Lorentz force acting on a charged particle. What is the Lorentz force, what are the magnitude and direction of this force

MINISTRY OF EDUCATION AND SCIENCE

RUSSIAN FEDERATION

FEDERAL STATE BUDGET EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION

"KURGAN STATE UNIVERSITY"

ESSAY

In the subject "Physics" Topic: "Application of the Lorentz force"

Completed by: Student group T-10915 Logunova M.V.

Teacher Vorontsov B.S.

Kurgan 2016

Introduction 3

1. Using the Lorentz force 4

1.1. Cathode ray devices 4

1.2 Mass spectrometry 5

1.3 MHD generator 7

1.4 Cyclotron 8

Conclusion 10

References 11

Introduction

Lorentz force- the force with which the electromagnetic field, according to classical (non-quantum) electrodynamics, acts on a point charged particle. Sometimes the Lorentz force is called the force acting on a moving with a speed υ charge q only from the side of the magnetic field, often full force- from the side electro magnetic field in general, in other words, from the side of the electric E non-magnetic B fields.

In the International System of Units (SI), it is expressed as:

F L = qυ B sinα

It is named after the Dutch physicist Hendrik Lorenz, who developed an expression for this force in 1892. Three years before Lorentz, the correct expression was found by O. Heaviside.

The macroscopic manifestation of the Lorentz force is the Ampère force.

Using the Lorentz force

The action exerted by a magnetic field on moving charged particles is very widely used in technology.

The main application of the Lorentz force (more precisely, its special case - the Ampère force) are electrical machines (electric motors and generators). The Lorentz force is widely used in electronic devices to act on charged particles (electrons and sometimes ions), for example, in television cathode ray tubes, in mass spectrometry and MHD generators.

Also, in the currently created experimental facilities for the implementation of a controlled thermonuclear reaction, the action of a magnetic field on the plasma is used to twist it into a cord that does not touch the walls of the working chamber. The movement of charged particles in a circle in a uniform magnetic field and the independence of the period of such movement from the speed of the particle are used in cyclic accelerators of charged particles - cyclotrons.

1. Electron beam devices

Electron beam devices (EBD) - a class of vacuum electronic devices that use a stream of electrons concentrated in the form of a single beam or beam of beams, which are controlled both by intensity (current) and by position in space, and interact with a fixed spatial target (screen) of the device. The main scope of ELP is the conversion of optical information into electrical signals and the inverse conversion of an electrical signal into an optical one, for example, into a visible television image.

The class of cathode-ray devices does not include X-ray tubes, photocells, photomultipliers, gas-discharge devices (dekatrons) and receiving-amplifying electronic lamps (beam tetrodes, electric vacuum indicators, secondary emission lamps, etc.) with a beam form of currents.

An electron beam device consists of at least three main parts:

An electronic searchlight (gun) forms an electron beam (or a beam of beams, for example, three beams in a color kinescope) and controls its intensity (current);

The deflecting system controls the spatial position of the beam (its deviation from the spotlight axis);

The target (screen) of the receiving ELP converts the energy of the beam into the luminous flux of the visible image; the target of the transmitting or storing ELP accumulates a spatial potential relief read by a scanning electron beam

Rice. 1 CRT device

General principles of the device.

A deep vacuum is created in the CRT tank. To create an electron beam, a device called an electron gun is used. The cathode heated by the filament emits electrons. By changing the voltage on the control electrode (modulator), you can change the intensity of the electron beam and, accordingly, the brightness of the image. After leaving the gun, the electrons are accelerated by the anode. Next, the beam passes through a deflecting system, which can change the direction of the beam. In television CRTs, a magnetic deflection system is used as it provides large deflection angles. In oscilloscope CRTs, an electrostatic deflection system is used as it provides faster response. The electron beam hits a screen coated with a phosphor. From bombardment by electrons, the phosphor glows and a rapidly moving spot of variable brightness creates an image on the screen.

2 Mass spectrometry

Rice. 2

The action of the Lorentz force is also used in devices called mass spectrographs, which are designed to separate charged particles according to their specific charges.

Mass spectrometry(mass spectroscopy, mass spectrography, mass spectral analysis, mass spectrometric analysis) - a method for studying a substance based on determining the mass-to-charge ratio of ions formed during ionization of sample components of interest. One of the most powerful methods for the qualitative identification of substances, which also allows quantitative determination. We can say that mass spectrometry is the "weighing" of the molecules in the sample.

The scheme of the simplest mass spectrograph is shown in Figure 2.

In chamber 1, from which the air is evacuated, there is an ion source 3. The chamber is placed in a uniform magnetic field, at each point of which the induction B⃗B → is perpendicular to the plane of the drawing and directed towards us (in Figure 1 this field is indicated by circles). An accelerating voltage is applied between electrodes A and B, under the action of which the ions emitted from the source are accelerated and enter the magnetic field at a certain speed perpendicular to the induction lines. Moving in a magnetic field along an arc of a circle, the ions fall on the photographic plate 2, which makes it possible to determine the radius R of this arc. Knowing the induction of the magnetic field B and the speed υ of the ions, according to the formula

(1)

the specific charge of the ions can be determined. And if the charge of an ion is known, its mass can be calculated.

The history of mass spectrometry begins with the fundamental experiments of J. J. Thomson at the beginning of the 20th century. The ending “-metry” in the name of the method appeared after the widespread transition from the detection of charged particles using photographic plates to electrical measurements of ion currents.

Especially wide application mass spectrometry finds in the analysis organic matter, because it provides reliable identification of both relatively simple and complex molecules. The only thing general requirement- that the molecule succumbed to ionization. However, by now it has been

there are so many ways to ionize sample components that mass spectrometry can be considered an almost universal method.

3 MHD generator

Magnetohydrodynamic generator, MHD generator - a power plant in which the energy of the working fluid (liquid or gaseous electrically conductive medium) moving in a magnetic field is converted directly into electrical energy.

The principle of operation of an MHD generator, like a conventional machine generator, is based on the phenomenon of electromagnetic induction, that is, on the occurrence of current in a conductor crossing the magnetic field lines. Unlike machine generators, the conductor in the MHD generator is the working fluid itself.

The working body moves across the magnetic field, and under the action of the magnetic field, oppositely directed flows of charge carriers of opposite signs arise.

The Lorentz force acts on a charged particle.

The following media can serve as the working body of the MHD generator:

The first MHD generators used electrically conductive liquids (electrolytes) as the working fluid. Currently, plasma is used, in which charge carriers are mainly free electrons and positive ions. Under the influence of a magnetic field, charge carriers deviate from the trajectory along which the gas would move in the absence of a field. In this case, in a strong magnetic field, a Hall field can occur (see the Hall effect) - an electric field formed as a result of collisions and displacements of charged particles in a plane perpendicular to the magnetic field.

4 Cyclotron

A cyclotron is a resonant cyclic accelerator of non-relativistic heavy charged particles (protons, ions), in which particles move in a constant and uniform magnetic field, and a high-frequency electric field of a constant frequency is used to accelerate them.

The scheme of the cyclotron device is shown in Fig.3. Heavy charged particles (protons, ions) enter the chamber from an injector near the center of the chamber and are accelerated variable field fixed frequency applied to accelerating electrodes (there are two of them and they are called dees). Particles with charge Ze and mass m move in a constant magnetic field of strength B, directed perpendicular to the plane of particle motion, along an unwinding spiral. The radius R of the trajectory of a particle with a velocity v is determined by the formula

Fig.5. Cyclotron scheme: top and side view: 1 - source of heavy charged particles (protons, ions), 2 - orbit of the accelerated particle, 3 - accelerating electrodes (dees), 4 - accelerating field generator, 5 - electromagnet. Arrows show lines of force magnetic field). They are perpendicular to the plane of the top figure.

where γ = -1/2 is the relativistic factor.

In a cyclotron for a nonrelativistic (γ ≈ 1) particle in a constant and uniform magnetic field, the radius of the orbit is proportional to the velocity (1), and the rotational frequency of a nonrelativistic particle (the cyclotron frequency does not depend on the energy of the particle

(2)

E = mv 2 /2 = (Ze) 2 B 2 R 2 /(2m) (3)

In the gap between the dees, particles are accelerated by a pulsed electric field (there is no electric field inside the hollow metal dees). As a result, the energy and radius of the orbit increase. By repeating the acceleration by the electric field at each revolution, the energy and radius of the orbit are brought to the maximum allowable values. In this case, the particles acquire the velocity v = ZeBR/m and the energy corresponding to it:

At the last turn of the spiral, the deflecting electric field, which brings the beam out. The constancy of the magnetic field and the frequency of the accelerating field make continuous acceleration possible. While some particles move along the outer turns of the spiral, others are in the middle of the path, and still others are just beginning to move.

The disadvantage of the cyclotron is the limitation by essentially non-relativistic particle energies, since even not very large relativistic corrections (deviations of γ from unity) violate the synchronism of acceleration on different turns and particles with significantly increased energies no longer have time to be in the gap between the dees in the phase of the electric field necessary for acceleration . In conventional cyclotrons, protons can be accelerated up to 20-25 MeV.

To accelerate heavy particles in the mode of an unwinding spiral to energies tens of times higher (up to 1000 MeV), a modification of the cyclotron is used, called isochronous(relativistic) cyclotron, as well as a phasotron. In isochronous cyclotrons, relativistic effects are compensated by a radial increase in the magnetic field.

Conclusion

Hidden text

Written conclusion (the most basic for all subparagraphs of the first section - principles of operation, definitions)

List of used literature

Wikipedia [Electronic resource]: Lorentz force. URL: https://ru.wikipedia.org/wiki/Lorenz_force

Wikipedia [Electronic resource]: Magnetohydrodynamic generator. URL: https://ru.wikipedia.org/wiki/Magnetohydrodynamic_generator

Wikipedia [Electronic resource]: Electron-beam devices. URL: https://ru.wikipedia.org/wiki/electron-beam_devices

Wikipedia [Electronic resource]: Mass spectrometry. URL: https://ru.wikipedia.org/wiki/Mass spectrometry

Nuclear physics on the Internet [Electronic resource]: Cyclotron. URL: http://nuclphys.sinp.msu.ru/experiment/accelerators/ciclotron.htm

Electronic textbook of physics [Electronic resource]: T. Applications of the Lorentz force //URL: http://www.physbook.ru/index.php/ T._Application_of_Lorentz_force

Academician [Electronic resource]: Magnetohydrodynamic generator //URL: http://dic.academic.ru/dic.nsf/enc_physics/MAGNETOHYDRODYNAMIC

Amp power, acting on a segment of the conductor of length Δ l with current I located in a magnetic field B,

The expression for the Ampere force can be written as:

This force is called Lorentz force . The angle α in this expression is equal to the angle between the speed and magnetic induction vector The direction of the Lorentz force acting on a positively charged particle, as well as the direction of the Ampère force, can be found from left hand rule or by gimlet rule. The mutual arrangement of the vectors , and for a positively charged particle is shown in fig. 1.18.1.

Figure 1.18.1.

Mutual arrangement of vectors , and Lorentz force modulus numerically equal to area parallelogram built on vectors and multiplied by the charge q

The Lorentz force is directed perpendicular to the vectors and

When a charged particle moves in a magnetic field, the Lorentz force does no work. Therefore, the modulus of the velocity vector does not change when the particle moves.

If a charged particle moves in a uniform magnetic field under the action of the Lorentz force, and its velocity lies in a plane perpendicular to the vector, then the particle will move along a circle of radius

The period of revolution of a particle in a uniform magnetic field is

called cyclotron frequency . The cyclotron frequency does not depend on the velocity (and hence also on the kinetic energy) of the particle. This fact is used in cyclotrons – accelerators of heavy particles (protons, ions). circuit diagram cyclotron is shown in fig. 1.18.3.

A vacuum chamber is placed between the poles of a strong electromagnet, in which there are two electrodes in the form of hollow metal half-cylinders ( dees ). An alternating electrical voltage is applied to the dees, whose frequency is equal to the cyclotron frequency. Charged particles are injected into the center of the vacuum chamber. The particles are accelerated by an electric field in the gap between the dees. Inside the dees, the particles move under the action of the Lorentz force along semicircles, the radius of which increases as the energy of the particles increases. Each time a particle passes through the gap between the dees, it is accelerated by the electric field. Thus, in a cyclotron, as in all other accelerators, a charged particle is accelerated by an electric field, and is kept on a trajectory by a magnetic field. Cyclotrons make it possible to accelerate protons to an energy of the order of 20 MeV.

Uniform magnetic fields are used in many devices and, in particular, in mass spectrometers - devices with which you can measure the masses of charged particles - ions or nuclei of various atoms. Mass spectrometers are used to separate isotopes, that is, nuclei of atoms with the same charge but different masses (for example, 20 Ne and 22 Ne). The simplest mass spectrometer is shown in fig. 1.18.4. Ions emitted from the source S, pass through several small holes that form a narrow beam. Then they get into speed selector , in which the particles move in crossed uniform electric and magnetic fields. An electric field is created between the plates of a flat capacitor, a magnetic field is created in the gap between the poles of an electromagnet. The initial velocity of charged particles is directed perpendicular to the vectors and

A particle moving in crossed electric and magnetic fields is subject to an electric force and Lorentz magnetic force. On condition E = υ B these forces exactly balance each other. If this condition is met, the particle will move uniformly and in a straight line and, having flown through the capacitor, will pass through the hole in the screen. For given values of the electric and magnetic fields, the selector will select particles moving at a speed υ = E / B.

Next, particles with the same velocity enter the mass spectrometer chamber, in which a uniform magnetic field is created. Particles move in the chamber in a plane perpendicular to the magnetic field, under the action of the Lorentz force. Particle trajectories are circles of radii R = mυ / qB". By measuring the radii of the trajectories for known values of υ and B" relationship can be defined q / m. In the case of isotopes ( q 1 = q 2) a mass spectrometer allows you to separate particles with different masses.

Modern mass spectrometers make it possible to measure the masses of charged particles with an accuracy better than 10–4.

If the speed of a particle has a component along the direction of the magnetic field, then such a particle will move in a uniform magnetic field in a spiral. In this case, the radius of the spiral R depends on the modulus of the component υ ┴ of the vector perpendicular to the magnetic field and the pitch of the helix p– on the modulus of the longitudinal component υ || (Fig. 1.18.5).

Thus, the trajectory of a charged particle, as it were, winds around the lines of magnetic induction. This phenomenon is used in technology for magnetic thermal insulation of high-temperature plasma, that is, a fully ionized gas at a temperature of about 10 6 K. A substance in this state is obtained in "Tokamak" type installations when studying controlled thermonuclear reactions. The plasma must not come into contact with the walls of the chamber. Thermal insulation is achieved by creating a magnetic field of a special configuration. As an example, in fig. 1.18.6 shows the trajectory of a charged particle in magnetic bottle(or trapped ).

A similar phenomenon occurs in the Earth's magnetic field, which is a protection for all living things from streams of charged particles from outer space. Fast charged particles from space (mainly from the Sun) are "captured" by the Earth's magnetic field and form the so-called radiation belts (Fig. 1.18.7), in which particles, like in magnetic traps, move back and forth along spiral trajectories between the north and south magnetic poles in times of the order of fractions of a second. Only in the polar regions do some of the particles invade the upper atmosphere, causing auroras. The Earth's radiation belts extend from distances of the order of 500 km to dozens of Earth's radii. It should be remembered that the south magnetic pole of the Earth is located near the north geographic pole (in the northwest of Greenland). The nature of terrestrial magnetism has not yet been studied.

test questions

1. Describe the experiments of Oersted and Ampère.

2. What is the source of the magnetic field?

3. What is Ampère's hypothesis explaining the existence of a magnetic field of a permanent magnet?

4. What is the fundamental difference between a magnetic field and an electric one?

5. Formulate the definition of the magnetic induction vector.

6. Why is the magnetic field called vortex?

7. Formulate laws:

A) Ampere;

B) Bio-Savart-Laplace.

8. What is the absolute value of the vector of magnetic induction of the direct current field?

9. Formulate the definition of the unit of current strength (ampere) in international system units.

10. Write down the formulas expressing the value:

A) the module of the magnetic induction vector;

B) Ampere's forces;

B) Lorentz forces;

D) the period of revolution of a particle in a uniform magnetic field;

E) the radius of curvature of the circle, when a charged particle moves in a magnetic field;

Test for self-control

What was observed in Oersted's experiment?

1) Interaction of two parallel conductors with current.

2) Interaction of two magnetic needles

3) Rotation of the magnetic needle near the conductor when current is passed through it.

4) The appearance of an electric current in the coil when a magnet is pushed into it.

How do two parallel conductors interact if currents are passed through them in the same direction?

Are attracted;

repel;

The force and moment of forces are equal to zero.

The force is zero, but the torque is not zero.

What formula determines the expression for the Ampere force modulus?

What formula determines the expression for the Lorentz force modulus?

AT)

0.6 N; 2) 1 N; 3) 1.4 N; 4) 2.4 N.

1) 0.5 T; 2) 1 T; 3) 2 T; 4) 0.8 T .

An electron with a speed V flies into a magnetic field with an induction modulus B perpendicular to the magnetic lines. What expression corresponds to the radius of the electron's orbit?

Answer: 1)
2)

4)

8. How will the period of revolution of a charged particle in a cyclotron change with an increase in its speed by 2 times? (V<< c).

1) will increase by 2 times; 2) Will increase by 2 times;

3) Increase by 16 times; 4) Will not change.

9. What formula determines the modulus of induction of a magnetic field created in the center of a circular current with a circle radius R?

1)
2)
3)
4)

10. The current in the coil is I. Which of the formulas determines the modulus of magnetic field induction in the middle of a coil with a length l with the number of turns N ?

1)
2)
3)
4)

Lab No.

Determination of the horizontal component of the induction of the Earth's magnetic field.

Brief theory for laboratory work.

A magnetic field is a material medium that transmits the so-called magnetic interactions. The magnetic field is one of the manifestations of the electromagnetic field.

The sources of magnetic fields are moving electric charges, current-carrying conductors and alternating electric fields. Generated by moving charges (currents), the magnetic field, in turn, acts only on moving charges (currents), while it does not have an effect on stationary charges.

The main characteristic of the magnetic field is the magnetic induction vector :

The modulus of the magnetic induction vector is numerically equal to the maximum force acting from the side of the magnetic field on a conductor of unit length, through which a current of unit strength flows. Vector forms a right triple with the force vector and current direction. Thus, magnetic induction is the power characteristic of a magnetic field.

The SI unit of magnetic induction is the Tesla (T).

Force lines of a magnetic field are called imaginary lines, at each point of which the tangents coincide with the direction of the magnetic induction vector. Magnetic field lines are always closed, never intersect.

Ampère's law determines the force action of a magnetic field on a current-carrying conductor.

If in a magnetic field with induction placed a current-carrying conductor, then on each current-directed element conductor, the Ampère force acts, determined by the relation

The direction of the Ampère force coincides with the direction of the cross product
, those. it is perpendicular to the plane in which the vectors lie and (Fig. 1).

Rice. 1. To determine the direction of the Ampère force

If a perpendicular , then the direction of the Ampère force can be determined by the rule of the left hand: direct four outstretched fingers along the current, place the palm perpendicular to the lines of force, then thumb will show the direction of the ampere force. Ampère's law is the basis for the definition of magnetic induction, i.e. relation (1) follows from formula (2) written in scalar form.

The Lorentz force is the force with which an electromagnetic field acts on a charged particle moving in this field. The Lorentz force formula was first obtained by G. Lorentz as a result of the generalization of experience and has the form:

where
is the force acting on a charged particle in an electric field with intensity ;
– force acting on a charged particle in a magnetic field.

The formula for the magnetic component of the Lorentz force can be obtained from Ampere's law, given that the current is an ordered movement of electric charges. If the magnetic field did not act on moving charges, it would not have an effect on a current-carrying conductor. The magnetic component of the Lorentz force is given by:

This force is directed perpendicular to the plane in which the velocity vectors lie and magnetic field induction ; its direction coincides with the direction of the vector product
for q > 0 and with direction
for q>0 (Fig. 2).

Rice. 2. To determine the direction of the magnetic component of the Lorentz force

If the vector perpendicular to the vector , then the direction of the magnetic component of the Lorentz force for positively charged particles can be found by the left hand rule, and for negatively charged particles by the rule right hand. Since the magnetic component of the Lorentz force is always directed perpendicular to the velocity , then it does not perform work to move the particle. It can only change the direction of the speed , bend the trajectory of the particle, i.e. act as a centripetal force.

The Biot-Savart-Laplace law is used to calculate magnetic fields (definitions ) created by conductors with current.

According to the Biot-Savart-Laplace law, each current-directed element of a conductor creates at a point at a distance from this element, the magnetic field, the induction of which is determined by the relation:

where
H/m is the magnetic constant; µ is the magnetic permeability of the medium.

Rice. 3. To the Biot-Savart-Laplace law

Direction
coincides with the direction of the vector product
, i.e.
perpendicular to the plane in which the vectors lie and . Simultaneously
is a tangent to the field line, the direction of which can be determined by the gimlet rule: if the translational movement of the tip of the gimlet is directed along the current, then the direction of rotation of the handle will determine the direction of the magnetic field line (Fig. 3).

To find the magnetic field created by the entire conductor, you need to apply the principle of superposition of fields:

For example, let's calculate the magnetic induction at the center of the circular current (Fig. 4).

Rice. 4. To the calculation of the field in the center of the circular current

For circular current
and
, so relation (5) in scalar form has the form:

The law of full current (theorem of the circulation of magnetic induction) is another law for calculating magnetic fields.

The total current law for a magnetic field in vacuum has the form:

where B l – projection on the conductor element directed by the current.

The circulation of the magnetic induction vector along any closed circuit is equal to the product of the magnetic constant and the algebraic sum of the currents covered by this circuit.

The Ostrogradsky-Gauss theorem for a magnetic field is as follows:

where B n – vector projection to normal to the site dS.

The flux of the magnetic induction vector through an arbitrary closed surface is equal to zero.

The nature of the magnetic field follows from formulas (9), (10).

Potentiality condition electric field is the equality to zero of the circulation of the intensity vector
.

The potential electric field is generated by immobile electric charges; field lines are not closed, they start at positive charges and end in negative.

From formula (9) we see that in a magnetic field the circulation of the magnetic induction vector is nonzero, therefore, the magnetic field is not potential.

It follows from relation (10) that there are no magnetic charges capable of creating potential magnetic fields. (In electrostatics, a similar theorem smolders of the form
.

Magnetic lines of force close on themselves. Such a field is called a vortex field. Thus, the magnetic field is a vortex field. The direction of the field lines is determined by the gimlet rule. In a rectilinear infinitely long conductor with current, the lines of force have the form of concentric circles covering the conductor (Fig. 3).

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Along with the Ampère force, Coulomb interaction, electromagnetic fields, the concept of the Lorentz force is often encountered in physics. This phenomenon is one of the fundamental in electrical engineering and electronics, along with, and others. It acts on charges that move in a magnetic field. In this article, we will briefly and clearly consider what the Lorentz force is and where it is applied.

Definition

When electrons move through a conductor, a magnetic field develops around it. At the same time, if you place the conductor in a transverse magnetic field and move it, an EMF of electromagnetic induction will occur. If a current flows through a conductor that is in a magnetic field, the Ampere force acts on it.

Its value depends on the flowing current, the length of the conductor, the magnitude of the magnetic induction vector and the sine of the angle between the magnetic field lines and the conductor. It is calculated by the formula:

The force under consideration is somewhat similar to the one discussed above, but it does not act on a conductor, but on a moving charged particle in a magnetic field. The formula looks like:

Important! The Lorentz force (Fl) acts on an electron moving in a magnetic field, and Ampere acts on a conductor.

From the two formulas it can be seen that in both the first and second cases, the closer the sine of the angle alpha to 90 degrees, the greater the effect Fa or Fl has on the conductor or charge, respectively.

So, the Lorentz force characterizes not a change in the magnitude of the velocity, but what kind of influence occurs from the side of the magnetic field on a charged electron or a positive ion. When exposed to them, Fl does not do work. Accordingly, it is the direction of the velocity of the charged particle that changes, and not its magnitude.

As for the unit of measurement of the Lorentz force, as in the case of other forces in physics, such a quantity as Newton is used. Its components:

How is the Lorentz force directed?

To determine the direction of the Lorentz force, as with the Ampère force, the left hand rule works. This means, in order to understand where the value of Fl is directed, you need to open the palm of your left hand so that the lines of magnetic induction enter the hand, and the outstretched four fingers indicate the direction of the velocity vector. Then the thumb, bent at right angles to the palm, indicates the direction of the Lorentz force. In the picture below you see how to determine the direction.

Attention! The direction of the Lorentzian action is perpendicular to the motion of the particle and the lines of magnetic induction.

In this case, to be more precise, for positively and negatively charged particles, it matters direction of four outstretched fingers. The left hand rule described above is formulated for a positive particle. If it is negatively charged, then the lines of magnetic induction should be directed not to the open palm, but to its back side, and the direction of the vector Fl will be opposite.

Now we will tell in simple words what this phenomenon gives us and what real effect it has on charges. Let us assume that an electron moves in a plane perpendicular to the direction of the lines of magnetic induction. We have already mentioned that Fl does not affect the speed, but only changes the direction of particle motion. Then the Lorentz force will have a centripetal effect. This is reflected in the figure below.

Application

Of all the areas where the Lorentz force is used, one of the largest is the movement of particles in the earth's magnetic field. If we consider our planet as a large magnet, then the particles that are near the north magnetic poles make an accelerated movement in a spiral. As a result of this, they collide with atoms from the upper atmosphere, and we see the northern lights.

However, there are other cases where this phenomenon applies. For example:

cathode ray tubes. In their electromagnetic deflecting systems. CRTs have been used for more than 50 years in a variety of devices, from the simplest oscilloscope to televisions. different forms and sizes. It is curious that in matters of color reproduction and work with graphics, some still use CRT monitors.
Electrical machines - generators and motors. Although the force of Ampere is more likely to act here. But these quantities can be considered as adjacent. However, this complex devices during the work of which the influence of many physical phenomena is observed.
In charged particle accelerators in order to set their orbits and directions.

Conclusion

To sum up and outline the four main theses of this article in simple terms:

The Lorentz force acts on charged particles that move in a magnetic field. This follows from the main formula.
It is directly proportional to the speed of the charged particle and the magnetic induction.
Does not affect particle speed.
Affects the direction of the particle.

Its role is quite large in the "electric" areas. A specialist should not lose sight of the basic theoretical information about fundamental physical laws. This knowledge will be useful, as well as those who are engaged in scientific work, designing and just for general development.

Now you know what the Lorentz force is, what it is equal to, and how it acts on charged particles. If you have any questions, ask them in the comments below the article!

materials

ESSAY

On the subject "Physics"
Topic: "Application of the Lorentz force"

Completed by: Student of group T-10915Logunova M.V.

TeacherVorontsov B.S.

Kurgan 2016

Introduction. 3

1. Using the Lorentz force. four

.. 4

1.2 Mass spectrometry. 6

1. 3 MHD generator. 7

1.4 Cyclotron. 8

Conclusion. eleven

List of used literature.. 13

Introduction

Lorentz force- the force with which the electromagnetic field, according to classical (non-quantum) electrodynamics, acts on a point charged particle. Sometimes the Lorentz force is called the force acting on a moving with a speed υ charge q only from the side of the magnetic field, often the full force - from the side of the electromagnetic field in general, in other words, from the side of the electric E and magnetic B fields.

In the International System of Units (SI) it is expressed as:

F L = q υ B sinα

It is named after the Dutch physicist Hendrik Lorenz, who developed an expression for this force in 1892. Three years before Lorentz, the correct expression was found by O. Heaviside.

The macroscopic manifestation of the Lorentz force is the Ampère force.

Using the Lorentz force

The action exerted by a magnetic field on moving charged particles is very widely used in technology.

1. 1. Electron-beam devices

An electron beam device consists of at least three main parts:

· An electronic searchlight (gun) forms an electron beam (or a beam of beams, for example, three beams in a color kinescope) and controls its intensity (current);

· The deflecting system controls the spatial position of the beam (its deviation from the spotlight axis);

· The target (screen) of the receiving ELP converts the energy of the beam into the luminous flux of the visible image; the target of the transmitting or storing ELP accumulates a spatial potential relief read by a scanning electron beam

Rice. 1 CRT device

General principles of the device.

A deep vacuum is created in the CRT tank. To create an electron beam, a device called electron gun. The cathode heated by the filament emits electrons. By changing the voltage on the control electrode (modulator), you can change the intensity of the electron beam and, accordingly, the brightness of the image. After leaving the gun, the electrons are accelerated by the anode. Next, the beam passes through a deflecting system, which can change the direction of the beam. In television CRTs, a magnetic deflection system is used as it provides large deflection angles. In oscilloscope CRTs, an electrostatic deflection system is used as it provides faster response. The electron beam hits a screen coated with a phosphor. From bombardment by electrons, the phosphor glows and a rapidly moving spot of variable brightness creates an image on the screen.

1.2 Mass spectrometry

Rice. 2

The action of the Lorentz force is also used in devices called mass spectrographs, which are designed to separate charged particles according to their specific charges.

Mass spectrometry(mass spectroscopy, mass spectrography, mass spectral analysis, mass spectrometric analysis) - a method for studying a substance based on determining the ratio of mass to charge of ions formed by the ionization of sample components of interest. One of the most powerful methods for the qualitative identification of substances, which also allows quantitative determination. We can say that mass spectrometry is the "weighing" of the molecules in the sample.

The scheme of the simplest mass spectrograph is shown in Figure 2.

In chamber 1, from which air is evacuated, there is an ion source 3. The chamber is placed in a uniform magnetic field, at each point of which the induction B⃗ B → is perpendicular to the plane of the drawing and directed towards us (in Figure 1 this field is indicated by circles). An accelerating voltage is applied between electrodes A and B, under the action of which the ions emitted from the source are accelerated and enter the magnetic field at a certain speed perpendicular to the induction lines. Moving in a magnetic field along an arc of a circle, the ions fall on the photographic plate 2, which makes it possible to determine the radius R of this arc. Knowing the induction of the magnetic field B and the speed υ of the ions, according to the formula

the specific charge of the ions can be determined. And if the charge of an ion is known, its mass can be calculated.

The history of mass spectrometry begins with the fundamental experiments of J. J. Thomson at the beginning of the 20th century. The ending "-metria" in the name of the method appeared after the widespread transition from the detection of charged particles using photographic plates to electrical measurements of ion currents.

Mass spectrometry is especially widely used in the analysis of organic substances, since it provides reliable identification of both relatively simple and complex molecules. The only general requirement is that the molecule be ionizable. However, by now it has been

there are so many ways to ionize sample components that mass spectrometry can be considered an almost universal method.

1. 3 MHD generator

The principle of operation of an MHD generator, like a conventional machine generator, is based on the phenomenon of electromagnetic induction, that is, on the appearance of a current in a conductor crossing the magnetic field lines. Unlike machine generators, the conductor in the MHD generator is the working fluid itself.

The working body moves across the magnetic field, and under the action of the magnetic field, oppositely directed flows of charge carriers of opposite signs arise.

The Lorentz force acts on a charged particle.

The following media can serve as the working body of the MHD generator:

· electrolytes;

· liquid metals;

plasma (ionized gas).

The first MHD generators used electrically conductive liquids (electrolytes) as the working fluid. Currently, plasma is used, in which charge carriers are mainly free electrons and positive ions. Under the influence of a magnetic field, charge carriers deviate from the trajectory along which the gas would move in the absence of a field. In this case, in a strong magnetic field, a Hall field (see the Hall effect) can arise - an electric field formed as a result of collisions and displacements of charged particles in a plane perpendicular to the magnetic field.

1.4 Cyclotron

A cyclotron is a resonant cyclic accelerator of nonrelativistic heavy charged particles (protons, ions), in which particles move in a constant and uniform magnetic field, and a high-frequency electric field of a constant frequency is used to accelerate them.

The scheme of the cyclotron device is shown in Fig.3. Heavy charged particles (protons, ions) enter the chamber from an injector near the center of the chamber and are accelerated by an alternating field of a fixed frequency applied to accelerating electrodes (there are two of them and they are called dees). Particles with charge Ze and mass m move in a constant magnetic field of strength B, directed perpendicular to the plane of particle motion, along an unwinding spiral. The radius R of the trajectory of a particle with a velocity v is determined by the formula

where γ = -1/2 is the relativistic factor.

E = mv 2 /2 = (Ze) 2 B 2 R 2 /(2m) (3)

At the last turn of the helix, a deflecting electric field is switched on, bringing the beam out. The constancy of the magnetic field and the frequency of the accelerating field make continuous acceleration possible. While some particles move along the outer turns of the spiral, others are in the middle of the path, and still others are just beginning to move.

Conclusion

Hidden text

Written conclusion (the most basic for all subparagraphs of the first section - principles of operation, definitions)

List of used literature

1. Wikipedia [Electronic resource]: Lorentz force. URL: https://ru.wikipedia.org/wiki/Lorenz_force

2. Wikipedia [Electronic resource]: Magnetohydrodynamic generator. URL: https://ru.wikipedia.org/wiki/ Magnetohydrodynamic_generator

3. Wikipedia [Electronic resource]: Electron-beam devices. URL: https://ru.wikipedia.org/wiki/ Electron-beam_devices

4. Wikipedia [Electronic resource]: Mass spectrometry. URL: https://ru.wikipedia.org/wiki/Mass spectrometry

5. Nuclear physics on the Internet [Electronic resource]: Cyclotron. URL: http://nuclphys.sinp.msu.ru/experiment/accelerators/ciclotron.htm

6. Electronic textbook of physics [Electronic resource]: T. Applications of the Lorentz force // URL: http://www.physbook.ru/index.php/ T._Application_of_Lorentz_force

7. Academician [Electronic resource]: Magnetohydrodynamic generator// URL: http://dic.academic.ru/dic.nsf/enc_physics/MAGNETOHYDRODYNAMIC