Magnetic moment is a fundamental property of elementary particles. Quant. Magnetic moment of current Magnetic moment in si

When placed in an external field, a substance can react to this field and become a source itself magnetic field(magnetize). Such substances are called magnets(compare with the behavior of dielectrics in an electric field). Based on their magnetic properties, magnets are divided into three main groups: diamagnetic, paramagnetic and ferromagnetic.

Different substances are magnetized in different ways. The magnetic properties of a substance are determined magnetic properties electrons and atoms. Most substances are weakly magnetized - these are diamagnetic and paramagnetic materials. Some substances under normal conditions (at moderate temperatures) are capable of being magnetized very strongly - these are ferromagnets.

For many atoms the resulting magnetic moment is zero. Substances consisting of such atoms are diamagetics. These, for example, include nitrogen, water, copper, silver, table salt NaCl, silicon dioxide Si0 2. Substances in which the resulting magnetic moment of the atom is different from zero are classified as paramagnetic Examples of paramagnetic materials are: oxygen, aluminum, platinum.

In the future, when speaking about magnetic properties, we will mainly mean diamagnetic and paramagnetic materials, and sometimes we will specifically discuss the properties of a small group of ferromagnetic materials.

Let us first consider the behavior of electrons of a substance in a magnetic field. For simplicity, we assume that an electron rotates in an atom around the nucleus at a speed v along an orbit of radius r. Such movement, which is characterized by orbital angular momentum, is essentially a circular current, which is characterized, accordingly, by orbital magnetic moment

volume r orb. Based on the period of revolution around the circle T= - we have that

an electron crosses an arbitrary point in its orbit per unit time -

once. Therefore, the circular current, equal to the charge passing through a point per unit time, is given by the expression

Respectively, electron orbital magnetic moment according to formula (22.3) is equal to

In addition to the orbital angular momentum, the electron also has its own angular momentum, called spin. Spin is described by the laws quantum physics and is an integral property of the electron - like mass and charge (see more details in the section on quantum physics). The intrinsic angular momentum corresponds to the intrinsic (spin) magnetic moment of the electron r sp.

The nuclei of atoms also have a magnetic moment, but these moments are thousands of times smaller than the moments of electrons, and they can usually be neglected. As a result, the total magnetic moment of the magnet R t is equal to the vector sum of the orbital and spin magnetic moments of the electrons of the magnet:

An external magnetic field acts on the orientation of particles of a substance having magnetic moments (and microcurrents), as a result of which the substance is magnetized. The characteristic of this process is magnetization vector J, equal to the ratio of the total magnetic moment of the particles of the magnet to the volume of the magnet AV:

Magnetization is measured in A/m.

If a magnet is placed in an external magnetic field B 0, then as a result

magnetization, an internal field of microcurrents B will arise, so that the resulting field will be equal

Let us consider a magnet in the form of a cylinder with a base area S and height /, placed in a uniform external magnetic field with induction At 0. Such a field can be created, for example, using a solenoid. The orientation of microcurrents in the external field becomes ordered. In this case, the field of diamagnetic microcurrents is directed opposite to the external zero, and the field of paramagnetic microcurrents coincides in direction with the external

In any section of the cylinder, the ordering of microcurrents leads to the following effect (Fig. 23.1). Ordered microcurrents inside the magnet are compensated by neighboring microcurrents, and uncompensated surface microcurrents flow along the side surface.

The direction of these uncompensated microcurrents is parallel (or antiparallel) to the current flowing in the solenoid, creating an external zero. On the whole they Rice. 23.1 give the total internal current This surface current creates an internal field of microcurrents Bv Moreover, the relationship between current and field can be described by formula (22.21) for the solenoid zero:

Here the magnetic permeability is taken equal to one, since the role of the medium is taken into account by introducing a surface current; The winding density of the solenoid turns corresponds to one for the entire length of the solenoid /: n = 1 //. In this case, the magnetic moment of the surface current is determined by the magnetization of the entire magnet:

From the last two formulas, taking into account the definition of magnetization (23.4), it follows

or in vector form

Then from formula (23.5) we have

Experience in studying the dependence of magnetization on the external field strength shows that the field can usually be considered weak and in the Taylor series expansion it is sufficient to limit ourselves to the linear term:

where the dimensionless proportionality coefficient x is magnetic susceptibility substances. Taking this into account we have

Comparing the last formula for magnetic induction with the well-known formula (22.1), we obtain the relationship between magnetic permeability and magnetic susceptibility:

Note that the values ​​of magnetic susceptibility for diamagnetic and paramagnetic materials are small and usually amount to 10 "-10 4 (for diamagnetic materials) and 10 -8 - 10 3 (for paramagnetic materials). Moreover, for diamagnetic materials X x > 0 and p > 1.

MAGNETIC MOMENT- physical value characterizing the magnetic charging system properties particles (or individual particles) and determining, along with other multipole moments (electric dipole moment, quadrupole moment, etc., see Multipoli) interaction of the system with external el-magn. fields and other similar systems.

According to the ideas of the classical electrodynamics, magnetic the field is created by moving electric waves. charges. Although modern the theory does not reject (and even predicts) the existence of particles with magnetic fields. charge ( magnetic monopoles), such particles have not yet been observed experimentally and are absent from ordinary matter. Therefore, the elementary characteristic of magnetic properties turns out to be precisely the magnetic mass. A system that has magnetic mass (axial vector) creates a magnetic field at large distances from the system. field

(- radius vector of the observation point). Electric has a similar appearance. field of a dipole consisting of two closely spaced electric charges of opposite sign. However, unlike electric dipole moment. M. m. is created not by a system of point “magnetic charges”, but by electric. currents flowing within the system. If a closed electrical density current flows in a limited volume V, then the M. m. created by him is determined by the f-loy

In the simplest case of a closed circular current I, flowing along a flat turn of area s, and the vector of the MM is directed along the right normal to the turn.

If the current is created by the stationary movement of point electric charges with masses having velocities, then the resulting magnetic mass, as follows from formula (1), has the form

where microscopic averaging is implied. magnitudes over time. Since the vector product on the right side is proportional to the vector of the angular momentum of the particle (it is assumed that the speeds), then the contributions of the department. particles in M. m. and at the moment of the number of movements turn out to be proportional:

Proportionality factor e/2ts called gyromagnetic ratio; this value characterizes the universal connection between magnets. and mechanical charger properties particles in classical electrodynamics. However, the movement of elementary charge carriers in matter (electrons) obeys the laws quantum mechanics, making adjustments to the classic. picture. In addition to the orbital mechanical moment of movement L the electron has an internal mechanical moment - spin. The total magnetism of an electron is equal to the sum of the orbital magnetism (2) and the spin magnetism.

As can be seen from this f-ly (following from the relativistic Dirac equations for electron), gyromagn. the ratio for the spin turns out to be exactly twice as large as for the orbital momentum. A feature of the quantum concept of magnet. and mechanical points is also that vectors cannot have a specific direction in space due to the non-commutativity of the projection operators of these vectors on the coordinate axes.

Spin M. m. charge. particles defined by f-loy (3), called. normal, for an electron it is equal magneton Bora. Experience shows, however, that the molecular mass of the electron differs from (3) by an amount of the order of ( - constant fine structure). A similar additive called anomalous magnetic moment, arises due to the interaction of an electron with photons, it is described within the framework of quantum electrodynamics. Other elementary particles also have anomalous magnetism; They are especially great for hadrons, which, according to modern ideas, have internal structure. Thus, the anomalous molecular mass of the proton is 2.79 times greater than the “normal” magnetic mass of the nuclear magneton, ( M- mass of the proton), and the M. M. of the neutron is equal to -1.91, i.e., it is significantly different from zero, although the neutron does not have electricity. charge. Such large anomalous M. M. of hadrons are due to internal. movement of the charges included in them. quarks.

Lit.: Landau L. D., Lifshits E. M., Field Theory, 7th ed., M., 1988; Huang K., Quarks, leptons and gauge fields, trans. from English, M., 1985. D. V. Giltsov.

The magnetic moment of a turn with current is physical quantity, like any other magnetic moment, characterizes the magnetic properties of a given system. In our case, the system is represented by a circular coil with current. This current creates a magnetic field that interacts with the external magnetic field. This can be either the field of the earth or the field of a permanent or electromagnet.

Drawing— 1 circular turn with current

A circular coil with current can be represented as a short magnet. Moreover, this magnet will be directed perpendicular to the plane of the coil. The location of the poles of such a magnet is determined using the gimlet rule. According to which the north plus will be located behind the plane of the coil if the current in it moves clockwise.

Drawing— 2 Imaginary strip magnet on the coil axis

This magnet, that is, our circular coil with current, like any other magnet, will be affected by an external magnetic field. If this field is uniform, then a torque will arise that will tend to turn the coil. The field will rotate the coil so that its axis is located along the field. In this case, the field lines of the coil itself, like a small magnet, must coincide in direction with the external field.

If the external field is not uniform, then translational motion will be added to the torque. This movement will occur due to the fact that sections of the field with higher induction will attract our magnet in the form of a coil more than areas with lower induction. And the coil will begin to move towards the field with greater induction.

The magnitude of the magnetic moment of a circular coil with current can be determined by the formula.

Formula - 1 Magnetic moment of a turn

Where, I is the current flowing through the turn

S area of ​​turn with current

n normal to the plane in which the coil is located

Thus, from the formula it is clear that the magnetic moment of the turn is vector quantity. That is, in addition to the magnitude of the force, that is, its modulus, it also has a direction. This property received a magnetic moment due to the fact that it includes the normal vector to the plane of the turn.

To consolidate the material, you can carry out a simple experiment. To do this, we need a circular coil of copper wire connected to the battery. In this case, the supply wires must be thin enough and preferably twisted together. This will reduce their impact on the experience.

Drawing—

Now let's hang the coil on the supply wires in a uniform magnetic field created, say, by permanent magnets. The coil is still de-energized, and its plane is parallel to the field lines. In this case, its axis and poles of the imaginary magnet will be perpendicular to the lines of the external field.

Drawing—

When current is applied to the coil, its plane will turn perpendicular to the force lines of the permanent magnet, and the axis will become parallel to them. Moreover, the direction of rotation of the coil will be determined by the gimlet rule. And strictly speaking, the direction in which the current flows along the turn.

Any substances. The source of the formation of magnetism, as stated by the classical electromagnetic theory, are microcurrents arising due to the movement of an electron in orbit. The magnetic moment is an indispensable property of all nuclei, atomic electron shells and molecules without exception.

Magnetism, which is inherent in all elementary particles, is accordingly due to the presence of a mechanical moment in them, called spin (their own mechanical impulse of a quantum nature). The magnetic properties of the atomic nucleus are composed of the spin impulses of the constituent parts of the nucleus - protons and neutrons. Electronic shells(intraatomic orbits) also have a magnetic moment, which is the sum of the magnetic moments of the electrons located on it.

In other words, the magnetic moments of elementary particles are caused by an intraatomic quantum mechanical effect known as spin momentum. This effect is similar to the angular momentum of rotation around its own central axis. Spin momentum is measured in Planck's constant- the main constant of quantum theory.

All neutrons, electrons and protons, of which, in fact, the atom consists, according to Planck, have a spin equal to ½. In the structure of an atom, electrons rotating around the nucleus, in addition to spin momentum, also have orbital angular momentum. The nucleus, although it occupies a static position, also has angular momentum, which is created by the effect of nuclear spin.

The magnetic field that generates the atomic magnetic moment is given by various forms this angular momentum. The most noticeable contribution to the creation is made by the spin effect. According to the Pauli principle, according to which two identical electrons cannot simultaneously be in the same quantum state, bound electrons merge, and their spin momenta acquire diametrically opposite projections. In this case, the magnetic moment of the electron is reduced, which reduces the magnetic properties of the entire structure. In some elements having even number electrons, this moment decreases to zero, and the substances cease to have magnetic properties. Thus, the magnetic moment of individual elementary particles has a direct impact on the magnetic properties of the entire nuclear-atomic system.

Ferromagnetic elements with an odd number of electrons will always have non-zero magnetism due to the unpaired electron. In such elements, neighboring orbitals overlap, and all spin moments of unpaired electrons take the same orientation in space, which leads to the achievement of the lowest energy state. This process is called exchange interaction.

With such alignment of the magnetic moments of ferromagnetic atoms, a magnetic field arises. And paramagnetic elements, consisting of atoms with disoriented magnetic moments, do not have their own magnetic field. But if you influence them external source magnetism, then the magnetic moments of the atoms will align, and these elements will also acquire magnetic properties.

Kikoin A.K. Magnetic moment of current // Quantum. - 1986. - No. 3. - P. 22-23.

By special agreement with the editorial board and editors of the journal "Kvant"

From the ninth grade physics course (“Physics 9”, § 88) it is known that a straight conductor of length l with current I, if it is placed in a uniform magnetic field with induction \(~\vec B\), a force \(~\vec F\) acts equal in magnitude

\(~F = BIl \sin \alpha\) ,

Where α - the angle between the direction of the current and the vector of magnetic induction. This force is directed perpendicular to both the field and the current (according to the left-hand rule).

Straight conductor is only part electrical circuit, since the electric current is always closed. How does a magnetic field act on a closed current, or more precisely, on a closed circuit with current?

Figure 1 shows, as an example, a contour in the shape of a rectangular frame with sides a And b, along which current flows in the direction indicated by the arrows I.

The frame is placed in a uniform magnetic field with induction \(~\vec B\) so that at the initial moment the vector \(~\vec B\) lies in the plane of the frame and is parallel to its two sides. Considering each side of the frame separately, we find that the sides (length A) forces are acting equal in magnitude F = BIA and directed in opposite directions. The forces do not act on the other two sides (for them sin α = 0). Each of the forces F relative to the axis passing through the midpoints of the upper and lower sides of the frame, creates a moment of force (torque) equal to \(~\frac(BIab)(2)\) (\(~\frac(b)(2)\) - shoulder strength). The signs of the moments are the same (both forces rotate the frame in the same direction), so the total torque M equals BIab, or, since the product ab equal to area S framework,

\(~M = BIab = BIS\) .

Under the influence of this moment, the frame will begin to rotate (if viewed from above, then clockwise) and will rotate until its plane becomes perpendicular to the induction vector \(~\vec B\) (Fig. 2).

In this position, the sum of forces and the sum of moments of forces are equal to zero, and the frame is in a state of stable equilibrium. (In fact, the frame will not stop immediately - for some time it will oscillate around its equilibrium position.)

It is easy to show (do it yourself) that in any intermediate position, when the normal to the contour plane makes an arbitrary angle β with magnetic field induction, the torque is equal to

\(~M = BIS \sin \beta\) .

From this expression it is clear that for a given value of field induction and for a certain position of the circuit with current, the torque depends only on the product of the area of ​​the circuit S on current strength I in it. Size IS and is called the magnetic moment of the current-carrying circuit. More precisely, IS is the magnitude of the magnetic moment vector. And this vector is directed perpendicular to the plane of the circuit and in such a way that if you mentally rotate the gimlet in the direction of the current in the circuit, then the direction of the translational movement of the gimlet will indicate the direction of the magnetic moment. For example, the magnetic moment of the circuit shown in Figures 1 and 2 is directed away from us beyond the plane of the page. The magnetic moment is measured in A m 2.

Now we can say that a circuit with a current in a uniform magnetic field is installed so that its magnetic moment “looks” in the direction of the field that caused its rotation.

It is known that not only current-carrying circuits have the property of creating their own magnetic field and rotating in an external field. The same properties are observed in a magnetized rod, for example, in a compass needle.

Back in 1820, the remarkable French physicist Ampere expressed the idea that the similarity in the behavior of a magnet and a circuit with a current is explained by the fact that closed currents exist in the magnet particles. It is now known that atoms and molecules actually contain tiny electric currents associated with the movement of electrons in their orbits around nuclei. Because of this, atoms and molecules of many substances, such as paramagnetic substances, have magnetic moments. The rotation of these moments in an external magnetic field leads to the magnetization of paramagnetic substances.

It turned out something else. All particles that make up an atom also have magnetic moments that are not at all associated with any movements of charges, that is, with currents. For them, the magnetic moment is the same “innate” quality as charge, mass, etc. Even a particle that does not have an electric charge, a neutron, has a magnetic moment. component atomic nuclei. Therefore, atomic nuclei also have a magnetic moment.

Thus, magnetic moment is one of the most important concepts in physics.