The action of the power of Lorentz. Lorentz Power

Netherlands Physicist X. A. Lorenz at the end of the XIX century. It established that the force acting on the part of the magnetic field on a moving charged particle is always perpendicular to the direction of movement of the particle and the power lines of the magnetic field in which this particle moves. The direction of the force of Lorentz can be determined using the rule of the left hand. If you position the palm of the left hand so that the four elongated fingers indicate the direction of the charge movement, and the vector of magnetic induction of the field entered the retired thumb indicate the direction of the Lorentz force acting on a positive charge.

If the charge of the particle is negative, the Lorentz power will be directed in the opposite direction.

The Lorentz power module is easily determined from the AMPER law and is:

F. = | q.| vB SIN?,

where q. - the charge of the particle, v. - the speed of her movement, ? - The angle between the velocity and induction of the magnetic poly.

If, besides the magnetic field, there is also an electric field that acts on the charge with force , then the full force acting on the charge is equal to:

.

Often it is this force called the force of Lorentz, and the force expressed by the formula ( F. = | q.| vB. sin?) Call magnetic part of Lorentz.

Since the Lorentz power is perpendicular to the direction of movement of the particle, it cannot change its speed (it does not work), and it can only change the direction of its movement, i.e. to spark the trajectory.

Such curvature of the electron trajectory in a television kinescope is easy to observe if you bring a permanent magnet to its screen - the image will distort.

Movement of the charged particle in a homogeneous magnetic field. Let the charged particle flies at speeds v. In a homogeneous magnetic field perpendicular to lines of tension.

The force acting on the part of the magnetic field on a particle will make it evenly rotate around the circle by the radius r.which is easy to find using the second law of Newton, the expression of the purposeful acceleration and the formula ( F. = | q.| vB. sin?):

.

From here we get

.

where m. - Mass of particles.

The use of the force of Lorentz.

The effect of the magnetic field on moving charges is used, for example, in mass spectrographsallowing to separate charged particles according to their specific charges, i.e., in relation to the charge of the particle to its mass, and according to the results obtained accurately determine the masses of particles.

The vacuum chamber of the device is placed in the field (induction vector perpendicular to the figure). The charged particles accelerated by the electric field (electrons or ions), describing the arc, fall on the photoplastic, where they leave the trace, allowing to measure the radius of the trajectory with great accuracy r.. For this radius, the specific charge of the ion is determined. Knowing the charge of the ion, easily calculate its mass.

Along with the strength of the ampere, Coulomb interaction, the concept of Lorentz's power is often found in physics. This phenomenon is one of the fundamental electrical engineering and electronics, on a series of C, and other. It affects charges that move in a magnetic field. In this article, we briefly and clearly consider what Lorentz power is and where it is applied.

Definition

When the electrons move through the conductor - the magnetic field occurs around it. At the same time, if you put the conductor into the transverse magnetic field and move it - the EMH of electromagnetic induction will occur. If through the conductor, which is in a magnetic field flows the current - the power of the ampere acts on it.

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

The strength under consideration is partly similar to the one that is considered above, but it does not act on the conductor, but on a moving charged particle in a magnetic field. The formula has the form:

Important! The Lorentz (FL) strength acts on an electron moving in a magnetic field, and on the conductor - ampere.

Of the two formulas it can be seen as in the first and in the second case, the closer the sine angle angle to 90 degrees, the greater the exposure to the conductor or the charge Fa or Fl, respectively.

So, Lorentz's power characterizes not a change in the speed, but what is the effect of the magnetic field on a charged electron or positive ion. When exposed to them, Fl does not work. Accordingly, it is precisely the direction of the speed of movement of the charged particle, and not its value.

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

How the power of Lorentz is sent

To determine the direction of the force of Lorenz, as with the force of the ampere, the rule of the left hand works. This means to understand where the value of the FL is directed to open the palm of the left hand so that the magnetic induction lines consisted in the hand, and the elongated four fingers indicated the direction of the velocity vector. Then the thumb, bent at a right angle to the palm, indicates the direction of Lorentz's strength. In the picture below you see how to determine the direction.

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

At the same time, to be more accurate, for positive and negatively charged particles, the direction of four deployed fingers is important. The above described left hand is formulated for a positive particle. If it is charged negatively, the magnetic induction line should not be directed in the open palm, but in its back side, but the direction of the vector Fl will be the opposite.

Now we will tell simple words, which gives us this phenomenon and what real impact it has on charges. Suppose that the electron is moving in a plane perpendicular to the direction of magnetic induction lines. We have already mentioned that Fl does not affect the speed, but only changes the direction of movement of particles. Then Lorentz's power will have a centripetal impact. This is reflected in the figure below.

Application

Of all areas where the Lorentz power is used, one of the large-scale movement of particles in the magnetic field of the Earth. If you consider our planet as a large magnet, then the particles that are near the northern magnetic poles are accelerated by the spiral movement. As a result, their collision occurs with atoms from the upper layers of the atmosphere, and we see the Northern Lights.

Nevertheless, there are other cases where this phenomenon is applied. For example:

• Electron beam tubes. In their electromagnetic deflecting systems. The ELT was used more than 50 years in a row in various devices, ranging from the simplest oscilloscope to televisions of different shapes and sizes. It is curious that in matters of color reproduction and work with graphics, some still use CRT monitors.
• Electrical machines - generators and engines. Although the ampere power is acting here. But these quantities can be viewed as related. However, these are complex devices in which the impact of many physical phenomena is observed.
• In accelerators of charged particles in order to ask them orbits and directions.

Conclusion

Let's summarize and denote the four main theses of this article in simple language:

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

Its role is large enough in the "electrical" spheres. A specialist should not miss the main theoretical information about fundamental physical laws. These knowledge will be useful as those who are engaged in scientific work, design and simply for general development.

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

Materials

The force acting from the magnetic field on the moving electrically charged particle.

where q is a particle charge;

V - charge rate;

a is the angle between the charge rate vector and the magnetic induction vector.

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

If you put the left hand so that perpendicular to the speed component of the induction vector was in the palm, and four fingers would be located in the direction of the speed of movement of the positive charge (or against the direction of the negative charge rate), then the bent thumb indicate the direction of the Lorentz force:

.

Since Lorentz's power is always perpendicular to the charge rate, it does not make work (that is, does not change the amount of charge speed and its kinetic energy).

If the charged particle moves parallel to the power lines of the magnetic field, then Fl \u003d 0, and the charge in the magnetic field is moving and straight.

If the charged particle moves perpendicular to the power lines of the magnetic field, the Lorentz force is centripetal:

and creates a centripetal acceleration equal:

In this case, the particle moves around the circumference.

.

According to Newton's second law: Lorentz's power is equal to the mass of the mass of the particle on the centripetal acceleration:

then the radius of the circle:

and the time of circulation of charge in a magnetic field:

Since the electric current is an ordered movement of charges, the magnetic field action on the conductor with the current is the result of its action on separate moving charges. If you make a conductor with a current in a magnetic field (FIGS. 96, a), then we will see that as a result of the addition of magnetic fields of the magnet and conductor, the resulting the resulting magnetic field will increase on one side of the conductor (on the drawing above) and loosening the magnetic field on the other side Explorer (on the drawing below). As a result of the operation of two magnetic fields, the magnetic lines curvature will occur and they striving to cut down, will push the conductor down (Fig. 96, b).

The direction of force acting on the conductor with a current in the magnetic field can be defined according to the "right hand". If the left hand is located in a magnetic field so that the magnetic lines emerging from the North Pole seem to be in the palm, and the four elongated fingers coincide with the direction of current in the conductor, then the large bent finger will show the direction of force. The force of the ampere acting on the element of the conductor length depends: on the magnitude of the magnetic induction in the current value in the conductor I, from the element of the conductor length and from the corner of the angle and between the direction of the conductor length element and the direction of the magnetic field.

This dependence can be expressed by the formula:

For a straight-line conductor of the final length, placed perpendicular to the direction of the uniform magnetic field, the force acting on the conductor will be equal to:

From the last formula, we define the dimension of magnetic induction.

Since the dimension of power:

i.e. the dimension of induction is the same as we received from the law of Bio and Savara.

Tesla (unit of magnetic induction)

Tesla, unit of magnetic induction International system units, equal magnetic induction, With which the magnetic flux through the cross section of 1 m.2 is 1. weber. Named by name N. Tesla. Designations: Russian tl International T. 1. tL \u003d. 104 gs(gauss).

Magnesium? Tat? NT, magic? Total DIPO? LINE MOM? NT - The main value characterizing the magnetic properties of the substance. The magnetic moment is measured in A⋅M 2 or J / T (SI), or ERG / GS (SGS), 1 erg / Gs \u003d 10 -3 J / TL. The specific unit of elementary magnetic moment is the magneton boron. In the case of a flat circuit with an electric current, the magnetic moment is calculated as

where - the current in the circuit, is the contour area, the unit vector of normal to the circuit plane. The direction of the magnetic moment is usually located according to the rule of the reel: if you rotate the panel knob in the current direction, then the direction of the magnetic moment will coincide with the direction of the progressive motion of the bouler.

For an arbitrary closed contour, the magnetic moment is from:

,

where - the radius vector spent from the start of the coordinates to the element of the contour length

In the general case of an arbitrary distribution of currents in the environment:

,

where - the current density in the volume element.

So, the torque acts on the circuit in the magnetic field. The circuit is oriented at this point point in only one way. We will take a positive direction of normal for the direction of the magnetic field at this point. The torque is directly proportional to the magnitude of the current I., Square contour S. and sinus angle between the direction of the magnetic field and normal.

here M. - torque , or moment of power , - magnetic moment Contour (similarly - electric moment of dipole).

In a non-uniform field () the formula is valid if the size of the contour is small enough (Then within the circuit, the field can be considered approximately homogeneous). Consequently, the circuit with the current is still striving to turn around so that its magnetic moment is directed along the lines of the vector.

But, in addition, the resulting force acts on the contour (in the case of a homogeneous field and. This force acts on the contour with the current or permanent magnet with the moment and pulls them into the region of a stronger magnetic field.
Work on moving contour with current in a magnetic field.

It is easy to prove that work on moving the contour with a current in a magnetic field is equal where and - magnetic streams through the contour area in the final and initial positions. This formula is valid if current in the circuit is constant. When moving the contour, the phenomenon of electromagnetic induction is not taken into account.

The formula is also valid for large contours in a strongly inhomogeneous magnetic field (provided I \u003d.const).

Finally, if the outline does not shift with the current, but to change the magnetic field, i.e. change the magnetic flux through the surface covered by the contour, from the value to then for this you need to make the same job . This work is called the operation of changing the magnetic flux associated with the contour. The flow of the magnetic induction vector (magnetic flow) Through the DS platform is called a scalar physical value that is equal

where b n \u003d bcosα - vector projection IN On the direction of normal to the DS site (α - angle between vectors n. and IN), D. S.\u003d ds. n. - vector in which the module is equal to DS, and its direction coincides with the direction of normal n. To the site. Stream vector IN It can be both positive and negative depending on the COSα sign (set by the choice of the positive direction of the normal n.). Stream vector IN Usually bind to the contour, according to which the current flows. In this case, the positive direction of normal to the contour we wondered: it binds to the current rule of the right screw. It means that the magnetic flow, which is created by the contour, through the surface limited to them itself is always positive.

The flow of the magnetic induction vector F B through an arbitrary specified surface s is equal

(2)

For a homogeneous field and a flat surface, which is located perpendicular to the vector IN, B n \u003d b \u003d const and

From this formula, the unit of magnetic flux is set weber (WB): 1 WB is a magnetic stream, which passes through the flat surface of 1 m 2, which is located perpendicular to a homogeneous magnetic field and the induction of which is 1 TL (1 WB \u003d 1 TL 2).

Gauss Theorem for Field in: Vector stream of magnetic induction through any closed surface is zero:

(3)

This theorem is a reflection of the fact that magnetic charges are absentAs a result, the magnetic induction line has no beginning, no end and are closed.

Consequently, for the streams of vectors IN and E. Through the closed surface in the vortex and potential fields, various formulas are obtained.

As an example, we will find the flow of the vector IN Through the solenoid. The magnetic induction of a homogeneous field inside a solenoid with a core with a magnetic permeability μ, equal

Magnetic stream Through one round of Solenoid Snemide S is equal

a full magnetic stream, which is connected with all the colors of the solenoid and called streaming,

The emergence of force acting on the electric charge moving in an external electromagnetic field

Animation

Description

Lorentz's force is called a progressive particle, moving in an external electromagnetic field.

The formula for the power of Lorentz (F) was first obtained by generalizing experienced facts H.A. Lorenz in 1892 and presented in the work "Electromagnetic theory of Maxwell and its application to moving bodies." It has the form:

F \u003d QE + Q, (1)

where q is a charged particle;

E - electric field strength;

B - vector magnetic induction, independent of the value of charge and the speed of its movement;

V is the velocity vector of the charged particle relative to the coordinate system, in which the values \u200b\u200bf and b are calculated.

The first term in the right-hand side of equation (1) is the force acting on the charged particle in the electric field F E \u003d QE, the second term is the force acting in the magnetic field:

F M \u003d Q. (2)

Formula (1) is universal. It is valid for both constant and variable power fields, as well as for any values \u200b\u200bof the speed of the charged particle. It is an important ratio of electrodynamics, as it allows you to associate the equations of the electromagnetic field with the equations of motion of charged particles.

In the nonrelativistic approximation, the force F, like any other force, does not depend on the choice of an inertial reference system. At the same time, the magnetic component of the Lorentz force F M varies with the transition from one reference system to another due to the change in speed, therefore the electrical component F E will change. In this connection, the separation of force F per magnetic and electrical makes sense only with the reference system.

In a scalar form, the expression (2) has the form:

FM \u003d QVBSINA, (3)

where A is the angle between velocity vectors and magnetic induction.

Thus, the magnetic part of the Lorentz force is maximal, if the direction of movement of the particle is perpendicular to the magnetic field (A \u003d P / 2), and is zero, if the particle moves along the direction of the field in (a \u003d 0).

The magnetic force F M is proportional to the vector product, i.e. It is perpendicular to the velocity vehicle of the charged particle and therefore does not make work on the charge. This means that in a constant magnetic field, only the trajectory of the moving charged particle is being twisted under the action of magnetic force, but its energy always remains unchanged, as if the particle either moved.

The direction of magnetic force for a positive charge is determined according to the vector product (Fig. 1).

Direction of force acting on a positive charge in a magnetic field

Fig. one

For a negative charge (electron), the magnetic force is directed in the opposite direction (Fig. 2).

Direction of the force of Lorentz acting on an electron in a magnetic field

Fig. 2.

Magnetic field in directed to the reader perpendicular to the figure. The electric field is missing.

If the magnetic field is uniformly and sent perpendicular to the speed, the charge M is moving around the circle. The radius of the circle R is determined by the formula:

where - the specific particle charge.

The particle circulation period (one turn time) does not depend on the speed if the particle speed is much less than the speed of light in vacuo. Otherwise, the particle conversion period increases due to the increase in the relativistic mass.

In the case of a non-relativistic particle:

where - the specific particle charge.

In vacuum in a homogeneous magnetic field, if the velocity vector is not perpendicular to the magnetic induction vector (A # P / 2), the charged particle under the action of the Lorentz force (its magnetic part) moves along the screw line with a constant velocity v. At the same time, its movement is made up of a uniform straight line move along the direction of the magnetic field at at a speed and a uniform rotational motion in the plane perpendicular to the field at speeds (Fig. 2).

Projection of the trajectory of the movement of the particle on the plane perpendicular in there is a circle of radius:

particle circulation period:

The distance H, which passes the particle during the time T along the magnetic field in (pitch of the screw trajectory) is determined by the formula:

h \u003d vcos a t. (6)

The axis of the screw line coincides with the direction of the field in, the center of the circle moves along the power line of the field (Fig. 3).

Movement of the charged particle flew at an anglea№P. / 2 in a magnetic field in

Fig. 3.

The electric field is missing.

If the electrical field E No. 0, the movement is more complex.

In a particular case, if the e-ib vectors are parallel, the velocity V 11, parallel to the magnetic field, changes, as a result of which changes the step of the screw trajectory (6).

In the event that E IB is not parallel, the particle rotation center is moved, called the drift, perpendicular to the field in. The drift direction is determined by the vector product and does not depend on the charge sign.

The effect of the magnetic field on moving charged particles lead to the redistribution of the current on the cross section of the conductor, which finds its manifestation in thermomagnetic and galvanized phenomena.

The effect is open to the Netherlands physicist H.A. Lorenz (1853-1928).

Temporary characteristics

Initiation time (log to -15 to -15);

Existence time (Log TC from 15 to 15);

Degradation time (Log TD from -15 to -15);

The time of optimal manifestation (Log TK from -12 to 3).

Diagram:

Technical implementation effect

Technical implementation of the Action of Lorentz

The technical implementation of the experiment on the direct observation of the force of the Lorentz force on a moving charge is usually quite complex, since the corresponding charged particles have a molecular characteristic size. Therefore, the observation of their trajectory in a magnetic field requires vacuuming of the working volume to avoid collisions that distort the trajectory. So specifically such demonstration settings are usually not created. It is easiest for the demonstration to use the standard sector magnetic mass analyzer, see the effect of 409005, the action of which is entirely based on the power of Lorenz.

Application effect

Typical use in the technique - Hall sensor, widely used in measuring equipment.

The metal or semiconductor plate is placed in a magnetic field in. When the electric current of the density j in the direction perpendicular to the magnetic field, the transverse electric field occurs through it in the plate, the strength of which E is perpendicular to both vectors and c. According to measurements are found in.

This effect is explained by the action of Lorentz's strength on a moving charge.

Galvanomagnetic magnetometers. Mass spectrometers. Accelerators of charged particles. Magnitohydrodynamic generators.

Literature

1. Sivukhin D.V. General course of physics. - M.: Science, 1977.- T.3. Electricity.

2. Physical Encyclopedic Dictionary. - M., 1983.

3. Detlaf A.A., Yavorsky B.M. Course of physics. - M.: Higher School, 1989.

Keywords

• electric charge
• magnetic induction
• a magnetic field
• electric field tension
• lorentz power
• particle speed
• radius of circle
• treatment period
• step screw trajectory
• electron
• proton
• positron

Sections of the Natural Sciences:

but the current and then

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

or

Lorentz power – the force acting on the part of the magnetic field on a positive charge moving at a speed(here - the rate of ordered movement of the carriers of a positive charge). Lorentz Power Module:

where α is the angle between and.

From (2.5.4) it can be seen that the power moving along the line does not work ().

Lorentz power is directed perpendicular to the plane in which the vectors lie and. To a moving positive charge applicable Left Hand Rule or« rule Braschik"(Fig. 2.6).

The direction of action for a negative charge is the opposite, therefore, electrons Applicable Right Hand Rule.

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

Often lorentz force call the amount of electric and magnetic forces:

,

(2.5.4)

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

Everyday the action of the magnetic force on a moving charge, we see on the television screen (Fig. 2.7).

The movement of the electron beam across the screen plane is stimulated by a magnetic field of a deflecting coil. If you bring a permanent magnet to the screen plane, it is easy to notice its effect on the electron beam according to the distortion in the image.

The effect of Lorentz Power in accelerators of charged particles is described in detail in clause 4.3.