Eddy current losses


A direct current i flowing in a closed circuit limited by a small area S Δ is called a magnetic dipole (Fig. 1.4). It has its own magnetic field, the parameters of which are determined by the magnitude of the current and the diameter of the circuit. Magnetization


Fig. 1.4

A magnetic dipole can be characterized by a vector called the magnetic moment of the dipole, whose value is

where is the vector normal to the plane of the current loop. ΔS As you know, physical bodies are composed of molecules and atoms. Atoms, on the other hand, can be thought of as nuclei containing positive charges and electrons rotating around them. Electrons are material particles with a mass and the lowest possible negative charge. Electrons moving around the nucleus are elementary currents, where is the electron charge in coulomb; 0 i e f = 19 0 1,592 10e – = ⋅ 0 f – orbit speed in Hz. Therefore, atoms are magnetic dipoles. The magnetic moment of each electron moving in a circular orbit of radius r is


where 0 2 f ω = π is the angular frequency of rotation of the electron. The negative sign in this expression is due to the fact that under the electric current we understand the movement of positive charges. The magnetic moment is called the orbital moment. om Since not only a charge is inherent in an electron, but also a rest mass 0e 31 0 9 10m – = ⋅ kg, a moving electron also has a angular momentum

The ratio of the orbital momentum to the moment of electron momentum is a constant

In addition to the motion in orbits, the electrons rotate around their own axis and have a certain mechanical angular momentum s G, called the electron spin. Thanks to the spin, the electron, in addition to the mechanical moment, also has, regardless of the circulation around the nucleus, the magnetic moment of the spin or spin moment equal to

The ratio of the spin moment to the moment of momentum is also a constant

The sum of magnetic moments per unit volume is called magnetization or magnetic polarization:


Magnetization is measured in the same units as magnetic induction. In most cases, the direction of the magnetization vector coincides with the direction of the magnetic field strength and can be represented as


where κ is the magnetic susceptibility coefficient.

In the neutral state, the magnetic moments inherent in electrons due to circulation and spins are mutually balanced and in the outer space the magnetic field of the dipoles does not appear. When the body enters a magnetic field, then interaction forces arise between it and the dipoles, which change the orientation of the dipoles. If, as a result of reorientation, the total magnetic flux decreases, then this phenomenon is called diamagnetism. If under the influence of an external field the magnetic flux increases, then the phenomenon is called paramagnetism. Diamagnetism is characteristic of all substances, but is expressed very weakly. The coefficient of magnetic susceptibility of diamagnetics κ is. For most substances, it is blocked by a more powerful paramagnetic phenomenon so that the external field is amplified. However, the magnetic susceptibility coefficient is. 64 0 (10 10) −− −− … 75 0 (10 10) −− μ … Magnetic field induction, taking into account (1.12) and (1.15), can be represented as


where is the absolute magnetic permeability of the medium. It consists of the magnetic permeability of a vacuum and the magnetic susceptibility of a medium. The ratio is called the relative magnetic permeability of the medium. For diamagnets, 11 0a μ = μ + κ = μμ 0 / a μ = μ μ μ <≈, and for paramagnets 11. The difference in the magnetic permeability of these substances from the permeability of vacuum is so small that in most cases it is neglected.

Reference Magnetization

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