Due to what the magnetic moment is formed. Magnetic moment

Any substances. The source of the formation of magnetism, according to the classical electromagnetic theory, are microcurrents arising from 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 due to the presence of a mechanical moment in them, called spin (its own mechanical momentum of quantum nature). The magnetic properties of the atomic nucleus are made up 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 due to the intra-atomic quantum mechanical effect, known as the spin momentum. This effect is similar to the angular momentum of rotation about its own central axis. Spin momentum is measured in Planck's constant, the fundamental 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 the spin momentum, also have an orbital angular momentum. The nucleus, although it occupies a static position, also has an angular momentum, which is created by the effect of nuclear spin.

The magnetic field that an atomic magnetic moment generates is determined by the various forms of 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 be simultaneously in the same quantum state, bound electrons merge, while 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 that have an even number of 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 this 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 act on them with an external source of magnetism, then the magnetic moments of the atoms will even out, and these elements will also acquire magnetic properties.

When placed in an external field, a substance can react to this field and itself become a source of a magnetic field (be magnetized). Such substances are called magnets(compare with the behavior of dielectrics in an electric field). According to their magnetic properties, magnets are divided into three main groups: diamagnets, paramagnets, and ferromagnets.

Different substances are magnetized in different ways. The magnetic properties of matter are determined by the magnetic properties of electrons and atoms. Most of the substances are weakly magnetized - these are diamagnets and paramagnets. Some substances under normal conditions (at moderate temperatures) are capable of being magnetized very strongly - these are ferromagnets.

Many atoms have a net magnetic moment equal to zero. Substances made up of such atoms are diamagetics. These include, for example, nitrogen, water, copper, silver, common salt NaCl, silicon dioxide Si0 2 . Substances, in which the resulting magnetic moment of the atom is different from zero, belong to paramagnets. Examples of paramagnets are: oxygen, aluminum, platinum.

In what follows, when speaking of magnetic properties, we will have in mind mainly diamagnets and paramagnets, and the properties of a small group of ferromagnets will sometimes be specially discussed.

Let us first consider the behavior of matter electrons in a magnetic field. Let us assume for simplicity that the electron rotates in the atom around the nucleus with a speed v along an orbit of radius r. Such a motion, which is characterized by an orbital angular momentum, is essentially a circular current, which is characterized, respectively, by an orbital magnetic moment.

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

an arbitrary point of the orbit the electron per unit time crosses -

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

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

In addition to the orbital angular momentum, the electron also has its own angular momentum, called back. Spin is described by the laws of quantum physics and is an inherent property of an electron - like mass and charge (see more details in the quantum physics section). 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 that have 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 В 0, then as a result

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

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 outer field becomes ordered. In this case, the field of microcurrents of diamagnets is directed opposite to the external field, and the field of microcurrents of paramagnets coincides in direction with the external field.

In any section of the cylinder, the orderliness 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 lateral surface.

The direction of these uncompensated microcurrents is parallel (or anti-parallel) to the current flowing in the solenoid creating an external zero. In general, they Rice. 23.1 give the total internal current This surface current creates an internal microcurrent field B v moreover, the connection between the current and the field can be described by the formula (22.21) for the zero of the solenoid:

Here, the magnetic permeability is taken equal to unity, since the role of the medium is taken into account by introducing the surface current; the density of winding turns of the solenoid corresponds to one for the entire length of the solenoid /: n = one //. 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

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

where the dimensionless coefficient of proportionality x - magnetic susceptibility substances. With this in mind, 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:

We note that the values ​​of the magnetic susceptibility for diamagnets and paramagnets are small and are usually modulo 10 "-10 4 (for diamagnets) and 10 -8 - 10 3 (for paramagnets). In this case, for diamagnets X x > 0 and p > 1.

It is known that the magnetic field has an orienting effect on the loop with current, and the loop rotates around its axis. This happens because in a magnetic field a moment of forces acts on the frame, equal to:

Here B is the magnetic field induction vector, is the current in the frame, S is its area and a is the angle between the lines of force and the perpendicular to the frame plane. This expression includes the product , which is called the magnetic dipole moment or simply the magnetic moment of the frame. It turns out that the magnitude of the magnetic moment completely characterizes the interaction of the frame with a magnetic field. Two frames, one of which has a large current and a small area, and the other has a large area and a small current, will behave in a magnetic field in the same way if their magnetic moments are equal. If the frame is small, then its interaction with the magnetic field does not depend on its shape.

It is convenient to consider the magnetic moment as a vector, which is located on a line perpendicular to the plane of the frame. The direction of the vector (up or down along this line) is determined by the "rule of the gimlet": the gimlet must be placed perpendicular to the frame plane and rotated in the direction of the frame current - the direction of movement of the gimlet will indicate the direction of the magnetic moment vector.

Thus, the magnetic moment is a vector perpendicular to the plane of the frame.

Now let's visualize the behavior of the frame in a magnetic field. She will strive to turn around like that. so that its magnetic moment is directed along the magnetic field vector B. A small loop with current can be used as the simplest "measuring device" to determine the magnetic field vector.

Magnetic moment is an important concept in physics. Atoms are made up of nuclei around which electrons revolve. Each electron moving around the nucleus as a charged particle creates a current, forming, as it were, a microscopic frame with current. Let us calculate the magnetic moment of one electron moving in a circular orbit of radius r.

Electric current, i.e., the amount of charge that is transferred by an electron in orbit in 1 s, is equal to the charge of the electron e, multiplied by the number of revolutions it makes:

Therefore, the magnitude of the magnetic moment of the electron is:

It can be expressed in terms of the magnitude of the angular momentum of the electron. Then the value of the magnetic moment of the electron associated with its orbital motion, or, as they say, the value of the orbital magnetic moment, is equal to:

An atom is an object that cannot be described using classical physics: for such small objects, completely different laws apply - the laws of quantum mechanics. Nevertheless, the result obtained for the orbital magnetic moment of the electron turns out to be the same as in quantum mechanics.

Otherwise, the situation is with the electron's own magnetic moment - the spin, which is associated with its rotation around its axis. For the spin of an electron, quantum mechanics gives the value of the magnetic moment, which is 2 times greater than classical physics:

and this difference between orbital and spin magnetic moments cannot be explained classically. The total magnetic moment of an atom is made up of the orbital and spin magnetic moments of all electrons, and since they differ by a factor of 2, a factor appears in the expression for the magnetic moment of the atom characterizing the state of the atom:

Thus, an atom, like an ordinary loop with current, has a magnetic moment, and in many respects their behavior is similar. In particular, as in the case of a classical frame, the behavior of an atom in a magnetic field is completely determined by the magnitude of its magnetic moment. In this regard, the concept of a magnetic moment is very important in explaining various physical phenomena that occur with matter in a magnetic field.

In the previous paragraph, it was found that the action of a magnetic field on a flat circuit with current is determined by the magnetic moment of the circuit, equal to the product of the current strength in the circuit and the area of ​​\u200b\u200bthe circuit (see formula (118.1)).

The unit of magnetic moment is the ampere-meter squared (). To give an idea of ​​​​this unit, we point out that with a current of 1 A, a magnetic moment equal to 1 has a circular contour with a radius of 0.564 m () or a square contour with a side of a square equal to 1 m. At a current of 10 A, a magnetic moment 1 has a circular radius contour 0.178 m ( ) etc.

An electron moving at high speed in a circular orbit is equivalent to a circular current, the strength of which is equal to the product of the electron charge and the frequency of rotation of the electron along the orbit: . If the radius of the orbit is , and the speed of the electron is , then and, therefore, . The magnetic moment corresponding to this current is

.

The magnetic moment is a vector quantity directed along the normal to the contour. Of the two possible directions of the normal, one is selected that is related to the direction of the current in the circuit by the rule of the right screw (Fig. 211). Rotation of the right-hand threaded screw in the same direction as the current in the circuit causes longitudinal movement of the screw in the direction . The normal chosen in this way is called positive. The direction of the vector is assumed to coincide with the direction of the positive normal.

Rice. 211. Rotation of the screw head in the direction of the current causes the screw to move in the direction of the vector

Now we can refine the definition of the direction of magnetic induction. The direction of magnetic induction is taken to be the direction in which the positive normal to the circuit with current is established under the action of the field, i.e. the direction in which the vector is established.

The SI unit of magnetic induction is called the tesla (T) after the Serbian scientist Nikola Tesla (1856-1943). One tesla is equal to the magnetic induction of a uniform magnetic field in which a flat current-carrying circuit with a magnetic moment of one ampere-meter squared is subjected to a maximum torque of one newton-meter.

From formula (118.2) it follows that

119.1. A circular contour with a radius of 5 cm, through which a current of 0.01 A flows, experiences a maximum torque equal to N × m in a uniform magnetic field. What is the magnetic induction of this field?

119.2. What torque acts on the same contour if the normal to the contour forms an angle of 30° with the direction of the field?

119.3. Find the magnetic moment of the current created by an electron moving in a circular orbit of radius m with a speed of m/s. The charge of an electron is Cl.

Various media, when considering their magnetic properties, are called magnets .

All substances in one way or another interact with a magnetic field. Some materials retain their magnetic properties even in the absence of an external magnetic field. The magnetization of materials occurs due to the currents circulating inside the atoms - the rotation of electrons and their movement in the atom. Therefore, the magnetization of a substance should be described using real atomic currents, called Ampere currents.

In the absence of an external magnetic field, the magnetic moments of the atoms of a substance are usually randomly oriented, so that the magnetic fields they create cancel each other out. When an external magnetic field is applied, the atoms tend to orient their magnetic moments in the direction of the external magnetic field, and then the compensation of magnetic moments is violated, the body acquires magnetic properties - it becomes magnetized. Most bodies are magnetized very weakly and the magnitude of the magnetic field induction B in such substances differs little from the magnitude of the magnetic field induction in vacuum. If the magnetic field is weakly amplified in a substance, then such a substance is called paramagnetic :

( , , , , , , Li, Na);

if it weakens, then it diamagnetic :

(Bi, Cu, Ag, Au, etc.) .

But there are substances that have strong magnetic properties. Such substances are called ferromagnets :

(Fe, Co, Ni, etc.).

These substances are able to retain magnetic properties even in the absence of an external magnetic field, representing permanent magnets.

All bodies when they are introduced into an external magnetic field are magnetized to one degree or another, i.e. create their own magnetic field, which is superimposed on an external magnetic field.

Magnetic properties of matter are determined by the magnetic properties of electrons and atoms.

Magnetics consist of atoms, which, in turn, consist of positive nuclei and, relatively speaking, electrons revolving around them.

An electron moving in an orbit in an atom is equivalent to a closed circuit with orbital current :

where e is the electron charge, ν is the frequency of its orbital rotation:

The orbital current corresponds to orbital magnetic moment electron

,

(6.1.1)

where S is the area of ​​the orbit, is the unit normal vector to S, is the electron velocity. Figure 6.1 shows the direction of the orbital magnetic moment of an electron.

An electron moving in an orbit has orbital angular momentum , which is directed opposite to and is related to it by the relation

where m is the mass of the electron.

In addition, the electron has own angular momentum, which is called electron spin

,

(6.1.4)

where , is Planck's constant

The spin of an electron corresponds to spin magnetic moment electron directed in the opposite direction:

,

(6.1.5)

The value is called gyromagnetic ratio of spin moments