but what does the current have to do with it, then

BecausenS d l – number of charges in volume S d l, Then for one charge

or

,

(2.5.2)

Lorentz force – force exerted by a magnetic field on a positive charge moving at speed(here is the speed of ordered movement of positive charge carriers). Lorentz force modulus:

,

(2.5.3)

where α is the angle between And .

From (2.5.4) it is clear that a charge moving along the line is not affected by force ().

Lorenz Hendrik Anton(1853–1928) – Dutch theoretical physicist, creator of classical electronic theory, member of the Netherlands Academy of Sciences. He derived a formula relating the dielectric constant to the density of the dielectric, gave an expression for the force acting on a moving charge in an electromagnetic field (Lorentz force), explained the dependence of the electrical conductivity of a substance on thermal conductivity, and developed the theory of light dispersion. Developed the electrodynamics of moving bodies. In 1904, he derived formulas connecting the coordinates and time of the same event in two different inertial reference systems (Lorentz transformations).

The Lorentz force is directed perpendicular to the plane in which the vectors lie And . To a moving positive charge left hand rule applies or« gimlet rule"(Fig. 2.6).

The direction of force for a negative charge is opposite, therefore, to The right hand rule applies to electrons.

Since the Lorentz force is directed perpendicular to the moving charge, i.e. perpendicular ,the work done by this force is always zero . Consequently, acting on a charged particle, the Lorentz force cannot change the kinetic energy of the particle.

Often Lorentz force is the sum of electric and magnetic forces:

,

(2.5.4)

here the electric force accelerates the particle and changes its energy.

Everyday we observe the effect of magnetic force on a moving charge on a television screen (Fig. 2.7).

The movement of the electron beam along the screen plane is stimulated by the magnetic field of the deflection coil. If you bring a permanent magnet close to the plane of the screen, you can easily notice its effect on the electron beam by the distortions that appear in the image.

The action of the Lorentz force in charged particle accelerators is described in detail in section 4.3.

MINISTRY OF EDUCATION AND SCIENCE

RUSSIAN FEDERATION

FEDERAL STATE BUDGET EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION

"KURGAN STATE UNIVERSITY"

ABSTRACT

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

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

Teacher Vorontsov B.S.

Kurgan 2016

Introduction 3

1. Use of Lorentz force 4

1.1. Electron beam 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 object with speed υ charge q only from the side of the magnetic field, often at full strength - 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 sin α

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

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

1. Using the Lorentz force

The effect 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 Ampere force) is electrical machines (electric motors and generators). The Lorentz force is widely used in electronic devices to influence charged particles (electrons and sometimes ions), for example, in television cathode ray tubes, V mass spectrometry And MHD generators.

Also, in the currently created experimental installations for carrying out 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 circular motion of charged particles in a uniform magnetic field and the independence of the period of such motion from the particle speed are used in cyclic accelerators of charged particles - cyclotrons.

1. 1. Electron beam devices

Electron beam devices (EBDs) are a class of vacuum electronic devices that use a flow of electrons, concentrated in the form of a single beam or beam of beams, which are controlled both in intensity (current) and position in space, and interact with a stationary spatial target (screen) of the device. The main area of ​​application of ELP is the conversion of optical information into electrical signals and the reverse conversion of the electrical signal into an optical signal - 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 and amplifying electron tubes (beam tetrodes, electric vacuum indicators, lamps with secondary emission, etc.) with a beam form of currents.

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

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

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

The target (screen) of the receiving ELP converts the energy of the beam into the luminous flux of a 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 cylinder. 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 deflection system, which can change the direction of the beam. Television CRTs use a magnetic deflection system as it provides large deflection angles. Oscillographic CRTs use an electrostatic deflection system as it provides greater performance. The electron beam hits a screen covered with phosphor. Bombarded by electrons, the phosphor glows and a rapidly moving spot of variable brightness creates an image on the screen.

Open the palm of your left hand and straighten all your fingers. Bend your thumb at an angle of 90 degrees relative to all other fingers, in the same plane as your palm.

Imagine that the four fingers of your palm, which you hold together, indicate the direction of the speed of the charge if it is positive, or the opposite direction to the speed if the charge is negative.

The magnetic induction vector, which is always directed perpendicular to the speed, will thus enter the palm. Now look where your thumb is pointing - this is the direction of the Lorentz force.

The Lorentz force can be zero and have no vector component. This occurs when the trajectory of a charged particle is parallel to the magnetic field lines. In this case, the particle has a rectilinear trajectory and constant speed. The Lorentz force does not affect the motion of the particle in any way, because in this case it is absent altogether.

In the simplest case, a charged particle has a trajectory of motion perpendicular to the magnetic field lines. Then the Lorentz force creates centripetal acceleration, forcing the charged particle to move in a circle.

note

The Lorentz force was discovered in 1892 by Hendrik Lorentz, a physicist from Holland. Today it is quite often used in various electrical appliances, the action of which depends on the trajectory of moving electrons. For example, these are cathode ray tubes in televisions and monitors. All kinds of accelerators that accelerate charged particles to enormous speeds, using the Lorentz force, set the orbits of their movement.

Helpful advice

A special case of the Lorentz force is the Ampere force. Its direction is calculated using the left-hand rule.

Sources:

• Lorentz force
• Lorentz force left hand rule

The effect of a magnetic field on a current-carrying conductor means that the magnetic field affects moving electric charges. The force acting on a moving charged particle from a magnetic field is called the Lorentz force in honor of the Dutch physicist H. Lorentz

Instructions

Force - means you can determine its numerical value (modulus) and direction (vector).

The modulus of the Lorentz force (Fl) is equal to the ratio of the modulus of force F acting on a section of a conductor with a current of length ∆l to the number N of charged particles moving in an orderly manner on this section of the conductor: Fl = F/N ( 1). Due to simple physical transformations, the force F can be represented in the form: F= q*n*v*S*l*B*sina (formula 2), where q is the charge of the moving one, n is on the conductor section, v is the speed of the particle, S is the cross-sectional area of ​​the conductor section, l is the length of the conductor section, B is the magnetic induction, sina is the sine of the angle between the velocity and induction vectors. And convert the number of moving particles to the form: N=n*S*l (formula 3). Substitute formulas 2 and 3 into formula 1, reduce the values ​​of n, S, l, it turns out for the Lorentz force: Fл = q*v*B*sin a. This means that to solve simple problems of finding the Lorentz force, define the following physical quantities in the task condition: the charge of a moving particle, its speed, the induction of the magnetic field in which the particle is moving, and the angle between the speed and induction.

Before solving the problem, make sure that all quantities are measured in units that correspond to each other or the international system. To obtain the answer in newtons (N - unit of force), charge must be measured in coulombs (K), speed - in meters per second (m/s), induction - in tesla (T), sine alpha - not a measurable number.
Example 1. In a magnetic field, the induction of which is 49 mT, a charged particle of 1 nC moves at a speed of 1 m/s. The velocity and magnetic induction vectors are mutually perpendicular.
Solution. B = 49 mT = 0.049 T, q = 1 nC = 10 ^ (-9) C, v = 1 m/s, sin a = 1, Fl = ?

Fl = q*v*B*sin a = 0.049 T * 10 ^ (-9) C * 1 m/s * 1 =49* 10 ^(12).

The direction of the Lorentz force is determined by the left-hand rule. To apply it, imagine the following relationship of three vectors perpendicular to each other. Position your left hand so that the magnetic induction vector enters the palm, four fingers are directed towards the movement of the positive (against the movement of the negative) particle, then the thumb bent 90 degrees will indicate the direction of the Lorentz force (see figure).
The Lorentz force is applied in television tubes of monitors and televisions.

Sources:

• G. Ya Myakishev, B.B. Bukhovtsev. Physics textbook. Grade 11. Moscow. "Education". 2003
• solving problems on the Lorentz force

The true direction of the current is the direction in which the charged particles are moving. It, in turn, depends on the sign of their charge. In addition, technicians use the conditional direction of charge movement, which does not depend on the properties of the conductor.

Instructions

To determine the true direction of movement of charged particles, follow the following rule. Inside the source, they fly out of the electrode, which is charged with the opposite sign, and move towards the electrode, which for this reason acquires a charge similar in sign to the particles. In the external circuit, they are pulled out by the electric field from the electrode, the charge of which coincides with the charge of the particles, and are attracted to the oppositely charged one.

In a metal, current carriers are free electrons moving between crystalline nodes. Since these particles are negatively charged, consider them moving from positive to negative electrode inside the source, and from negative to positive in the external circuit.

In non-metallic conductors, electrons also carry charge, but the mechanism of their movement is different. An electron leaving an atom and thereby turning it into a positive ion causes it to capture an electron from the previous atom. The same electron that leaves an atom negatively ionizes the next one. The process is repeated continuously as long as there is current in the circuit. The direction of movement of charged particles in this case is considered the same as in the previous case.

There are two types of semiconductors: with electron and hole conductivity. In the first, the carriers are electrons, and therefore the direction of movement of particles in them can be considered the same as in metals and non-metallic conductors. In the second, the charge is carried by virtual particles - holes. To put it simply, we can say that these are a kind of empty spaces in which there are no electrons. Due to the alternating shift of electrons, holes move in the opposite direction. If you combine two semiconductors, one of which has electronic and the other hole conductivity, such a device, called a diode, will have rectifying properties.

In a vacuum, charge is carried by electrons moving from a heated electrode (cathode) to a cold one (anode). Note that when the diode rectifies, the cathode is negative relative to the anode, but relative to the common wire to which the transformer secondary winding terminal opposite the anode is connected, the cathode is positively charged. There is no contradiction here, given the presence of a voltage drop on any diode (both vacuum and semiconductor).

In gases, charge is carried by positive ions. Consider the direction of movement of charges in them to be opposite to the direction of their movement in metals, non-metallic solid conductors, vacuum, as well as semiconductors with electronic conductivity, and similar to the direction of their movement in semiconductors with hole conductivity. Ions are much heavier than electrons, which is why gas-discharge devices have high inertia. Ionic devices with symmetrical electrodes do not have one-way conductivity, but those with asymmetrical electrodes do have it in a certain range of potential differences.

In liquids, charge is always carried by heavy ions. Depending on the composition of the electrolyte, they can be either negative or positive. In the first case, consider them to behave similarly to electrons, and in the second, similar to positive ions in gases or holes in semiconductors.

When specifying the direction of current in an electrical circuit, regardless of where the charged particles actually move, consider them moving in the source from negative to positive, and in the external circuit from positive to negative. The indicated direction is considered conditional, and it was accepted before the discovery of the structure of the atom.

Sources:

• direction of current

Force Lorenz determines the intensity of the effect of the electric field on a point charge. In some cases, it means the force with which a magnetic field acts on a charge q, one that moves at a speed V, in others it means the total influence of the electric and magnetic fields.

Instructions

1. In order to determine direction strength Lorenz, a mnemonic rule for the left hand was made. It is easy to remember due to the fact that direction determined with the help of fingers. Open the palm of your left hand and straighten all your fingers. Bend the huge finger at an angle of 90 degrees relative to each other fingers, in the same plane as the palm.

2. Imagine that the four fingers of your palm that you hold together are pointing direction the speed of charge movement, if it is correct, or the opposite of the speed direction, if the charge is negative.

3. The magnetic induction vector, the one that is invariably directed perpendicular to the speed, will thus enter the palm. Now look where your big finger is pointing - this is it direction strength Lorenz .

4. Force Lorenz may be equal to zero and have no vector component. This occurs when the trajectory of a charged particle is parallel to the magnetic field lines. In this case, the particle has a clear trajectory and continuous speed. Force Lorenz does not affect the motion of the particle in any way, since in this case it is completely absent.

5. In the simplest case, a charged particle has a trajectory of motion perpendicular to the magnetic field lines. Then strength Lorenz creates centripetal acceleration, forcing the charged particle to move in a circle.

It is absolutely reasonable and clear that on different parts of the path the speed of the body’s movement is uneven, somewhere it is more rapid, and somewhere more leisurely. In order to measure the metamorphosis of body speed over time intervals, the representation “ acceleration“. Under acceleration m is perceived as a metamorphosis of the speed of movement of a body object over a certain time interval, during which the metamorphosis of speed happened.

You will need

• Know the speed of movement of an object in different areas at different time intervals.

Instructions

1. Definition of acceleration during uniformly accelerated motion. This type of motion means that an object accelerates by the same value over equal intervals of time. Let at one of the moments of movement t1 the speed of its movement be v1, and at the moment t2 the speed would be v2. Then acceleration object could be calculated using the formula: a = (v2-v1)/(t2-t1)

2. Determination of the acceleration of an object if it does not have uniformly accelerated motion. In this case, the “average” representation is introduced acceleration“. This representation characterizes the metamorphosis of the speed of an object during the entire time of its movement along a given path. This is expressed by the formula: a = (v2-v1)/t

Magnetic induction is a vector quantity, and therefore, in addition to the unconditional quantity, it is characterized direction. In order to detect it, it is necessary to detect the poles of a continuous magnet or the direction of the current, the one that generates the magnetic field.

You will need

• – reference magnet;
• – current source;
• – right gimlet;
• – direct conductor;
• – coil, turn of wire, solenoid.

Instructions

1. magnetic induction of a continuous magnet. To do this, locate its north and south poles. Typically, the north pole of a magnet is blue, and the south pole is scarlet. If the poles of the magnet are unknown, take a reference magnet and bring its north pole to the unfamiliar one. That end, the one that is attracted to the north pole of the reference magnet, will be the south pole of the magnet whose field induction is measured. Lines magnetic inductions leave the north pole and enter the south pole. The vector at any point on the line goes tangentially in the direction of the line.

2. Determine the direction of the vector magnetic induction of a straight conductor carrying current. The current flows from the positive pole of the source to the negative. Take the gimlet, the one that is screwed in when rotated clockwise, it is called the right one. Start screwing it in the direction where the current flows in the conductor. Rotating the handle will show the direction of the closed circular lines magnetic induction. Vector magnetic induction in this case will be tangent to the circle.

3. Find the direction of the magnetic field of the current coil, coil, or solenoid. To do this, connect the conductor to a current source. Take the right gimlet and rotate its handle in the direction of the current flowing through the turns from the correct pole of the current source to the negative one. The forward movement of the gimlet rod will show the direction of the magnetic field lines. For example, if the handle of a gimlet rotates in the direction of the current counterclockwise (to the left), then it, unscrewing, moves progressively towards the observer. Consequently, the magnetic field lines are also directed towards the observer. Inside the turn, coil or solenoid, the magnetic field lines are straight, in direction and absolute value they coincide with the vector magnetic induction.

Helpful advice
As a right gimlet, you can use an ordinary corkscrew for opening bottles.

Induction appears in a conductor when crossing field lines if it is moved in a magnetic field. Induction is characterized by a direction that can be determined according to established rules.

You will need

• – conductor with current in a magnetic field;
• – a gimlet or screw;
• – solenoid with current in a magnetic field;

Instructions

1. In order to find out the direction of induction, you should use one of 2 rules: the gimlet rule or the right hand rule. The first is used mainly for straight wires in which current flows. The right-hand rule is used for a current-fed coil or solenoid.

2. The gimlet rule says: If the direction of the gimlet or screw moving forward is the same as the current in the wire, then turning the handle of the gimlet shows the direction of induction.

3. To find out the direction of induction using the gimlet rule, determine the polarity of the wire. Current invariably flows from the right pole to the negative pole. Place a gimlet or screw along the wire with current: the tip of the gimlet should look towards the negative pole, and the handle towards the positive pole. Start rotating the gimlet or screw as if twisting it, that is, clockwise. The resulting induction has the form of closed circles around the current-fed wire. The direction of induction will coincide with the direction of rotation of the gimlet handle or screw head.

4. The right hand rule says: If you take a coil or solenoid in the palm of your right hand, so that four fingers lie in the direction of current flow in the turns, then the large finger placed to the side will indicate the direction of induction.

5. In order to determine the direction of induction, using the right hand rule, you need to take a solenoid or coil with current so that the palm lies on the correct pole, and the four fingers of the hand are in the direction of the current in the turns: the little finger is closer to the plus, and the index finger is closer to the minus. Place your large finger to the side (as if showing a “class” gesture). The direction of the thumb will indicate the direction of induction.

Video on the topic

Note!
If the direction of the current in the conductor is changed, then the gimlet should be unscrewed, that is, rotated counterclockwise. The direction of induction will also coincide with the direction of rotation of the gimlet handle.

Helpful advice
You can determine the direction of induction by mentally imagining the rotation of a gimlet or screw. You don't have to have it on hand.

Induction lines are understood as magnetic field lines. In order to obtain information about this type of matter, it is not sufficient to know the absolute value of induction, it is necessary to know its direction. The direction of induction lines can be detected using special devices or using rules.

You will need

• – straight and circular conductor;
• – continuous current source;
• – continuous magnet.

Instructions

1. Connect a straight conductor to a continuous current source. If a current flows through it, it is surrounded by a magnetic field, the lines of force of which are concentric circles. Determine the direction of the field lines using the right gimlet rule. A right-hand gimlet is a screw that moves forward when rotated to the right (clockwise).

2. Determine the direction of current in a conductor by considering that it flows from the right pole of the source to the negative pole. Place the screw rod parallel to the conductor. Start rotating it so that the rod begins to move in the direction of the current. In this case, the direction of rotation of the handle will indicate the direction of the magnetic field lines.

3. Find the direction of the induction lines of the coil with current. To do this, use the same right gimlet rule. Position the gimlet in such a way that the handle rotates in the direction of current flow. In this case, the movement of the gimlet rod will show the direction of the induction lines. Let's say, if the current flows clockwise in a coil, then the lines of magnetic induction will be perpendicular to the plane of the coil and will go into its plane.

4. If a conductor moves in an external uniform magnetic field, determine its direction using the left-hand rule. To do this, position your left hand so that four fingers show the direction of the current, and the outstretched huge finger shows the direction of movement of the conductor. Then the induction lines of a uniform magnetic field will enter the palm of the left hand.

5. Detect the direction of the magnetic induction lines of a continuous magnet. To do this, determine where its north and south poles are located. The lines of magnetic induction are directed from the north to the south pole outside the magnet and from the south pole to the north inside the continuous magnet.

Video on the topic

In order to determine the modulus of point charges of identical magnitude, measure the force of their interaction and the distance between them and make a calculation. If you need to detect the charge modulus of individual point bodies, introduce them into an electric field with a known intensity and measure the force with which the field acts on these charges.

You will need

• – torsion scales;
• - ruler;
• - calculator;
• – electrostatic field meter.

Instructions

1. If there are two charges identical in modulus, measure the force of their interaction using a Coulomb torsion balance, which is also an emotional dynamometer. Later, when the charges come into balance and the wire of the scales compensates for the force of electrical interaction, record the value of this force on the scale. Later, using a ruler, caliper, or a special scale on the scale, find the distance between these charges. Consider that unlike charges attract, and like charges repel. Measure force in Newtons and distance in meters.

2. Calculate the value of the modulus of one point charge q. To do this, divide the force F with which two charges interact by the exponent 9 10^9. Take the square root of the result. Multiply the result by the distance between charges r, q=r?(F/9 10^9). You will receive the charge in Coulombs.

3. If the charges are unequal, then one of them must be previously known. Determine the force of interaction between the known and unknown charges and the distance between them using Coulomb torsion balances. Calculate the modulus of the unknown charge. To do this, divide the force of interaction of charges F by the product of the exponent 9 10^9 by the modulus of the charge q0. Take the square root of the resulting number and multiply the total by the distance between the charges r; q1=r ?(F/(9 10^9 q2)).

4. Determine the modulus of an unfamiliar point charge by introducing it into an electrostatic field. If its intensity at a given point is not previously known, insert an electrostatic field meter sensor into it. Measure voltage in volts per meter. Place a charge at a point of known tension and, with the support of an emotional dynamometer, measure the force in Newtons acting on it. Determine the charge modulus by dividing the value of the force F by the electric field strength E; q=F/E.

Video on the topic

Note!
The Lorentz force was discovered in 1892 by Hendrik Lorentz, a physicist from Holland. Today it is quite often used in various electrical appliances, the action of which depends on the trajectory of moving electrons. Let's say these are cathode ray tubes in TVs and monitors. All kinds of accelerators that accelerate charged particles to high speeds use the Lorentz force to set the orbits of their motion.

Helpful advice
A special case of the Lorentz force is the Ampere force. Its direction is calculated using the left-hand rule.

DEFINITION

Lorentz force– the force acting on a point charged particle moving in a magnetic field.

It is equal to the product of the charge, the modulus of the particle velocity, the modulus of the magnetic field induction vector and the sine of the angle between the magnetic field vector and the particle velocity.

Here is the Lorentz force, is the particle charge, is the magnitude of the magnetic field induction vector, is the particle velocity, is the angle between the magnetic field induction vector and the direction of motion.

Unit of force – N (newton).

The Lorentz force is a vector quantity. The Lorentz force takes its greatest value when the induction vectors and direction of the particle velocity are perpendicular ().

The direction of the Lorentz force is determined by the left-hand rule:

If the magnetic induction vector enters the palm of the left hand and four fingers are extended towards the direction of the current movement vector, then the thumb bent to the side shows the direction of the Lorentz force.

In a uniform magnetic field, the particle will move in a circle, and the Lorentz force will be a centripetal force. In this case, no work will be done.

Examples of solving problems on the topic “Lorentz force”

EXAMPLE 1

EXAMPLE 2

Exercise	Under the influence of the Lorentz force, a particle of mass m with charge q moves in a circle. The magnetic field is uniform, its strength is equal to B. Find the centripetal acceleration of the particle.
Solution	Let us recall the Lorentz force formula: In addition, according to Newton's 2nd law: In this case, the Lorentz force is directed towards the center of the circle and the acceleration created by it is directed there, that is, this is centripetal acceleration. Means: