Magnetism (redirected from magnetics)

magnetism, force of attraction or repulsion between various substances, especially those made of iron and certain other metals; ultimately it is due to the motion of electric charges.

Magnetic Poles, Forces, and Fields

Any object that exhibits magnetic properties is called a magnet. Every magnet has two points, or poles, where most of its strength is concentrated; these are designated as a north-seeking pole, or north pole, and a south-seeking pole, or south pole, because a suspended magnet tends to orient itself along a north-south line. Since a magnet has two poles, it is sometimes called a magnetic dipole, being analogous to an electric dipole, composed of two opposite charges. The like poles of different magnets repel each other, and the unlike poles attract each other.

One remarkable property of magnets is that whenever a magnet is broken, a north pole will appear at one of the broken faces and a south pole at the other, such that each piece has its own north and south poles. It is impossible to isolate a single magnetic pole, regardless of how many times a magnet is broken or how small the fragments become. (The theoretical question as to the possible existence in any state of a single magnetic pole, called a monopole, is still considered open by physicists; experiments to date have failed to detect one.)

From his study of magnetism, C. A. Coulomb in the 18th cent. found that the magnetic forces between two poles followed an inverse-square law of the same form as that describing the forces between electric charges. The law states that the force of attraction or repulsion between two magnetic poles is directly proportional to the product of the strengths of the poles and inversely proportional to the square of the distance between them.

As with electric charges, the effect of this magnetic force acting at a distance is expressed in terms of a field of force. A magnetic pole sets up a field in the space around it that exerts a force on magnetic materials. The field can be visualized in terms of lines of induction (similar to the lines of force of an electric field). These imaginary lines indicate the direction of the field in a given region. By convention they originate at the north pole of a magnet and form loops that end at the south pole either of the same magnet or of some other nearby magnet (see also flux, magnetic). The lines are spaced so that the number per unit area is proportional to the field strength in a given area. Thus, the lines converge near the poles, where the field is strong, and spread out as their distance from the poles increases.

A picture of these lines of induction can be made by sprinkling iron filings on a piece of paper placed over a magnet. The individual pieces of iron become magnetized by entering a magnetic field, i.e., they act like tiny magnets, lining themselves up along the lines of induction. By using variously shaped magnets and various combinations of more than one magnet, representations of the field in these different situations can be obtained.

Magnetic Materials

The term magnetism is derived from Magnesia, the name of a region in Asia Minor where lodestone, a naturally magnetic iron ore, was found in ancient times. Iron is not the only material that is easily magnetized when placed in a magnetic field; others include nickel and cobalt. Carbon steel was long the material commonly used for permanent magnets, but more recently other materials have been developed that are much more efficient as permanent magnets, including certain ferroceramics and Alnico, an alloy containing iron, aluminum, nickel, cobalt, and copper.

Materials that respond strongly to a magnetic field are called ferromagnetic [Lat. ferrum = iron]. The ability of a material to be magnetized or to strengthen the magnetic field in its vicinity is expressed by its magnetic permeability. Ferromagnetic materials have permeabilities of as much as 1,000 or more times that of free space (a vacuum). A number of materials are very weakly attracted by a magnetic field, having permeabilities slightly greater than that of free space; these materials are called paramagnetic. A few materials, such as bismuth and antimony, are repelled by a magnetic field, having permeabilities less than that of free space; these materials are called diamagnetic.

The Basis of Magnetism

The electrical basis for the magnetic properties of matter has been verified down to the atomic level. Because the electron has both an electric charge and a spin, it can be called a charge in motion. This charge in motion gives rise to a tiny magnetic field. In the case of many atoms, all the electrons are paired within energy levels, according to the exclusion principle, so that the electrons in each pair have opposite (antiparallel) spins and their magnetic fields cancel. In some atoms, however, there are more electrons with spins in one direction than in the other, resulting in a net magnetic field for the atom as a whole; this situation exists in a paramagnetic substance. If such a material is placed in an external field, e.g., the field created by an electromagnet, the individual atoms will tend to align their fields with the external one. The alignment will not be complete, due to the disruptive effect of thermal vibrations. Because of this, a paramagnetic substance is only weakly attracted by a magnet.

In a ferromagnetic substance, there are also more electrons with spins in one direction than in the other. The individual magnetic fields of the atoms in a given region tend to line up in the same direction, so that they reinforce one another. Such a region is called a domain. In an unmagnetized sample, the domains are of different sizes and have different orientations. When an external magnetic field is applied, domains whose orientations are in the same general direction as the external field will grow at the expense of domains with other orientations. When the domains in all other directions have vanished, the remaining domains are rotated so that their direction is exactly the same as that of the external field. After this rotation is complete, no further magnetization can take place, no matter how strong the external field; a saturation point is said to have been reached. If the external field is then reduced to zero, it is found that the sample still retains some of its magnetism; this is known as hysteresis.

Evolution of Electromagnetic Theory

The connections between magnetism and electricity were discovered in the early part of the 19th cent. In 1820 H. C. Oersted found that a wire carrying an electrical current deflects the needle of a magnetic compass because a magnetic field is created by the moving electric charges constituting the current. It was found that the lines of induction of the magnetic field surrounding the wire (or any other conductor) are circular. If the wire is bent into a coil, called a solenoid, the magnetic fields of the individual loops combine to produce a strong field through the core of the coil. This field can be increased manyfold by inserting a piece of soft iron or other ferromagnetic material into the core; the resulting arrangement constitutes an electromagnet.

Following Oersted's discovery the various magnetic effects of an electric current were extensively investigated by J. B. Biot, Félix Savart, and A. M. Ampère. Ampère showed in 1825 that not only does a current-carrying conductor exert a force on a magnet but magnets also exert forces on current-carrying conductors. In 1831 Michael Faraday and Joseph Henry independently discovered that it is possible to produce a current in a conductor by changing the magnetic field about it. The discovery of this effect, called electromagnetic induction, together with the discovery that an electric current produces a magnetic field, laid the foundation for the modern age of electricity. Both the electric generator, which makes electricity widely available, and the electric motor, which converts electricity to useful mechanical work, are based on these effects.

Another relationship between electricity and magnetism is that a regularly changing electric current in a conductor will create a changing magnetic field in the space about the conductor, which in turn gives rise to a changing electrical field. In this way regularly oscillating electric and magnetic fields can generate each other. These fields can be visualized as a single wave that is propagating through space. The formal theory underlying this electromagnetic radiation was developed by James Clerk Maxwell in the middle of the 19th cent. Maxwell showed that the speed of propagation of electromagnetic radiation is identical with that of light, thus revealing that light is intimately connected with electricity and magnetism.

Bibliography

See D. Wagner, Introduction to the Theory of Magnetism (1972); D. J. Griffiths, Introduction to Electrodynamics (1981).

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magnetism

Phenomenon associated with magnetic fields, the effects of such fields, and the motion of electric charges. Some types of magnetism are diamagnetism, paramagnetism, ferromagnetism, and ferrimagnetism. Magnetic fields exert forces on moving electric charges. The effects of such forces are evident in the deflection of an electron beam in a cathode-ray tube and the motor force on a current-carrying conductor. Other applications of magnetism range from the simple magnetic door catch to medical imaging devices and electromagnets used in high-energy particle accelerators.

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Magnetism

The branch of science that describes the effects of the interactions between charges due to their motion and spin. These interactions may appear in various forms, including electric currents and permanent magnets. They are described in terms of the magnetic field, although the field hypothesis cannot be tested independently of the electrokinetic effects by which it is defined. The magnetic field complements the concept of the electrostatic field used to describe the potential energy between charges due to their relative positions. Special relativity theory relates the two, showing that magnetism is a relativistic modification of the electrostatic forces. The two together form the electromagnetic interactions which are propagated as electromagnetic waves, including light. They control the structure of materials at distances between the long-range gravitational actions and the short-range “strong” and “weak” forces most evident within the atomic nucleus. See Electromagnetic radiation, Relativity

The magnetic field can be visualized as a set of lines (Fig. 1) illustrated by iron filings scattered on a suitable surface. The intensity of the field is indicated by the line spacing, and the direction by arrows pointing along the lines. The sign convention is chosen so that the Earth's magnetic field is directed from the north magnetic pole toward the south magnetic pole. The field can be defined and measured in various ways, including the forces on the equivalent magnetic poles, and on currents or moving charges. Bringing a coil of wire into the field, or removing it, induces an electromotive force (emf) which depends on the rate at which the number of field lines, referred to as lines of magnetic flux, linking the coil changes in time. This provides a definition of flux, &PHgr;, in terms of the emf, e, given by Eq. (1)

(1) 

for a coil of N turns wound sufficiently closely to make the number of lines linking each the same. The International System (SI) unit of &PHgr;, the weber (Wb), is defined accordingly as the volt-second. The symbol B is used to denote the flux, or line, density, as in Eq. (2),

(2) 

when the area of the coil is sufficiently small to sample conditions at a point, and the coil is oriented so that the induced emf is a maximum. The SI unit of B, the tesla (T), is the Wb/m². The sign of the emf, e, is measured positively in the direction of a right-hand screw pointing in the direction of the flux lines. It is often convenient, particularly when calculating induced emfs, to describe the field in terms of a magnetic vector potential function instead of flux.

Magnetic lines of a bar magnet

Magnetic circuits

The magnetic circuit provides a useful method of analyzing devices with ferromagnetic parts, and introduces various quantities used in magnetism. It describes the use of ferromagnetic materials to control the flux paths in a manner analogous to the role of conductors in carrying currents around electrical circuits. For example, pieces of iron may be used to guide the flux which is produced by a magnet along a path which includes an air gap (Fig. 2), giving an increase in the flux density, B, if the cross-sectional area of the gap is less than that of the magnet. See Magnet, Magnetic materials

Magnetic circuit with an air gap

The magnet may be replaced by a coil of N turns carrying a current, i, wound over a piece of iron, or ferromagnetic material, in the form of a ring of uniform cross section. The flux linking each turn of the coil, and each turn of a secondary coil wound separately from the first, is then approximately the same, giving the same induced emf per turn [according to Eq. (1)] when the supply current, i, and hence the flux, &PHgr;, changes in time. The arrangement is typical of many different devices. It provides, for example, an electrical transformer whose input and output voltages are directly proportional to the numbers of turns in the windings. Emf's also appear within the iron, and tend to produce circulating currents and losses. These are commonly reduced by dividing the material into thin laminations. See Eddy current

The amount of flux produced by a given supply current is reduced by the presence of any air gaps which may be introduced to contribute constructional convenience or to allow a part to move. The effects of the gaps, and of different magnetic materials, can be predicted by utilizing the analogy between flux, &PHgr;, and the flow of electric current through a circuit consisting of resistors connected in series (Fig. 3). Since &PHgr; depends on the product, iN, of the winding current and number

(3) 

of turns, as in Eq. (3), the ratio between them, termed the reluctance, , is the analog of electrical resistance. It may be constant or may vary with &PHgr;. The quantity iN is the magnetomotive force (mmf), analogous to voltage or emf in the equivalent electrical circuit. The relationship between the two exchanges the potental and flow quantities, since the magnetic mmf depends on current, i, and the electrical emf on d&PHgr;/dt. Electric and magnetic equivalent circuits are referred to as duals. See Reluctance

Circuit analogy

Any part of the magnetic circuit of length l, in which the cross section, a, and flux density, B, are uniform has a reluctance given by Eq. (4). This equation parallels Eq. (5)

(4) 

(5) 

for the resistance, R, of a conduct of the same dimensions. The permeability, μ, is the magnetic equivalent of the conductivity, &sgr;, of the conducting material. Using a magnet as a flux source (Fig. 2) gives an mmf which varies with the air gap reluctance. In the absence of any magnetizable materials, as in the air gaps, the permeability is given by Eq. (6)

(6) 

in SI units (Wb/A-m). The quantity μ₀ is sometimes referred to as the permeability of free space. Material properties are described by the relative permeability, μ_r in accordance with Eq. (7).

(7) 

The materials which are important in magnetic circuits are the ferromagnetics and ferrites characterized by large value of μ_r, sometimes in excess of 10,000 at low flux densities.

Magnetic field strength

It is convenient to introduce two different measures of the magnetic field: the flux density, B, and the field strength, or field intensity, H. The field strength, H, can be defined as the mmf per meter. It provides a measure of the currents and other magnetic field sources, excluding those representing polarizable materials. It may also be defined in terms of the force on a unit pole.

A straight wire carrying a current I sets up a field (Fig. 4) whose intensity at a point at distance r is given by Eq. (8).

(8) 

The field strength, H, like B, is a vector quantity pointing in the direction of rotation of a right-hand screw advancing in the direction of current flow. The intensity of the field is shown by the number of field lines intersecting a unit area. The straight wire provides one example of the circuital law, known as Ampère's law, given by Eq. (9).

(9) 

Here, Θ is the angle between H and the element dl of any closed path of summation, or integration, and I is the current which links this path. Choosing a circular path, centered on a straight wire, reduces the integral to H (2&pgr;r).

Magnetic field of a straight wire

A long, straight, uniformly wound coil (Fig. 5), for example, produces a field which is uniform in the interior and zero outside. The interior magnetic field, H, points in the direction parallel to the coil axis. Applying Eq. (14) to the rectangle pqrs of unit length in the axial direction shows that the only contribution is from pq, giving Eq. (10),

(10) 

where n is the number of turns, per unit length, carrying the current, I. The magnetic field strength, H, remains the same, by definition, whether the interior of the coil is empty or is filled with ferromagnetic material of uniform properties. The interior forms part of a magnetic circuit in which In is the mmf per unit length, where mmf is the magnetic analog of electric voltage, or scalar potential, in an electric circuit. The magnetic field strength, H, is the analog of the electric field vector, E, as a measure of potential gradient, pointing down the gradient. The flux density, B, describes the effect of the field, in the sense of the voltage which is induced in a search coil by changes in time [Eq. (1)]. The ratio of H to B is the reluctance of a volume element of unit length and unit cross section in which the field is uniform, so that, from Eq. (4), the two quantities are related by Eq. (11).

(11) 

The permeability, μ, is defined by Eq. (11). The relative permeability, μ_r, of polarizable materials is measured accordingly by subjecting a sample to a uniform field inside a long coil such as that shown in Fig. 5 and using the emf induced in a search coil wound around the specimen to observe the flux in it.

Cross section of part of a long, straight uniformly wound coil

Magnetic flux and flux density

Magnetic flux is defined in terms of the forces exerted by the magnetic field on electric charge. The forces can be described in terms of changes in flux with time [Eq. (1)], caused either by motion relative to the source or by changes in the source current, describing the effect of charge acceleration.

Since the magnetic, or electrokinetic, energy of current flowing in parallel wires depends on their spacing, the wires are subject to forces tending to change the configuration. The force, dF, on an element of wire carrying a current, i, is given by Eq.

(12) 

(12), and this provides a definition of the flux density, B, due to the wires which exert the force. The SI unit of B, called the tesla, or Wb/m², is the N/A-m. The flux density, B, equals μ₀ H in empty space, or in any material which is not magnetizable [Eq. (11)]. An example is the force, F, per meter (length) which is exerted by a long straight wire on another which is parallel to it, at distance r. From Eq. (8), this force is given by Eq. (13),

(13) 

when the wires carry currents I and i. The force, F, is accounted for by the electrokinetic interactions between the conduction charges, and describes the relativistic modification of the electric forces between them due to their relative motion.

In general, any charge, q, moving at velocity u is subject to a force given by Eq. (14),

(14) 

where u × B denotes the cross-product between vector quantities. That is, the magnitude of f depends on the sine of the angle Θ between the vectors u and B , of magnitudes u and B, according to Eq. (15).

(15) 

The force on a positive charge is at right angles to the plane containing u and B and points in the direction of a right-hand screw turned from u to B .

The same force also acts in the axial direction on the conduction electrons in a wire moving in a magnetic field, and this force generates an emf in the wire. The emf in an element of wire of length dl is greatest when the wire is at right angles to the B vector, and the motion is at right angles to both. The emf is then given by Eq. (16).

(16) 

More generally, u is the component of velocity normal to B , and the emf depends on the sine of the angle between dl and the plane containing the velocity and the B vectors. The sign is given by the right-hand screw rule, as applied to Eq. (15).

Magnetic flux linkage

The magnetic flux linking any closed path is obtained by counting the number of flux lines passing through any surface, s, which is bounded by the path. Stated more formally, the linkage

(17) 

depends on the sum given in Eq. (17), where B_n denotes the component of B in the direction normal to the area element, ds. The rate of change of linkage gives the emf induced in any conducting wire which follows the path [Eq. (1)].

The flux linkage with a coil (Fig. 6) is usually calculated by assuming that each turn of the coil closes on itself, giving a flux pattern which likewise consists of a large number of separate closed loops. Each links some of the turns, so that the two cannot be separated without breaking, or “tearing,” either the loop or the turn. The total linkage with the coil is then obtained by adding the contributions from each turn.

B (magnetic flux) field of a short coil

The inductance, L, is a property of a circuit defined by the emf which is induced by changes of current in time, as

(18) 

in Eq. (18). The SI unit of inductance is the henry (H), or V-s/A. The negative sign shows that e opposes an increase in current (Lenz's law). From Eq. (1) the inductance of a coil of N turns, each linking the same flux, &PHgr;, is given by Eq. (19),

(19) 

so that the henry is also the Wb/A. When different turns, or different parts of a circuit, do not link the same flux, the product N&PHgr; is replaced by the total flux linkage, &PHgr;, with the circuit as a whole.

The mutual inductance, M, between any two coils, or circuit parts, is defined by emf which is induced in one by a change of current in the other. Using 1 and 2 to distinguish between them, the emf induced in coil 1 is given by Eq. (20a),

(20{\em a}) 

(20{\em b}) 

where the sign convention is consistent with that used for L, referred to as the self-inductance. Likewise, the emf induced in coil 2 when the roles of the windings are reversed is given by Eq. (20b). The interaction satisfies the reciprocity condition of Eq. (21), so that the suffixes may be omitted.

(21) 

Magnetostatics

The term “magnetostatics” is usually interpreted as the magnet equivalent of the electrostatic interactions between electric charges. The equivalence is described most directly in terms of the magnetic pole, since the forces between poles, like those between charges, vary inversely with the square of the separation distance. Although no isolated poles, or monopoles, have yet been observed, the forces which act on both magnets and on coils are consistent with the assumption that the end surfaces are equivalent to magnetic poles.

Magnetic moment

The magnetic moment of a small current loop, or magnet, can be defined in terms of the torque which acts on it when placed in a magnetic flux density, B, which is sufficiently uniform in the region of the loop. For a rectangular loop with dimensions a and b and with N turns, carrying a current, i, equal but opposite forces act on the opposite sides of length a (Fig. 7). The force is iNBa [Eq. (12)], and the torque, given by

(22) 

Eq. (22), depends on the effective distance, b sin Θ, between the wires. It is proportional to the area ab, and is a maximum when the angle Θ between B and the axis of the loop is 90°. A current loop of any other shape can be replaced by a set of smaller rectangles placed edge to edge, and the torques of these added to give the total on the loop. The magnetic moment of any loop of area s is defined as the ratio of the maximum torque to the flux density, so

(23) 

its magnitude is given by Eq. 23). It is a vector quantity pointing in the direction of a right-hand screw turned in the direction of current flow. It is expressed in vector cross-product notation by Eq. (24).

(24) 

See Torque

Cross section of a rectangular current loop placed in magnetic flux density B

An electron orbiting at frequency f is the equivalent of a current i = q f, giving

(25) 

Eq. (25) for the moment, where s is the area of the orbit. The permissible values are determined by the quantum energy levels. The electron spin is a quantum state which can likewise be visualized as a small current loop. Atomic nuclei also possess magnetic moments. See Electron spin, Magneton, Nuclear moments

Magnetic polarization

Materials are described as magnetic when their response to the magnetic field controls the ratio of B to H. The behavior is accounted for by the magnetic moments produced mainly by the electron spins and orbital motions. These respond to the field and contribute to it in a process referred to as magnetic polarization. The effects are greatest in ferromagnetics and in ferrites, in which the action is described as ferrimagnetic. See Ferrimagnetism, Ferromagnetism

The sources are the equivalent of miniature “Ampèrean currents” whose sum, in any volume element, is equivalent to a loop of current flowing along the surface of the element. The flux density, B, depends on the field intensity, H, which is defined so that its value inside a long ferromagnetic rod of uniform cross section placed inside a long coil (Fig. 5) is the same as in the annular gap between the rod and the coil, in accordance with Eq. (10). If the field is not sufficiently uniform, H can be measured by using a search coil to observe the flux density, μ₀ H, in the gap. The flux density inside the rod is given by Eq. (26),

(26) 

where B₀ denotes μ₀H, and μ_r is the relative permeability [Eqs. (7) and (11)]. The same flux, B, is obtained by replacing the material by a coil in which the current in amperes per unit length

(27) 

is given by Eq. (27). The magnetic moment, dm, of a volume element of length dz is due to the current flowing over the surface enclosing the area, dydz; from Eq. (23), it is given by Eq. (28). The moment per unit volume defines the magnetic polarization, as

(28) 

(29) 

in Eq. (29). The polarization, M , is a vector pointing in the direction of dm with magnitude J_s. The surface current produces an H -like, or B /μ₀, field which is entirely different from H in the material. Substituting from Eq. (27) gives Eq. (30).

(30) 

This model of the material accounts for the flux field, B , as observed by the voltage induced in a search coil wound around the specimen, and H , becomes an auxiliary quantity representing the sum of the polarization, M , and the magnetizing field, B μ₀, to which M responds. The polarization, M , also makes the largest contribution to that field, since the equivalent surface current is in the same direction as the current in the magnetizing coil.

Magnetic hysteresis

The relationship between the flux density, B, and the field intensity, H, in ferromagnetic materials depends on the past history of magnetization. The effect is known as hysteresis. It is demonstrated by subjecting the material to a symmetrical cycle of change during which H is varied continuously between the positive and negative limits +H_m and -H_m (Fig. 8). The path that is traced by repeating the cycle a sufficient number of times is the hysteresis loop. The sequence is counterclockwise, so that B is larger when H is diminishing than when it is increasing, in the region of positive H. The flux density, B_r, which is left when H falls to zero is called the remanence, or retentivity. The magnetically “hard” materials used for permanent magnets are characterised by a high B_r, together with a high value of the field strength, -H_c, which is needed to reduce B to zero. The field strength, H_c, is known as the coercive force, or coercivity. Cycling the material over a reduced range in H gives the path in Fig. 8 traced by the broken line, lying inside the larger loop. The locus of the tips of such loops is known as the normal magnetization curve. The initial magnetization curve is the B-H relationship which is followed when H is progressively increased in one direction after the material has first been demagnetized (B = H = 0).

Hysteresis behavior of a ferromagnetic material