EntranceLorentz force in a magnetic field. Application of Ampere and Lorentz forces in science and technology
Why alone scientists history adds gold letters to its pages, and erases some without a trace? Everyone who comes to science is obliged to leave their mark on it. It is by the size and depth of this trace that history judges. Thus, Ampere and Lorentz made an invaluable contribution to the development of physics, which made it possible not only to develop scientific theories, but received significant practical value. How did the telegraph come about? What are electromagnets? Today's lesson will answer all these questions.
For science, the acquired knowledge is of great value, which can subsequently find its practical use. New discoveries not only expand research horizons, but also raise new questions and problems.
Let's highlight the main Ampere's discoveries in the field of electromagnetism.
Firstly, these are the interactions of conductors with current. Two parallel conductors with currents are attracted to each other if the currents in them are in the same direction, and repel if the currents in them are in the opposite direction (Fig. 1).
Rice. 1. Current carrying conductors
Ampere's law reads:
The force of interaction between two parallel conductors is proportional to the product of the currents in the conductors, proportional to the length of these conductors and inversely proportional to the distance between them.
The force of interaction between two parallel conductors,
The magnitude of currents in conductors,
− length of conductors,
Distance between conductors,
Magnetic constant.
The discovery of this law made it possible to introduce into units of measurement a current value that did not exist before that time. So, if we proceed from the definition of current strength as the ratio of the amount of charge transferred through the cross-section of the conductor per unit time, then we obtain a fundamentally unmeasurable quantity, namely the amount of charge transferred through the cross-section of the conductor. Based on this definition, we will not be able to introduce a unit of current. Ampere's law allows us to establish a connection between the magnitudes of current in conductors and quantities that can be measured experimentally: mechanical force and distance. Thus, it is possible to introduce into consideration the unit of current - 1 A (1 ampere).
One ampere current - this is a current at which two homogeneous parallel conductors located in a vacuum at a distance of one meter from each other interact with Newton’s force.
Law of interaction of currents - two parallel conductors in a vacuum, the diameters of which are much smaller than the distances between them, interact with a force directly proportional to the product of the currents in these conductors and inversely proportional to the distance between them.
Another discovery of Ampere is the law of action magnetic field to a current-carrying conductor. It is expressed primarily in the action of a magnetic field on a coil or frame with current. Thus, a coil with current in a magnetic field is acted upon by a moment of force, which tends to rotate this coil so that its plane becomes perpendicular to the lines of the magnetic field. The angle of rotation of the coil is directly proportional to the amount of current in the coil. If the external magnetic field in the coil is constant, then the value of the magnetic induction module is also constant. The area of the turn at not very high currents can also be considered constant, therefore, it is true that current strength is equal to the product of the moment of forces turning the coil with current by some constant value under constant conditions.
– current strength,
– the moment of forces unwinding the coil with current.
Consequently, it becomes possible to measure the current strength by the angle of rotation of the frame, which is implemented in measuring device– ammeter (Fig. 2).
Rice. 2. Ammeter
After discovering the effect of a magnetic field on a current-carrying conductor, Ampere realized that this discovery could be used to make a conductor move in a magnetic field. So, magnetism can be turned into mechanical movement - to create an engine. One of the first to operate on direct current was an electric motor (Fig. 3), created in 1834 by the Russian electrical engineer B.S. Jacobi.
Rice. 3. Engine
Let's consider a simplified model of a motor, which consists of a stationary part with magnets attached to it - the stator. Inside the stator, a frame of conductive material called a rotor can rotate freely. So that the frame can flow electricity, it is connected to the terminals using sliding contacts (Fig. 4). If you connect the motor to a source direct current into a circuit with a voltmeter, then when the circuit is closed, the frame with current will begin to rotate.
Rice. 4. Operating principle of the electric motor
In 1269, the French naturalist Pierre de Maricourt wrote a work entitled “Letter on the Magnet.” The main goal of Pierre de Maricourt was to create a perpetual motion machine, in which he planned to use the amazing properties of magnets. How successful his attempts were is unknown, but what is certain is that Jacobi used his electric motor to propel the boat, and he managed to accelerate it to a speed of 4.5 km/h.
It is necessary to mention one more device that works on the basis of Ampere's laws. Ampere showed that a current-carrying coil behaves like a permanent magnet. This means that it is possible to design electromagnet– a device whose power can be adjusted (Fig. 5).
Rice. 5. Electromagnet
It was Ampere who came up with the idea that by combining conductors and magnetic needles, one could create a device that transmits information over a distance.
Rice. 6. Electric telegraph
The idea of the telegraph (Fig. 6) arose in the very first months after the discovery of electromagnetism.
However, the electromagnetic telegraph became widespread after Samuel Morse created a more convenient device and, most importantly, developed a binary alphabet consisting of dots and dashes, which is called Morse code.
From the transmitting telegraph apparatus, using a “Morse key” that closes the electrical circuit, short or long electrical signals corresponding to dots or dashes of Morse code are generated in the communication line. On a receiving telegraph apparatus (writing instrument), while the signal (electric current) is passing, an electromagnet attracts an armature, to which a metal writing wheel or scribe is rigidly connected, which leaves an ink mark on the paper tape (Fig. 7).
Rice. 7. Telegraph operation diagram
The mathematician Gauss, when he became acquainted with Ampere's research, proposed creating an original cannon (Fig. 8), working on the principle of the action of a magnetic field on an iron ball - a projectile.
Rice. 8. Gauss gun
It is necessary to pay attention to the historical era in which these discoveries were made. In the first half of the 19th century, Europe took leaps and bounds along the path of the industrial revolution - it was a fertile time for scientific research discoveries and their rapid implementation into practice. Ampere undoubtedly made a significant contribution to this process, giving civilization electromagnets, electric motors and the telegraph, which are still in wide use today.
Let us highlight the main discoveries of Lorenz.
Lorentz established that a magnetic field acts on a particle moving in it, causing it to move along a circular arc:
The Lorentz force is a centripetal force perpendicular to the direction of velocity. First of all, the law discovered by Lorentz allows us to determine such an important characteristic as the ratio of charge to mass - specific charge.
The specific charge value is a value unique to each charged particle, which allows them to be identified, be it an electron, a proton or any other particle. Thus, scientists received a powerful research tool. For example, Rutherford was able to analyze radioactive radiation and identified its components, among which there are alpha particles - the nuclei of the helium atom - and beta particles - electrons.
In the twentieth century, accelerators appeared, the operation of which is based on the fact that charged particles are accelerated in a magnetic field. The magnetic field bends the trajectories of particles (Fig. 9). The direction of the bend of the trace allows one to judge the sign of the particle's charge; By measuring the radius of the trajectory, you can determine the speed of the particle if its mass and charge are known.
Rice. 9. Curvature of particle trajectory in a magnetic field
The Large Hadron Collider was developed on this principle (Fig. 10). Thanks to Lorentz's discoveries, science received a fundamentally new tool for physical research, opening the way to the world of elementary particles.
Rice. 10. Large Hadron Collider
In order to characterize the scientist’s influence on technological progress, let us remember that from the expression for the Lorentz force it follows that it is possible to calculate the radius of curvature of the trajectory of a particle moving in a constant magnetic field. Under constant external conditions, this radius depends on the mass of the particle, its speed and charge. Thus, we get the opportunity to classify charged particles according to these parameters and, therefore, we can analyze any mixture. If a mixture of substances in gaseous state ionize, accelerate and direct into a magnetic field, then the particles will begin to move along circular arcs with different radii - the particles will leave the field in different points, and all that remains is to fix these departure points, which is realized using a screen covered with a phosphor, which glows when charged particles hit it. This is exactly how it works mass analyzer(Fig. 11) . Mass analyzers are widely used in physics and chemistry to analyze the composition of mixtures.
Rice. 11. Mass analyzer
This is not all the technical devices that work on the basis of the developments and discoveries of Ampere and Lorentz, because scientific knowledge sooner or later ceases to be the exclusive property of scientists and becomes the property of civilization, while it is embodied in various technical devices, which make our life more comfortable.
Bibliography
- Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 p.: ill., 8 l. color on
- Gendenstein L.E., Dick Yu.I., Physics 11. - M.: Mnemosyne.
- Tikhomirova S.A., Yavorsky B.M., Physics 11. - M.: Mnemosyne.
- Internet portal “Chip and Dip” ().
- Internet portal “Kiev City Library” ().
- Internet portal "Institute distance education» ().
Homework
1. Kasyanov V.A., Physics 11th grade: Textbook. for general education institutions. - 4th ed., stereotype. - M.: Bustard, 2004. - 416 p.: ill., 8 l. color on, st. 88, v. 1-5.
2. In a cloud chamber, which is placed in a uniform magnetic field with an induction of 1.5 Tesla, an alpha particle, flying perpendicular to the induction lines, leaves a trace in the form of a circular arc with a radius of 2.7 cm. Determine the momentum and kinetic energy particles. The mass of the alpha particle is 6.7∙10 -27 kg, and the charge is 3.2∙10 -19 C.
3. Mass spectrograph. A beam of ions, accelerated by a potential difference of 4 kV, flies into a uniform magnetic field with a magnetic induction of 80 mT perpendicular to the magnetic induction lines. The beam consists of two types of ions with molecular weights 0.02 kg/mol and 0.022 kg/mol. All ions have a charge of 1.6 ∙ 10 -19 C. The ions fly out of the field in two beams (Fig. 5). Find the distance between the beams of ions that fly out.
4. * Using a DC electric motor, the load is lifted on a cable. If you disconnect the electric motor from the voltage source and short-circuit the rotor, the load will descend at a constant speed. Explain this phenomenon. What form does the potential energy of the load go into?
Definition of Lorentz force
The Lorentz force is a combination of magnetic and electric force on a point charge, which is caused by electromagnetic fields. Or in other words, the Lorentz force is a force acting on any charged particle that falls in a magnetic field at a certain speed. Its value depends on the magnitude of magnetic induction IN, electric charge of the particle q and the speed with which the particle falls into the field – V. What is the formula for calculating the Lorentz force, as well as its practical significance in physics, read on.
A little history
The first attempts to describe electromagnetic force were made back in the 18th century. Scientists Henry Cavendish and Tobias Mayer suggested that the force on magnetic poles and electrically charged objects obeys the inverse square law. However experimental proof this fact was not complete and convincing. It was only in 1784 that Charles Augustine de Coulomb, using his torsion balance, was able to finally prove this assumption.
In 1820, the physicist Oersted discovered the fact that a volt current acts on the magnetic needle of a compass, and Andre-Marie Ampere in the same year was able to develop a formula for the angular dependence between two current elements. In fact, these discoveries became the foundation modern concept electric and magnetic fields. The concept itself received its further development in the theories of Michael Faraday, especially in his idea of lines of force. Lord Kelvin and James Maxwell added detailed mathematical descriptions to Faraday's theories. In particular, Maxwell created the so-called “Maxwell field equation” - which is a system of differential and integral equations, describing the electromagnetic field and its connection with electric charges and currents in vacuum and continuous media.
JJ Thompson was the first physicist to try to derive from Maxwell's field equation the electromagnetic force that acts on a moving charged object. In 1881, he published his formula F = q/2 v x B. But due to some miscalculations and an incomplete description of the bias current, it turned out to be not entirely correct.
And finally, in 1895, the Dutch scientist Hendrik Lorenz deduced correct formula, which is still used today, and also bears his name, just like the force that acts on a flying particle in a magnetic field is now called the “Lorentz force.”
Lorentz force formula
The formula for calculating the Lorentz force is as follows:
Where q is the electric charge of the particle, V is its speed, and B is the magnitude of the magnetic induction of the magnetic field.
In this case, field B acts as a force perpendicular to the direction of the velocity vector V of the loads and the direction of vector B. This can be illustrated in the diagram:
The left-hand rule allows physicists to determine the direction and return of the vector of magnetic (electrodynamic) energy. Imagine that our left hand is positioned in such a way that the magnetic field lines are directed perpendicular to the inner surface of the hand (so that they penetrate into the hand), and all fingers except the thumb point in the direction of flow of positive current, deflected thumb indicates the direction of the electrodynamic force acting on positive charge, placed in this field.
This is how it will look schematically.
There is also a second way to determine the direction electromagnetic force. It consists of placing the thumb, index and middle fingers at right angles. In this case, the index finger will show the direction of the magnetic field lines, the middle finger will show the direction of current movement, and the thumb will show the direction of the electrodynamic force.
Application of Lorentz force
The Lorentz force and its calculations have their practical application in the creation of both special scientific instruments - mass spectrometers, used to identify atoms and molecules, and in the creation of many other devices of a wide variety of applications. The devices include electric motors, loudspeakers, and rail guns.
The Lorentz force is a force that acts from electromagnetic field to a moving electric charge. Quite often, only the magnetic component of this field is called the Lorentz force. Formula to determine:
F = q(E+vB),
Where q— particle charge;E- tension electric field; B— magnetic field induction;v— particle speed.
The Lorentz force is very similar in principle to, the difference is that the latter acts on the entire conductor, which is generally electrically neutral, and The Lorentz force describes the influence of the electromagnetic field only for 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 capable of changing the direction of movement of charged particles.
In nature, the Lorentz force allows us 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 technology, the Lorentz force is used very often: in all engines and generators it is this that drives the rotor under the influence of the electromagnetic field of the stator.
Thus, in any electric motors and electric drives the main type of force is Lorentzian. In addition, it is used in charged particle accelerators, as well as in electron guns, which were previously installed in tube televisions. In a kinescope, electrons emitted by a gun are deflected under the influence of an electromagnetic field, which occurs with the participation of the Lorentz force.
Additionally, this force is used in mass spectrometry and mass electrography for instruments that can sort 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 (flow meters). This is very important if the liquid medium has a very high temperature (melt of metals, glass, etc.).