screen and the greater its permeability μ, the more effectual will be the shielding action. Since μ can never be infinite, complete shielding is not possible.
Magneto-Crystallic Phenomenon.—In anisotropic bodies, such as crystals, the direction of the magnetization does not in general coincide with that of the magnetic force. There are, however, always three principal axes at right angles to one another along which the magnetization and the force have the same direction. ”

“ They produce lines of force which may exhaust the
permeability of the iron, or may, if in an opposite direction, add to
its apparent permeability.
Magnetic Induction, Coefficient of.
The number, obtained by dividing the magnetization of a body, expressed
in lines of force produced in it, by the magnetizing force which has
produced such magnetization, expressed in lines of force producible by
the force in question in air. It always exceeds unity for iron, nickel
and cobalt. It is also obtained by multiplying the coefficient of
induced magnetization by 4 PI (4 * 3.14159) and adding 1. ”

“ For strong magnetizing forces (which in these experiments did not exceed H = 48.9) the permeability remains almost constant at its initial value (about 400) , until the temperature is within nearly 100° of the critical point; then the permeability diminishes more and more rapidly until the critical point is reached and the magnetization vanishes. Steel behaves in a similar manner, but the maximum permeability is not so high as in iron, and the fall, when the critical point is approached, is less abrupt. ”

“ The intensity (at any point) of the field due to the magnetization may be denoted by Hi, that of the external field by H0, and that of the resultant field by H. In certain cases, as, for instance, in an iron ring wrapped uniformly round with a coil of wire through which a current is passing, the induction is entirely within the metal; there are, consequently, no free poles, and the ring, though magnetized, constitutes a poleless magnet. Magnetization is usually regarded as the direct effect of the resultant magnetic force, which is therefore often termed the magnetizing force. ”

“ Bismuth, the strongest of the diamagnetics, has a negative susceptibility which is numerically 20 times less than that of liquid oxygen.
Many of the physical properties of a metal are affected by magnetization. The dimensions of a piece of iron, for example, its elasticity, its thermo-electric power and its electric conductivity are all changed under the influence of magnetism. On the other hand, the magnetic properties of a substance are affected by such causes as mechanical stress and changes of temperature. ”

“ We represent to ourselves magnetization as a separation of the magnetic fluids. Admitting this representation, the mode of action of the fluids (repulsion of similar and attraction of dissimilar particles inversely as the square of the distance) belongs to the number of established physical truths. No alteration in the results would be caused by changing this mode of representation for that of Ampère, whereby, instead of magnetic fluids, magnetism is held to consist in constant galvanic currents in the minutest particles of bodies. ”

“ Analogous changes are observed in the residual magnetization which remains after the wire has been subjected to fields of different strength. The effects of longitudinal pressure are opposite to those of traction; when the cyclic condition has been reached, pressure reduces the magnetization of iron in weak fields and increases it in strong fields (Ewing, Magnetic Induction, 1900, 223) .
The influence of traction in diminishing the susceptibility of nickel was first noticed by Kelvin (W. Thomson) , and was subsequently investigated by Ewing and Cowan. ”

“ If the structure of the molecule is so perfectly symmetrical that, in the absence of any external field, the resultant magnetic moment of the circulating electrons is zero, then the application of a field, by accelerating the right-handed (negative) revolutions, and retarding those which are left-handed, will induce in the substance a resultant magnetization opposite in direction to the field itself ”

“ But at any intermediate frequency the ascending and descending curves of magnetization will enclose a space, and energy will be dissipated. It is remarkable that the phenomena of magnetic viscosity are much more evident in a thick rod than in a thin wire, or even in a large bundle of thin wires. ”

“ According to this theory the molecules of any magnetizable substance are little permanent magnets the axes of which are, under ordinary conditions, disposed in all possible directions indifferently. The process of magnetization consists in turning round the molecules by the application of magnetic force, so that their north poles may all point more or less approximately in the direction of the force; thus the body as a whole becomes a magnet which is merely the resultant of an immense number of molecular magnets. ”

“ The only assumption relative to induced magnetism which is involved in these equations is, that if a magnetic force X due to external magnetism produces in the iron of the ship an induced magnetization, and if this induced magnetization exerts on the compass needle a disturbing force whose components are X', Y', Z', then, if the external magnetic force is altered in a given ratio, the components of the disturbing force will be altered in the same ratio. ”

“ For small magnetizing forces the magnetization of iron steadily increases with rise of temperature till the critical temperature is approached, when the rate of increase becomes very high, the permeability in some cases attaining a value of about 11,000 ”

“ It is in consequence of the inductive action of the magnetism of the earth that all masses of iron, especially when they are perpendicular, are found to be endowed with magnetic polarity; hence the reaction of the iron in ships upon the compasses, which have to be corrected and adjusted before a voyage, or else serious errors in steering the vessel would occur, and there is no doubt that many shipwrecks are due to this cause. No other metals beside iron, steel, nickel, cobalt, and possibly manganese, can receive or retain magnetism after contact with a magnet. ”

“ Magnetism, in one or other of its forms, is now proved to be universal, and to its power we are disposed to refer the structural conditions of all material bodies, both organic and inorganic. This view has scarcely yet been recognised by philosophers; but as we find a certain law of polarity prevailing through every atom of created matter, in whatever state it may be presented to our senses, it is evident that every particle must have a polar and directing influence upon the mass, and every coherent mass becomes thus only a larger and more powerful representative of the magnetic unit. ”

“ Therein he shows, as the result of his customary careful experimental explorations that the magnetism of every known substance (even tissues of the human frame) is manifested in one of two ways. Either the body is, like iron, attracted by the magnet, taking a position coincident with the magnetic forces which he calls paramagnetic (para beside or near, magnetes, magnes, magnet) or bodies—like bismuth, for instance—are repelled by the poles and should therefore be called diamagnetic (dia, across) for they set themselves across, equatorially, or at right angles to the magnetic lines. ”

“ Laying off on the axis of ordinates
the quantities of magnetism evoked, and the corresponding strengths of
the exciting current on the axis of abscissas, the curve can be plotted.
It first rises rapidly, indicating a rapid increase of magnetization,
but grows nearly horizontal as the iron becomes more saturated. The
effect due to the coils alone, or the effect produced in the absence of
iron is a straight line, because air does not change in permeability.
Curve of Distribution of Potential in Armature. ”

“ The magnetism acquired by soft iron while it is in a magnetic field. Soft iron will lose its induced magnetism when it is removed from a magnetic field. The strength and polarity of the induced magnetism will alter immediately as its magnetic latitude, or its orientation in a magnetic field, is changed. The induced magnetism has an immediate effect upon the magnetic compass as the magnetic latitude or heading of a craft changes. ”

“ Certain bodies, as, for instance, the iron ore called load stone, the earth itself, and pieces of steel which have been subjected to certain treatment, are found to possess the following properties, and are called Magnets.
If, near any part of the earth's surface except the Magnetic Poles, a magnet be suspended so as to turn freely about a vertical axis, it will in general tend to set itself in a certain azimuth, and if disturbed from this position it will oscillate about it. An unmagnetized body has no such tendency, but is in equilibrium in all azimuths alike. ”

“ Those substances which are attracted, or rather which tend, like iron, to move from weaker to stronger parts of the magnetic field, are termed paramagnetic; those which are repelled, or tend to move from stronger to weaker parts of the field, are termed diamagnetic. Between the ferromagnetics and the paramagnetics there is an enormous gap. The maximum magnetic susceptibility of iron is half a million times greater than that of liquid oxygen, one of the strongest paramagnetic substances known. ”

“ We can produce a more perfect and shorter circle of attractions by the superposition of magnetism, as at B, Fig. 1. If we magnetize a piece of steel or iron in a given direction with a strong magnetic directing power, the magnetism penetrates to a certain depth. If we slightly diminish the magnetizing power, and magnetize the rod in a contrary direction, we may reduce it to zero, by the superposition of an exterior magnetism upon one of a contrary name existing at a greater depth ”

“ We know, however, that the magnetic force in the region in the neighbourhood of a magnet is maintained as long as the steel retains its magnetization, and as we have no reason to believe that a steel magnet would lose all its magnetization by the mere lapse of time, we conclude that the molecular vortices do not require a continual expenditure of work in order to maintain their motion, and that therefore this motion does not necessarily involve dissipation of energy. ”

“ In an unmagnetized piece of steel the atoms are not arranged symmetrically, so that the orbits of their electrons lie some in one plane and some in another. Consequently, although the electron stream of each atom undoubtedly produces an infinitesimally small magnetic field, no magnetic effect that we can detect is produced, because the different streams are not working in unison and adding together their forces. ”