magnetic field

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magnetic field

a field of force surrounding a permanent magnet or a moving charged particle, in which another permanent magnet or moving charge experiences a force

magnetic field

The region surrounding a magnet, a conductor carrying an electric current, a stream of charged particles, etc., in which such a body or system exerts a detectable force. This force will be experienced by another magnetic substance or by a moving charged particle, such as an electron. The magnetic flux density is a measure of the strength of the field, usually quoted in teslas or sometimes in gauss. See also galactic magnetic field; geomagnetism; interplanetary medium; magnetic stars; sunspot cycle.

Magnetic Field

a force field that acts on moving electric charges and on bodies that have a magnetic moment, regardless of the state of their motion. A magnetic field is characterized by the vector of magnetic induction B, which defines the force acting on a moving electric charge at a given point in the field, the action of a magnetic field on bodies that have a magnetic moment, and also other properties of the magnetic field.

The term “magnetic field” was introduced in 1845 by M. Faraday, who believed that both electrical and magnetic interactions are accomplished by means of a single material field. The classical theory of the electromagnetic field was developed by J. Maxwell in 1873, and quantum theory was devised in the 1920’s.

Magnetized bodies, current-carrying conductors, and moving electrically charged bodies are sources of a macroscopic magnetic field. The nature of these sources is the same: a magnetic field arises as a result of the motion of charged microscopic particles (electrons, protons, or ions), and also because of the presence in the microscopic particles of an intrinsic (spin) magnetic moment.

The magnetic field of an electric current is defined by the Biot-Savart law; the magnetic field of bodies that have a magnetic moment is defined by formulas that describe the field of a magnetic dipole (in the general case, a multipole).

A variable magnetic field also arises when an electric field changes over time. In turn, an electric field arises when a magnetic field changes over time. Maxwell’s equations give a complete description of electric and magnetic fields in their interrelation. Lines of force of a field (lines of magnetic induction) are often introduced to characterize a magnetic field. The tangent at each point of such a line has the direction of the vector B at that point. The induction of the field is determined quantitatively by the number of lines of force that pass through a unit area perpendicular to them. The lines of induction converge at points where the values of B are high and diverge at points where the field is weaker (see, for example, Figure 1).

The following manifestations are most characteristic of a magnetic field.

(1) In a permanent uniform magnetic field the torque moment N = [pmB] acts on a magnetic dipole having a magnetic moment pm (for example, a magnetic pointer in a magnetic field turns with the field; a coil carrying a current / that also has a magnetic moment tends to assume a position in which its plane is perpendicular to the induction lines; and an atomic dipole precesses around a line of force with a characteristic frequency; see Figure l,a).

(2) In a permanent uniform magnetic field the action of the Lorentz force leads to a situation in which the trajectory of an electric charge has the form of a spiral whose curvature is inversely proportional to velocity (Figure l,b). The curvature of the trajectory of electric charges under the action of the Lorentz force affects, for example, the distribution of current in a cross section of a conductor placed in a magnetic field. This effect underlies galvanomagnetic, thermomagnetic, and other related phenomena.

(3) In a spatially nonuniform magnetic field a magnetic dipole is acted on by a force F that displaces the dipole in the direction of the field gradient: F = grad (p«B); thus, in a nonuniform magnetic field a beam of atoms containing atoms with oppositely oriented magnetic moments separates into two divergent beams (Figure l,a).

Figure 1. (a) Action of a uniform permanent magnetic field on a magnetic pointer, a coil carrying a current /, and an atomic dipole (e is an electron of an atom); (b) action of a uniform permanent magnetic field on freely moving electric charges q (in the general case their trajectory is a spiral); (c) separation of a beam of magnetic dipoles in a nonuniform magnetic field; (d) appearance of an induction current in a coil upon intensification of an external magnetic field B (the arrows indicate the direction of the induction current and the generated magnetic field B,nd). Here pw is the magnetic moment, q is the electric charge, and v is the velocity of the charge.

(4) A magnetic field that varies over time has a force effect on stationary electric charges and sets them in motion; the current Imd that arises in the circuit (Figure l,d) counteracts, with its own magnetic field Bind, the change in the original magnetic field.

The magnetic induction B determines the average macroscopic magnetic field generated at each point in the field both by conduction currents (the motion of free charge carriers) and by magnetized bodies (ions and atoms of the substance) that are present. A magnetic field that is generated by conduction currents and is independent of the magnetic properties of the substance is characterized by the vector of magnetic field intensity H = B — 4πJ or H =(B/μ0) — J (in the cgs system of units and the International System of Units, respectively). In these equations, the vector J is the magnetization of the substance (the magnetic moment per unit volume) and μ0 is the magnetic constant.

The relation μ, = B/μ0H, which defines the magnetic properties of a substance, is called its magnetic permeability. Depending on the value of μ, substances are divided into diamagnets (μ < 1) and paramagnets (μ, > 1); substances with μ <<; 1 are called ferromagnets.

The volume density of the energy of a magnetic field in the absence of ferromagnets is wm = μH2/8π or wm = BH/8π (in cgs units); wm = μμ0H2/2 or BH/2 (in the International System of Units). In the general case wm = 1/2 f HdB, where the integration limits are determined by the initial and final values of the magnetic induction B, which is intricately dependent on the field H.

Various types of magnetometers are used to measure the characteristics of a magnetic field and the magnetic properties of substances. The gauss (G) is the unit of induction for a magnetic field in the cgs system, and the tesla (1 tesla = 104 G) is used in the International System of Units. The field intensity is measured in oersteds and amperes per meter (A/m), respectively, where 1 A/m = 4π/103 oersted ≈ 0.01256 oersted; the energy density of a magnetic field is measured in ergs/cm3 or joules per cu m (J/m3); 1 J/m3 = 10 ergs/cm3.

Occurrence. In nature, magnetic fields are extraordinarily diverse both in size and in the effects they produce. The magnetic field of the earth, which forms the earth’s magnetosphere, extends to a distance of 70,000-80,000 km in the direction of the

Figure 2. Superconducting solenoid with a 30-kG Nb-Zr alloy winding (the working volume, 32 mm in diameter, is at room temperature): (1) solenoid, (2) liquid helium, (3) liquid nitrogen, (4) nitrogen shield, (5) housing, (6) filling neck

sun and for many millions of kilometers in the opposite direction. Near the surface of the earth the magnetic field is equal to an average of 0.5 G, and at the boundary of the magnetosphere it is of the order of 10~3 G. The geomagnetic field shields the surface of the earth and the biosphere from the flux of charged particles in the solar wind and, in part, from cosmic rays. The influence of the geomagnetic field itself on the vital activity of organisms is studied in magnetobiology. In circumterrestrial space the magnetic field forms a magnetic trap for high-energy charged particles—the Van Allen radiation belt. The particles contained in the belt present a significant danger in space flight. The origin of the earth’s magnetic field is associated with convective movement of the conducting liquid matter in the earth’s core.

Direct measurements by means of spacecraft have demonstrated that the heavenly bodies closest to the earth—the moon and the planet Venus—do not have an intrinsic magnetic field similar to the earth’s. Of the other planets in the solar system, only Mercury, Mars, Saturn, and especially Jupiter have intrinsic magnetic fields sufficient to create planetary magnetic traps. A magnetic field of up to 10 G and a number of characteristic phenomena (such as magnetic storms and synchrotron radio-frequency radiation) that indicate the significant role of magnetic fields in planetary processes have been found on Jupiter.

The interplanetary magnetic field is primarily the field of the solar wind (the continuously expanding plasma of the solar corona). Near the earth’s orbit the interplanetary field is of the order of 10~4-10~5 G. The lines of force of the regular interplanetary magnetic field have the shape of uncoiling spirals that emanate from the sun (their shape is due to the addition of the radial motion of the plasma and the sun’s rotation). The magnetic field of the interplanetary plasma has a sectorial structure: in some sectors it is directed away from the sun, and in others, toward it. The regularity of the interplanetary magnetic field can be disrupted by the development of various types of plasma instability, the passage of shock waves, and the propagation of fluxes of fast particles produced by solar flares.

The magnetic field plays a very important role in all processes on the sun—flares, the appearance of sunspots and solar prominences, and the production of solar cosmic rays. Measurements based on the Zeeman effect have shown that the magnetic field of sunspots reaches several thousand gauss and that prominences are restrained by fields of the order of 10-100 G (the average value of the total magnetic field of the sun is of the order of 1 G). The remoteness of stars has prevented the observation in them of magnetic fields of the solar type. At the same time, anomalously large fields (up to 3.4 ×104 G) have been found in more than 200 magnetic stars. Fields of the order of 107 G have been measured in several white dwarfs. According to current concepts, particularly intense magnetic fields (of the order of 1010-1012 G) should be found in neutron stars.

The acceleration of charged particles (electrons, protons, and nuclei) to relativistic velocities (close to the speed of light) is closely associated with the magnetic fields of heavenly bodies. Upon motion of such particles in a cosmic magnetic field, electromagnetic synchrotron radiation arises. The induction of the interstellar magnetic field, as determined from the Zeeman effect (in the 21-cm line of the hydrogen spectrum) and the Faraday effect (the rotation of the plane of polarization of electromagnetic radiation in a magnetic field) is only of the order of 5 ×10 ~6 G. However, the total energy of the interstellar (galactic) magnetic field exceeds the energy of the random motion of particles in interstellar gas and is comparable to the energy of cosmic rays.

Figure 3. Cross section of a 250-kG water-cooled solenoid (the water flow is indicated by arrows). The first section weighs 2 kg, consumes 0.4 MW, and generates a field Bmax ~ 45 kG; the second section weighs 16 kg, consumes 2 MW, and generates a field of 65 kG; the third section weighs 1,250 kg, consumes 12 MW, and generates a field of 140 kG.

The role of magnetic fields is just as significant in phenomena of the microcosm as on a cosmic scale. This is because all particles that are structural components of matter (electrons, protons, and neutrons) have a magnetic moment, and also because of the action of magnetic fields on moving electric charges. If the total magnetic moment M of the particles that form an atom or molecule is equal to zero, then such atoms and molecules are called diamagnetic. Atoms, ions, or molecules with M ≠ 0 are said to be paramagnetic. When an external magnetic field is applied, an induced magnetic moment directed opposite to the magnetizing field arises in all atoms (both with M = 0 and M ≠ 0). However, in paramagnetic atoms in a magnetic field this effect is masked by the preferential rotation of their magnetic moments with the field. In paramagnets and ferromagnets, magnetization increases to saturation with the strength of the external magnetic field. The shape of the magnetization curves of ferromagnets and antiferromagnets is determined largely by the magnetic interaction of the atomic carriers of magnetism. This interaction also is responsible for the great diversity of the types of atomic magnetic structure in ferrimagnets (ferrites).

The intracrystalline magnetic field that has been measured in ferrimagnets (iron garnets) has been found to be of the order of 5 ×l05 G on the nuclei of iron ions and 8 ×106 G on the nuclei of the rare earth dysprosium. At a distance of the order of the atomic dimension (~ 10-8 cm) the magnetic field of the nucleus is of the order of 50 G. An external magnetic field and the intra-atomic magnetic fields created by the electrons and nucleus of the atom split the energy levels of the atom (the Zeeman effect); as a result, the atomic spectra assume a complex structure. The distances between the Zeeman energy sublevels (and the corresponding spectral lines) are proportional to the magnitude of the magnetic field. This makes possible determination of the magnitude of the magnetic field by spectral methods.

Another important physical phenomenon—the resonance absorption of radio waves by matter (the phenomenon of magnetic resonance)—is related to the appearance of Zeeman energy sub-levels in a magnetic field and to the quantum transitions between them. The dependence of the position and shape of magnetic resonance spectral lines on the peculiarities of the interaction of molecules, atoms, and ions—and also of nuclei in liquids and solids—makes possible the study of the structure of liquids, crystals, and complex molecules and the kinetics of chemical and biochemical reactions by using electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR).

A magnetic field is capable of exerting an appreciable effect on the optical properties of a medium and on the processes of the interaction of electromagnetic radiation with matter, and also of inducing galvanomagnetic and thermomagnetic phenomena in conductors and semiconductors. A magnetic field affects the superconductivity of substances: when a certain level is reached, the magnetic field destroys superconductivity. Upon magnetization of ferromagnetic bodies the magnetic field changes their shape and elastic properties. Plasma acquires special properties in a magnetic field. A magnetic field impedes the motion of charged plasma particles across the lines of force of the field. This effect is used, for example, for thermal insulation of the plasma and to ensure its stability in units designed for studying the properties of high-temperature plasma.

Figure 4. Model of a pulsed single-coil solenoid (length, 10 mm; diameter of opening, 2 mm). The power source is a battery of 2.4-kJ capacitors. The fields produced are up to 1.6 MG.

Use in science and technology. Magnetic fields are usually subdivided into weak fields (up to 500 G), medium fields (500 G-40 kG), strong fields (40 kG-1 MG), and superstrong fields (more than 1 MG). Virtually all of electrical engineering, radio engineering, and electronics is based on the use of weak and medium magnetic fields. In research, medium magnetic fields are used in particle accelerators, cloud chambers, spark chambers, bubble chambers, other track detectors of ionizing particles, and mass spectrometers, and in the study of the action of magnetic fields on living organisms. Weak and medium magnetic fields are produced by permanent magnets, electromagnets, uncooled solenoids, and superconducting magnets.

Magnetic fields of up to about 500 kG are used extensively for scientific and applied purposes: in solid-state physics they are used to study the energy spectra of electrons in metals, semiconductors, and superconductors; to study ferromagnetism and antiferromagnetism; to confine plasma in magnetohydrodynamic generators and motors; to produce superlow temperatures; and to focus electron beams in electron microscopes. Superconducting solenoids (up to 150-200 kG; Figure 2), water-cooled solenoids (up to 250 kG; Figure 3), and pulsed solenoids (up to 1.6 MG; Figure 4) are used to produce strong magnetic fields. The forces acting on conductors carrying a current in strong magnetic fields may be very great (for example, in fields of the order of 250 kG the mechanical stresses reach 4 ×108 N/m2—that is, the ultimate strength of copper). The pressure effect of magnetic fields is taken into account in the design of electromagnets and solenoids and is used to stamp products from metal. The maximum value of a field that can be produced without destroying the solenoid does not exceed 0.9 MG.

Superstrong magnetic fields are used to obtain data on the properties of substances in fields stronger than 1 MG and at the accompanying pressures of tens of millions of atmospheres. In particular, these studies make possible an understanding in greater depth of the processes that transpire in the interior of planets and stars. Superstrong magnetic fields are produced by the directed-explosion method (Figure 5). A copper pipe within which a strong pulsed magnetic field has been generated is radially

Figure 5. Magnetoexplosive generator. The primary pulsed field is generated by the discharge of a battery of capacitors. When the field reaches its maximum strength, an explosion takes place, leading to a sharp increase in the field in the copper pipe (the “trap” of the magnetic field). A trigger was used to synchronize the primary pulses magnetic field and the detonation of the explosive.

compressed by the pressure of an explosion. As the radius R of the pipe decreases, the strength of the magnetic field in it increases as I/R2 (if the magnetic flux through the pipe is maintained). The magnetic field produced in this type of unit (called magnetoexplosive generators) may reach several dozen megagauss. The brevity of the existence of the magnetic field (a few microseconds), the small volume of the extremely strong magnetic field, and the destruction of the unit in the explosion are among the shortcomings of this method.

REFERENCES

Landau, L. D., and E. M. Lifshits. Teoriia polia, 6th ed. Moscow, 1973. (Teoreticheskaia fizika, vol. 2.)
Tamm, I. E. Osnovy teorii elektrichestva, 8th ed. Moscow, 1966.
Purcell, E. Elektrichestvo i magnetizm. Moscow, 1971. (Berkeley Physics Course, vol. 2; translated from English.)
Karasik, V. R. Fizika i tekhnika siVnykh magnitnykh polei. Moscow, 1964.
Montgomery, D. B. Poluchenie siVnykh magnitnykh polei spomoshch’iu solenoidov. Moscow, 1971. (Translated from English.)
Knoepfel, H. Sverkhsil’nye impuVsnye magnitnye polia. Moscow, 1972. (Translated from English.)
Kolm, H., and A. Freeman. “Sil’nye magnitnye polia.” Uspekhi fizicheskikh nauk, 1966, vol. 88, fasc. 4, p. 703.
Sakharov, A. D. “Vzryvomagnitnye generatory.” Ibid., p. 725.
Bitter, F. “Sverkhsil’nye magnitnye polia.” Ibid., p. 735.
Vainshtein, S. I., and Ia. B. Zel’dovich. “O proiskhozhdenii magnitnykh polei v astrofizike.” Ibid., 1972, vol. 106, fasc. 3.

L. G. ASLAMAZOV, V. R. KARASIK and S. B. PIKEL’NER

magnetic field

[mag′ned·ik ′fēld]
(electromagnetism)
One of the elementary fields in nature; it is found in the vicinity of a magnetic body or current-carrying medium and, along with electric field, in a light wave; charges moving through a magnetic field experience the Lorentz force.

magnetic field

A distribution of magnetic lines of force in space, such as those found in and about a magnet, an electric motor, or the earth.

magnetic field

An invisible energy emitted by a magnet. Same as flux.
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