§8 The Hall effect


If a metal plate, along which runs a constant electric current to put it in a perpendicular magnetic field is parallel to the direction between current and field face potential difference Ux = φ1 - φ2. This phenomenon is called the Hall effect or galvanomagnetic phenomenon.


Hall potential difference Ux depends on the material of the plate, the current density , the height h of the plate hand the magnetic field .

Explanation of the Hall effect can be given in terms of the classical electron theory of metals.
If a metal plate, the charge carriers are electrons. In a magnetic field
 electrons experience the action of the Lorentz force, which in this case is directed upwards. Thus, on the upper side there is an excess of negative charges, and on the bottom - it is a lack of electrons and positively charged. Between the upper and lower bounds of the potential difference occurs and additional transverse electric field directed upward. when the intensity this field reaches a value such that its action on the charges will balance the Lorentz force, the charges will no longer be deflected by the magnetic field and in the transverse direction the steady distribution charges. Then

FL = FEl,

qvB = qE,

vB = E,



S = hd,






Hall coefficient R is inversely proportional to the charge and the charge carrier concentration.
The use of the Hall effect:

  1. The measured value of the Hall coefficient can be determined n - concentration of carriers in a conductor
  2. Determine the conductivity type semiconductor: p - or n – type


3. Hall sensors:

a) for the measurement of the magnetic field B.

b) for the measurement of high amperage 103 ÷ 106 A.

c) in cars.

4. Keyboard to PC


§ 10 Flux of magnetic induction.

Gauss’s theorem for the magnetic field

Consider a uniform magnetic field with magnetic induction . Select the area S, which permeate the field lines vector    angularly α.

The flow of the magnetic induction is called a scalar physical quantity , equal to the scalar product of the vectoron the vector of square .

Flux of magnetic induction can be positive or negative depending on the sign of . At 0 < α < 90° , If α obtuse : 90° < α < 180°, then . At α = 90° .

Magnetic flux is measured in Weber


1 Weber - is the magnetic flux generated by the magnetic field with the induction of 1 T over an area of ??1 m2.

In the case of non-uniform field is considered an elementary stream through an elementary area dS.

Then the total magnetic flux is equal to the integral of the square S


2. Because lines of force of vector is always closed, when considering the magnetic flux through a closed surface can be noted that each line, part of the surface that comes out of it. Therefore the net flux through a closed surface is always zero

 - the Gauss theorem for the magnetic field .



§ 11 The work on moving current-carrying conductor in a magnetic field

Consider the contour containing the EMF has such a feature: the conductor AB can move freely. Circuit is placed in a uniform magnetic field directed perpendicular to the figure for the square ??the circuit. On current-carrying conductor in a magnetic field experiences a force Ampere


This force moves the conductor AB on Δх. Then the work of Ampere force on the movement of the conductor on Δх is equal to

The work done in moving the current-carrying conductor in a magnetic field is determined by the product of the current flowing through a conductor, the change of the magnetic flux. And the change of the magnetic flux is determined by the product of the magnetic induction on the area, crossed when moving conductor. Work on moving current-carrying conductor is made current source. A magnetic field no work. The magnetic field in the process does not change.






§ 1 the Magnetic moments of electrons and atoms.

Microcurrents. Magnetization

Magnetic materials are substances that can acquire an external magnetic field magnetic properties - magnetized, ie create their own magnetic field.

Explain the magnetization of matter by using Ampere's hypothesis: the motion of electrons in atoms and molecules leads to the (existence) of the elementary currents, called microcurrents. We can assume that the electron in an atom moves in a circular orbit. This is equivalent to a circular motion of the electron current


where ν –frequency of rotation of the electron ,

еelectron charge .

Velocity of the particle can be associated with the frequency by ratio

therefore ,

The magnetic moment of the electron moving around the nucleus (orbital magnetic moment) is

Electron along with the magnetic moment has an orbital mechanical angular momentum

Gyromagnetic ratio g

The minus sign indicates that the  and in opposite directions

In quantum mechanics, it is proved that the mechanical angular momentum L can take only a few well-defined (discrete) values ??of multiple , ie ,where hthe Planck constant h = 6,62·10-34 J·s, m = 1, 2, 3 …

Electron, in addition behaves as if constantly rotates around its own axis. This property is called electron spin. Spin - an intrinsic property of the particle in the same intrinsic electron, as well as mass and charge. Therefore, the electron is assigned its own angular momentum (spin)  and accordingly the intrinsic magnetic moment . The absolute value of the spin of the electron is

Spin has only two projections on the direction of the magnetic field  -along and against the field

where g - the gyromagnetic ratio of the spin moments.

The magnetic moment of the atom - the value of the total



Moreover, this value is quite difficult to give due consideration, the numerical values ??of the magnetic moments of individual particles as well as their direction. The magnetic moments of protons and neutrons is much smaller magnetic moments of electrons. Therefore, their magnetic moments can be neglected in comparison with the magnetic moments of electrons and we can assume that the magnetic properties of an atom are determined mainly by the magnetic properties of electrons.

Because electrons are part of all atoms, this means that the magnetic field will have an effect on any substance, therefore, non-magnetic materials do not exist.

Each electron behaves as an elementary magnet. Therefore, making the body in a magnetic field should affect the configuration of the field and, conversely, the presence of a magnetic field will affect the behavior of matter. The magnetic field of all the bodies are magnetized, ie elementary volume of the body acts as the magnet and the magnetic moment of the body is the sum of the magnetic moments of the volume elements.

To estimate the intensity of magnetization of the body treated magnetic moment per unit volume – magnetization


N total number of atoms in a small volume



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