Known since ancient times, the phenomena of attraction of unlike and repulsion of like poles of a magnet resemble the phenomena of interaction of unlike and like electric charges. However, numerous attempts by scientists to establish a connection between electrical and magnetic phenomena over many centuries remained unsuccessful. This connection is also evidenced by the observed fact of magnetization of iron objects and compass reversal during a thunderstorm.

This connection was first discovered by H. Oersted and A. Ampere in 1820. A. Ampere showed that two parallel conductors with currents are attracted or repelled depending on the direction of the current in them (Fig. 1, a, b). This interaction cannot be caused by an electrostatic field for the following reasons. Firstly, when the circuit is opened (in Figure 1, the jumper between the upper terminals is disconnected), the interaction of the conductors stops, although the charges on the conductors and their electrostatic fields remain. Secondly, like charges (electrons in a conductor) always just repel each other.

In the experiment of X. Oersted, the conductor is placed above the magnetic needle (or under it) parallel to its axis (Fig. 2). When current passes through a conductor, the needle deviates from its original position. When the circuit is opened, the magnetic needle returns to its original position. This experiment shows that in the space surrounding a current-carrying conductor, forces act that cause the magnetic needle to rotate, that is, forces similar to those that act on it near permanent magnets.

The action of magnetic forces has been detected in the space around separately moving charged particles. Thus, A.F. Ioffe in 1911 observed the deflection of magnetic needles located near a beam of moving electrons. The diagram of his experiment is presented in Figure 3. Above and below the tube there were two identical, but oppositely directed magnetic arrows, mounted on a common ring suspended on an elastic thread. As the flow of electrons passed through the tube, the magnetic needles turned.

If part of a flexible conductor connected to one pole of the source, and therefore charged, is placed near an arc-shaped magnet (Fig. 4, a), then the effect of the magnet field on the conductor is not observed. However, after the circuit is closed (Fig. 4, b, c), the conductors begin to move. Thus, magnetic forces act only on moving charges.

Topic 10. FORCES ACTING ON MOVING CHARGES IN A MAGNETIC FIELD.

10.1. Ampere's law.

10.3. The effect of a magnetic field on a current-carrying frame. 10.4. Units of measurement of magnetic quantities. 10.5. Lorentz force.

10.6. Hall effect.

10.7. Circulation of the magnetic induction vector.

10.8. Magnetic field of the solenoid.

10.9. Magnetic field of a toroid.

10.10. The work of moving a current-carrying conductor in a magnetic field.

10.1. Ampere's law.

In 1820, A. M. Amper experimentally established that two current-carrying conductors interact with each other with force:

where b is the distance between the conductors, аk is the proportionality coefficient depending on the system of units.

The original expression of Ampere's law did not include any quantity characterizing the magnetic field. Then we figured out that the interaction of currents occurs through a magnetic field and therefore the law should include the characteristic of the magnetic field.

In modern SI notation, Ampere's law is expressed by the formula:

If the magnetic field is uniform and the conductor is perpendicular to the magnetic field lines, then

where I = qnυ dr S – current through a conductor with cross-section S.

The direction of the force F is determined by the direction of the vector product or the left-hand rule (which is the same thing). We orient the fingers in the direction of the first vector, the second vector should enter the palm and the thumb shows the direction of the vector product.

Ampere's law is the first discovery of fundamental forces that depend on speeds. Power depends on movement! This has never happened before.

10.2. Interaction of two parallel infinite conductors with current.

Let b be the distance between the conductors. The problem should be solved this way: one of the conductors I 2 creates a magnetic field, the second I 1 is in this field.

Magnetic induction created by current I 2 at a distance b from it:

B 2 = µ 2 0 π I b 2 (10.2.1)

If I 1 and I 2 lie in the same plane, then the angle between B 2 and I 1 is straight, therefore

(of course, from the side of the first conductor, exactly the same force acts on the second). The resulting force is equal to one of these forces! If these two conductors are

influence the third, then their magnetic fields B 1 and B 2 need to be added vectorially.

10.3. The effect of a magnetic field on a current-carrying frame.

The frame with current I is in a uniform magnetic field B, α is the angle between n and B (the direction of the normal is related to the direction of the current by the gimlet rule).

The Ampere force acting on the side of a frame of length l is equal to:

F1 = IlB(B l ).

The same force acts on the other side of length l. The result is a “couple of forces” or “torque.”

M = F1 h = IlB bsinα,

where arm h = bsinα. Since lb = S is the area of ​​the frame, then we can write

M = IBS sinα = Pm sinα.

This is where we wrote the expression for magnetic induction:

where M is the torque of the force, P is the magnetic moment.

The physical meaning of magnetic induction B is a quantity numerically equal to the force with which the magnetic field acts on a conductor of unit length along which it flows.

unit current. B = I F l ; Induction dimension [B] = A N m. .

So, under the influence of this torque the frame will rotate so that n r ||B . The sides of length b are also affected by the force of Ampere F 2 - it stretches the frame and so on

since the forces are equal in magnitude and opposite in direction, the frame does not move, in this case M = 0, a state of stable equilibrium

When n and B are antiparallel, M = 0 (since the arm is zero), this is a state of unstable equilibrium. The frame shrinks and, if it moves a little, it immediately appears

torque such that it will turn so that n r ||B (Fig. 10.4).

In an inhomogeneous field, the frame will rotate and extend into an area of ​​stronger field.

10.4. Units of measurement of magnetic quantities.

As you might guess, it is Ampere's law that is used to establish the unit of current - the Ampere.

So, Ampere is a current of constant magnitude, which, passing through two parallel straight conductors of infinite length and negligible cross-section, located at a distance of one meter, one from the other in a vacuum

causes a force of 2 10 − 7 N m between these conductors.

One Tesla 1 T = 104 Gauss.

Gauss is a unit of measurement in the Gaussian system of units (GUS).

1 T (one tesla is equal to the magnetic induction of a uniform magnetic field in which) a torque of 1 Nm acts on a flat circuit with a current having a magnetic moment of 1 A m2.

The unit of measurement B is named after the Serbian scientist Nikola Tesla (1856 - 1943), who had a huge number of inventions.

Another definition: 1 T is equal to the magnetic induction at which the magnetic flux through an area of ​​1 m2 perpendicular to the direction of the field is 1 Wb.

The unit of measurement of magnetic flux Wb, got its name in honor of the German physicist Wilhelm Weber (1804 - 1891), a professor at universities in Halle, Göttingham, and Leipzig.

As we already said, magnetic flux Ф through the surface S is one of the characteristics of the magnetic field (Fig. 10.5)

The scientist also made the first attempt to classify chemical elements based on a comparison of their properties. But it was not these studies, interesting in themselves, and not his mathematical works that made Ampere’s name famous. He became a classic of science and a world-famous scientist thanks to his research in the field of electromagnetism. In 1820, the Danish physicist G.-H. Oersted discovered that near a conductor carrying current, a magnetic needle deviates. This is how the remarkable property of electric current was discovered - to create a magnetic field. Ampere studied this phenomenon in detail. A new view of the nature of magnetic phenomena arose in him as a result of a whole series of experiments. Already at the end of the first week of hard work, he made a discovery of no less importance than Oersted - he discovered the interaction of currents. He found that two parallel wires through which current flows in the same direction attract each other, and if the directions of the currents are opposite, the wires repel. Ampere explained this phenomenon by the interaction of magnetic fields that create currents. The effect of the interaction of wires with current and magnetic fields is now used in electric motors, electric relays and many electrical measuring instruments. Ampere immediately reported the results to the Academy. In a report given on September 18, 1820, he demonstrated his first experiments and concluded them with the following words: “In this regard, I have reduced all magnetic phenomena to purely electrical effects.” At a meeting on September 25, he developed these ideas further, demonstrating experiments in which coils flowing around a current (solenoids) interacted with each other like magnets. Ampere's new ideas were not understood by all scientists. Some of his eminent colleagues also disagreed. Contemporaries said that after Ampere’s first report on the interaction of conductors with current, the following curious episode occurred. “What, exactly, is new in what you told us? - one of his opponents asked Ampere. “It goes without saying that if two currents have an effect on a magnetic needle, then they also have an effect on each other.” Aliper did not immediately find an answer to this objection. But then Arago came to his aid. He took two keys out of his pocket and said: “Each of them also has an effect on the arrow, but they have no effect on each other, and therefore your conclusion is wrong. Ampere discovered, in essence, a new phenomenon, of much greater significance than the discovery of Professor Oersted, whom I respect.” 182 Despite the attacks of his scientific opponents. Ampere continued his experiments. He decided to find the law of interaction of currents in the form of a strict mathematical formula and found this law, which now bears his name. Thus, step by step in Ampere’s work, a new science grew up - electrodynamics, based on experiments and mathematical theory. All the basic ideas of this science, as Maxwell put it, essentially “came out of the head of this Newton of electricity” in two weeks. From 1820 to 1826, Ampere published a number of theoretical and experimental works on electrodynamics and gave a report on this topic at almost every meeting of the Academy's physics department. In 1826, his final classic work, “The Theory of Electrodynamic Phenomena Deduced Exclusively from Experience,” was published. The work on this book took place under very difficult conditions. In one of the letters written at that time. Ampere reported: “I am forced to stay awake late at night... Being loaded with reading two courses of lectures, I, however, do not want to completely abandon my work on voltaic conductors and magnets. I have only a few minutes.”

Andre Marie Ampere

Ampere Andre Marie (AMPERE Andre-Marie) (1775-1836), French scientist, foreign member of the St. Petersburg Academy of Sciences (1830), one of the founders of electrodynamics. He proposed a rule named after him, discovered (1820) the mechanical interaction of currents and established the law of this interaction (Ampere's law). Constructed the first theory of magnetism.

Ampere (Ampere Andre Marie) is a famous mathematician and natural scientist, born in Lyon on January 22. 1775; After the death of his father, who was guillotined in 1793, A. was first a tutor at the Polytechnic School in Paris, then first occupied the Department of Physics in Burg, and from 1805, the Department of Mathematics at the Paris Polytechnic School, where he also distinguished himself in the literary field, for the first time he published the essay: “Considerations sur la théorie mathematique dujeu” (Lyon, 1802). In 1814 he became a member of the Academy of Sciences, in 1824 - professor of experimental physics at the College of France; died June 10, 1836 in Marseille. Mathematics, mechanics and physics owe A. important research; his electrodynamic theory earned him unfading fame. His view of the single original essence of electricity and magnetism, in which he essentially agreed with the Danish physicist Erstedt, is excellently outlined by him in “Recueil d” observations lectrodynamiques” (Paris, 1822), in “Precis de la theorie des phenomenes electrodynamiques” (Paris , 1824) and in “Theorio des phenomenes electrodynamiques.” A.’s versatile talent did not remain indifferent in the history of developed chemistry, which gives him one of the honorable pages and considers him, together with Avogadro, the author of the most important law of modern chemistry. scientist, the unit of galvanic current is called the “ampere”, and the measuring instruments are called “amperometers”. In addition, Ampere also owns the work “Essais sui la philosophie des Sciences” (2 vols., 1834-43; 2nd edition, 1857). Cf. Barthelemy and Sentiler, “Philosophie ae deux Amperes” (Paris, 1866). .

F. Brockhaus, I.A. Efron Encyclopedic Dictionary.

Ampere Andre Marie

André Marie Ampère was born on January 22, 1775. His father Jean-Jacques Ampère, along with his brothers, traded in Lyon silks. Mother Jeanne Sarce is the daughter of one of the major Lyon merchants. Andre's childhood was spent on the small estate of Polemier, bought by his father in the vicinity of Lyon.

He never went to school, but he learned reading and arithmetic very quickly. Already at the age of 14, he read all twenty-eight volumes of the French Encyclopedia. Andre showed particular interest in the physical and mathematical sciences. Andre began visiting the library of the College of Lyon to read the works of great mathematicians.

At the age of thirteen, he submitted his first works on mathematics to the Lyon Academy.

In 1793, a rebellion broke out in Lyon, which was soon suppressed. Jean-Jacques Ampère was beheaded for sympathizing with the rebels. Following a court verdict, almost all property was confiscated. Ampère decided to move to Lyon and give private mathematics lessons.

In 1802, Ampère was invited to teach physics and chemistry at the Central School of Bourg-en-Brésse, sixty kilometers from Lyon.

At the end of 1804, Ampère left Lyon and moved to Paris, where he received a teaching position at the École Polytechnique. The main objective of the school was to train highly educated technical specialists with deep knowledge of physical and mathematical sciences.

In 1807 Ampere was appointed professor at the Ecole Polytechnique. In 1808 he received the post of chief inspector of universities. The heyday of Ampère's scientific activity dates back to 1814-1824 and is associated with the Academy of Sciences, to which he was elected on November 28, 1814 for his services in the field of mathematics.

Almost until 1820, the scientist’s main interests focused on problems of mathematics, mechanics and chemistry. At that time he dealt very little with issues of physics. Ampere always considered mathematics as a powerful apparatus for solving various applied problems in physics and technology. He also does not give up his studies in chemistry. His achievements in the field of chemistry include the discovery, independently of Avogadro, of the law of equality of molar volumes of different gases.

In 1820, physicist Oersted discovered that a magnetic needle deviates near a current-carrying conductor. This is how the property of electric current was discovered - to create a magnetic field. Ampere studied this phenomenon in detail and discovered the interaction of currents.

He found that two parallel wires through which current flows in the same direction attract each other, and if the directions of the currents are opposite, the wires repel. Ampere explained this phenomenon by the interaction of magnetic fields that create currents. Ampere immediately reported the results to the Academy. At a meeting on September 25, he developed these ideas further, demonstrating experiments in which coils flowing around a current (solenoids) interacted with each other like magnets.

Ampere decided to find the law of interaction of currents in the form of a strict mathematical formula and found this law, which now bears his name. Thus, step by step in Ampere’s work, a new science grew up - electrodynamics, based on experiments and mathematical theory. From 1820 to 1826, Ampere published a number of theoretical and experimental works on electrodynamics. In 1826, “The Theory of Electrodynamic Phenomena Derived Exclusively from Experience” was published.

In 1824, Ampère was elected to the position of professor at the College de France. He was given the chair of general and experimental physics.

In 1835, he published a paper in which he proved the similarity between light and thermal radiation and showed that all radiation is converted into heat when absorbed. Ampere developed a system of classification of sciences, which he intended to present in a two-volume work. In 1834, the first volume of “Essays in the Philosophy of Sciences or Analytical Exposition of the Natural Classification of All Human Knowledge” was published. Ampere introduced words such as “electrostatics”, “electrodynamics”, “solenoid”. Ampere suggested that a new science about the general laws of control processes would probably emerge. He suggested calling it “cybernetics”.

Ampere died of pneumonia on July 10, 1836 in Marseilles during an inspection trip. He was buried there.

(1775-1836) French physicist, mathematician and chemist

Andre Marie Ampere is the founder of classical electrodynamics. He introduced many concepts and terms into physics: “voltage”, “current strength”, “direction of current”, “galvanometer”. He also came up with the idea of ​​the galvanometer itself, based on the action of current on a needle.

The scientist was born on January 22, 1775 in the family of a Lyon merchant and was educated at home. The young man's scientific inclinations manifested themselves very early: already at the age of 13 he mastered differential calculus.

The father of the future famous scientist had a good library, and as a fourteen-year-old teenager Andre read all 20 volumes of the famous French “Encyclopedia” by D. Diderot and J. D'Alembert. His interests were extremely broad: various branches of mathematics (for example, game theory, geometry, conic sections), biology, physics, geology, linguistics, philosophy and chemistry. In a few weeks he learned Latin in order to read the works of Euler and Bernoulli in the original. By the age of eighteen, Andre had studied higher mathematics and natural sciences, as well as Greek and Italian. languages.

The Life of André Marie Ampere was very difficult. In the revolution of 1793, his father was among the victims and was executed by guillotine. The death of his father was a great shock for him. From that time on, the young man had to earn his own living. He gave private lessons, then taught physics and chemistry at the Central School of Bourcan-Brès. In 1803, Ampère was appointed teacher of mathematics and astronomy at the Lyceum Lyceum. After publishing a paper on probability theory about the mathematical theory of games in 1802, he was offered a position as a tutor at the École Polytechnique in Paris in 1804, and in 1807 he became its professor. Ampere worked there from 1804 to 1824.

Before leaving for Paris, where the second half of his life passed, the scientist experienced another event - the death of his beloved wife. He could not recover from this shock for the rest of his life. Ampère was constantly haunted by misfortunes: an unsuccessful second marriage, the unfulfilled life of his son Jean-Jacques Ampère, who later became one of the famous historians of French literature. To those around him, Andre Ampere seemed a strange man: absent-minded, short-sighted, gullible, paying little attention to his appearance. He also had a habit of telling people directly what he thought about them.

The first works of A. Ampere (1802-1809) were devoted to probability theory and differential equations, and in 1814 he was elected a member of the Paris Academy of Sciences for them. Works on solving partial differential equations constituted an era in the history of mathematics. Independently of the Italian scientist Amedeo Avogadro Ampere proposed a theory of the molecular structure of gases, which was a significant contribution to the development of chemistry.

In 1820, the Danish physicist Hans Christian Oersted (1777-1851) discovered the magnetic field of electric current, establishing the connection between electricity and magnetism. On September 4, 1820, the French scientist Dominique Francois Arago (1786-1853) at a meeting of the Paris Academy of Sciences made an oral report about Oersted's experiments, and at the next meeting, on September 11, having assembled a simple installation, he demonstrated them. Ampere became interested in Oersted's experiments, repeated them and began to work intensively in this direction, developing a new branch of electricity - electrodynamics. He built a small laboratory table himself. Already on September 18, at the next meeting of the Academy, he makes the first report on his research. Ampere established that the magnitude of the magnetic effect depends on the intensity of the movement of electricity. To measure this intensity, for the first time in the world, he introduces the concept of current strength, the unit of which - ampere - is named in his honor.

On September 25, 1820, he again ascended to the department of the academy and demonstrated his famous experiments establishing the presence of mechanical interaction between parallel conductors and current. He formulated a law that determines the nature of this interaction (attraction or repulsion) depending on the mutual direction of the currents. Ampere then derived a formula for calculating the force of interaction between two current elements.

During the remaining three months of 1820, he makes 9 communications, which contain the fundamental results of his work on the interaction of electric currents. Subsequently, he established the equivalence of an elementary magnet to a circular current and came to the idea that all magnetic interactions are reduced to the interaction of so-called circular electric molecular currents hidden in bodies. This hypothesis of Ampere was confirmed only in the 20th century. In the same year, he proposed using electromagnetic phenomena to transmit signals.

In 1822, Andre discovered the magnetic effect of a solenoid - a coil with current: a solenoid flown by current is the equivalent of a permanent magnet. The scientist also put forward an idea, the essence of which was to strengthen the magnetic field of the solenoid by placing a soft iron core inside it. Thus, Ampere invented the electromagnet without knowing it, so the honor of discovering the electromagnet went to the English physicist William Sturgeon (1783-1850) in 1825.

Since 1824, Ampère worked as a professor at the École Normale Supérieure in Paris. He summarized his research in 1826 in a work entitled “The Theory of Electrodynamic Phenomena Deduced from Experience.” It was the first to present a quantitative law for the force of interaction of currents, now known as Ampere’s law, which was one of the fundamental laws of electrodynamics. Many physicists noted the universality of this formula. The most accurate and succinct description of the scientist’s discoveries was given by the founder of the theory of the electromagnetic field, James Clerk Maxwell (1831-1879), calling Ampere the “Newton of electricity.”

In 1829, the physicist invented the commutator and the electromagnetic telegraph. In 1830 he was elected a member of the St. Petersburg Academy of Sciences. In the last years of his life, he again began to study mathematics, and then the philosophy of science.

The life of the great French scientist did not get easier, despite his fame. He still bought and made instruments with his own money. Lacking funds, he was forced to beg for additional work from the university authorities. For several months at a time, abandoning his work on electrodynamics, Ampere inspected provincial schools, testing students' knowledge in various subjects, and wrote reports on expenses for furniture, ink and chalk. The authorities apparently took pleasure in the opportunity to humiliate the physicist, but he was an extremely modest person, tormented by his powerlessness, from the need to waste precious time on completely trivial activities. Despite all life's trials, he always remained a kind, sympathetic and cheerful person.

His discoveries were met by many colleagues with skeptical grins and misunderstanding. Ampere's works were appreciated only after his death. As Francois Arago said, “Ampère’s death is a national misfortune.”

André Marie Ampere died of pneumonia on June 10, 1836 in Marseille on his way south, where he hoped to improve his health. At this time he was in the prime of his creative powers. His ashes were transported from Marseille to Paris to the Montmartre cemetery in 1869. On his tombstone are carved the words: “He was as kind and as simple as he was great.”