Lorentz force is a branch of physics. Lorentz force in a magnetic field

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« Physics - Grade 11 "

The magnetic field acts with force on moving charged particles, including current-carrying conductors.
What is the force acting on one particle?

1.
The force exerted on a moving charged particle by a magnetic field is called Lorentz force in honor of the great Dutch physicist X. Lorenz, who created the electronic theory of the structure of matter.
The Lorentz force can be found using Ampère's law.

Lorentz force modulus is equal to the ratio of the modulus of force F, acting on a section of the conductor of length Δl, to the number N of charged particles moving in an orderly manner in this section of the conductor:

Since the force (Ampère force) acting on the section of the conductor from the magnetic field
is equal to F=| I | BΔl sin α,
and the current in the conductor is I = qnvS
where
q - particle charge
n is the concentration of particles (i.e. the number of charges per unit volume)
v - speed of particles
S is the cross section of the conductor.

Then we get:
Each moving charge is affected by the magnetic field Lorentz force equal to:

where α is the angle between the velocity vector and the magnetic induction vector.

The Lorentz force is perpendicular to the vectors and .

2.
Direction of the Lorentz force

The direction of the Lorentz force is determined using the same left hand rules, which is the direction of the Ampère force:

If the left hand is positioned so that the component of magnetic induction, perpendicular to the charge velocity, enters the palm, and four outstretched fingers are directed along the movement of the positive charge (against the movement of the negative), then the thumb bent by 90 ° will indicate the direction of the Lorentz force acting on the charge F l

3.
If in the space where the charged particle moves, there is both an electric field and a magnetic field, then the total force acting on the charge is equal to: = el + l where the force with which the electric field acts on the charge q is equal to F el = q .

4.
The Lorentz force does no work, because it is perpendicular to the velocity vector of the particle.
This means that the Lorentz force does not change the kinetic energy of the particle and, consequently, the modulus of its velocity.
Under the action of the Lorentz force, only the direction of the particle's velocity changes.

5.
Motion of a charged particle in a uniform magnetic field

There is homogeneous magnetic field directed perpendicular to the particle's initial velocity.

The Lorentz force depends on the moduli of the particle velocity vectors and the magnetic field induction.
The magnetic field does not change the modulus of the velocity of a moving particle, which means that the modulus of the Lorentz force remains unchanged.
The Lorentz force is perpendicular to the velocity and therefore determines the centripetal acceleration of the particle.
The invariance in modulus of the centripetal acceleration of a particle moving with a constant modulo velocity means that

In a uniform magnetic field, a charged particle moves uniformly along a circle of radius r.

According to Newton's second law

Then the radius of the circle along which the particle moves is equal to:

The time it takes for a particle to make a complete revolution (orbital period) is:

6.
Using the action of a magnetic field on a moving charge.

The action of a magnetic field on a moving charge is used in television kinescope tubes, in which electrons flying towards the screen are deflected by a magnetic field created by special coils.

The Lorentz force is used in the cyclotron - charged particle accelerator to produce particles with high energies.

The device of mass spectrographs is also based on the action of a magnetic field, which makes it possible to accurately determine the masses of particles.

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.

It can be seen from the two formulas 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, the direction of the four extended fingers matters. 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 Fl vector will be opposite.

Now we will tell in simple terms 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, ranging from the simplest oscilloscope to televisions of various 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 motors. Although the force of Ampere is more likely to act here. But these quantities can be considered as adjacent. However, these are complex devices during the operation 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:

1. The Lorentz force 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 the magnetic induction.
3. Does not affect particle speed.
4. 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 for those who are engaged in scientific work, design 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

The Lorentz force is the force that acts from the side of the electromagnetic field on a moving electric charge. Quite often, only the magnetic component of this field is called the Lorentz force. Formula for determining:

F = q(E+vB),

where q is the particle charge;E is the electric field strength;B— magnetic field induction;v is the speed of the particle.

The Lorentz force is very similar in principle to, the difference lies in the fact that the latter acts on the entire conductor, which is generally electrically neutral, and the Lorentz force describes the influence of an electromagnetic field only on a single moving charge.

It is characterized by the fact that it does not change the speed of movement of charges, but only affects the velocity vector, that is, it is able to change the direction of movement of charged particles.

In nature, the Lorentz force allows you to protect the Earth from the effects of cosmic radiation. Under its influence, charged particles falling on the planet deviate from a straight path due to the presence of the Earth's magnetic field, causing auroras.

In engineering, the Lorentz force is used very often: in all engines and generators, it is she who drives the rotor under the influence of the electromagnetic field of the stator.

Thus, in any electric motors and electric drives, the Lorentz force is the main type of force. In addition, it is used in particle accelerators, as well as in electron guns, which were previously installed in tube televisions. In a kinescope, the electrons emitted by the gun are deflected under the influence of an electromagnetic field, which occurs with the participation of the Lorentz force.

In addition, this force is used in mass spectrometry and mass electrography for instruments capable of sorting charged particles based on their specific charge (the ratio of charge to particle mass). This makes it possible to determine the mass of particles with high accuracy. It also finds application in other instrumentation, for example, in a non-contact method for measuring the flow of electrically conductive liquid media (flowmeters). This is very important if the liquid medium has a very high temperature (melt of metals, glass, etc.).

Dutch physicist X. A. Lorentz at the end of the 19th century. found that the force acting from the magnetic field on a moving charged particle is always perpendicular to the direction of particle motion and the lines of force of the magnetic field in which this particle moves. The direction of the Lorentz force can be determined using the left hand rule. If you place the palm of your left hand so that four outstretched fingers indicate the direction of movement of the charge, and the vector of the magnetic induction of the field enters the retracted thumb, it will indicate the direction of the Lorentz force acting on the positive charge.

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

The Lorentz force modulus is easily determined from Ampère's law and is:

F = | q| vB sin?,

where q is the charge of the particle, v- the speed of its movement, ? - the angle between the velocity and induction vectors of the magnetic field.

If, in addition to the magnetic field, there is also an electric field, which acts on a charge with a force , then the total force acting on the charge is:

.

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

Since the Lorentz force is perpendicular to the direction of motion of the particle, it cannot change its speed (it does not do work), but can only change the direction of its motion, i.e., bend the trajectory.

Such a curvature of the trajectory of electrons in the TV kinescope is easy to observe if you bring a permanent magnet to its screen - the image will be distorted.

Movement of a charged particle in a uniform magnetic field. Let a charged particle fly in with a speed v into a uniform magnetic field perpendicular to the lines of tension.

The force exerted by the magnetic field on the particle will cause it to rotate uniformly in a circle of radius r, which is easy to find using Newton's second law, the purposeful acceleration expression, and the formula ( F = | q| vB sin?):

.

From here we get

.

where m is the mass of the particle.

Application of the Lorentz force.

The action of a magnetic field on moving charges is used, for example, in mass spectrographs, which make it possible to separate charged particles according to their specific charges, i.e., according to the ratio of the charge of a particle to its mass, and, based on the results obtained, accurately determine the masses of particles.

The vacuum chamber of the device is placed in a field (the induction vector is perpendicular to the figure). Charged particles (electrons or ions) accelerated by an electric field, having described an arc, fall on a photographic plate, where they leave a trace, which makes it possible to measure the radius of the trajectory with great accuracy r. The specific charge of the ion is determined from this radius. Knowing the charge of an ion, you can easily calculate its mass.