Physics of electricity: definition, experiments, unit of measurement. Box of quality problems in physicselectricity Artificial permanent magnets

Formulas of electricity and magnetism. The study of the fundamentals of electrodynamics traditionally begins with an electric field in a vacuum. To calculate the force of interaction between two point charges and to calculate the strength of the electric field created by a point charge, you need to be able to apply Coulomb's law. To calculate the field strengths created by extended charges (charged thread, plane, etc.), Gauss's theorem is used. For a system of electric charges it is necessary to apply the principle

When studying the topic "Direct Current" it is necessary to consider Ohm's and Joule-Lenz's laws in all forms. When studying "Magnetism" it is necessary to keep in mind that the magnetic field is generated by moving charges and acts on moving charges. Here you should pay attention to the Biot-Savart-Laplace law. Particular attention should be paid to the Lorentz force and consider the motion of a charged particle in a magnetic field.

Electrical and magnetic phenomena are connected by a special form of existence of matter - the electromagnetic field. The basis of the theory of the electromagnetic field is Maxwell's theory.

Table of basic formulas of electricity and magnetism

Physical laws, formulas, variables	Formulas electricity and magnetism
Coulomb's Law: Where q 1 and q 2 - values ​​of point charges,ԑ 1 - electrical constant; ε - dielectric constant of an isotropic medium (for vacuum ε = 1), r is the distance between charges.
Electric field strength: where Ḟ - force acting on the charge q 0 , located at a given point in the field.
Field strength at a distance r from the field source: 1) point charge 2) an infinitely long charged thread with linear charge density τ: 3) a uniformly charged infinite plane with surface charge density σ: 4) between two oppositely charged planes
Electric field potential: where W is the potential energy of the charge q 0 .
Field potential of a point charge at a distance r from the charge:
According to the principle of field superposition, tension:
Potential: where Ē i and ϕ i- tension and potential at a given point in the field created by the i-th charge.
The work done by electric field forces to move charge q from a point with potentialϕ 1 to a point with potentialϕ 2:
The Relationship Between Tension and Potential 1) for a non-uniform field: 2) for a uniform field:
Electrical capacity of a solitary conductor:
Capacitance of the capacitor:
Electrical capacity of a flat capacitor: where S is the area of ​​the plate (one) of the capacitor, d is the distance between the plates.
Energy of a charged capacitor:
Current strength:
Current Density: where S is the cross-sectional area of ​​the conductor.
Conductor resistance: l is the length of the conductor; S is the cross-sectional area.
Ohm's law 1) for a homogeneous section of the chain: 2) in differential form: 3) for a section of the circuit containing EMF: Where ε is the emf of the current source, R and r - external and internal resistance of the circuit; 4) for a closed circuit:
Joule-Lenz law 1) for a homogeneous section of a DC circuit: where Q is the amount of heat released in the current-carrying conductor, t - current passage time; 2) for a section of a circuit with a current varying over time:
Current power:
Relationship between magnetic induction and magnetic field strength: where B is the magnetic induction vector, μ √ magnetic permeability of an isotropic medium, (for vacuum μ = 1), µ 0 - magnetic constant, H - magnetic field strength.
Magnetic induction(magnetic field induction): 1) in the center of the circular current where R is the radius of the circular current, 2) fields of infinitely long forward current where r is the shortest distance to the conductor axis; 3) the field created by a section of conductor with current where ɑ 1 and ɑ 2 - angles between the conductor segment and the line connecting the ends of the segment and the field point; 4) fields of an infinitely long solenoid where n is the number of turns per unit length of the solenoid.

Investments in knowledge always give the greatest return.
Benjamin Franklin

BOX OF QUALITY PROBLEMS IN PHYSICS
ELECTRICITY

I bring to the attention of readers 50 high-quality physics problems on the topic: “Electricity”, as well as some interesting facts...
Atmospheric electricity:
Lightning over an erupting volcano.
Biological electricity:
Electric fish.
Physics and military technology:
Galvanic impact mine.
And according to tradition... a little painting :-)
The tasks are divided into three groups:
1) Electrification of bodies;
2) Conductors and dielectrics. Electricity;
3) .

Benjamin Franklin(01/17/1706–04/17/1790) - politician, diplomat, scientist, inventor, journalist, publisher. The first American to become a foreign member of the Russian Academy of Sciences.
Benjamin Franklin named one type of charge positive"+" and the other negative"–"; explained the principle of operation Leyden jar, having established that the main role in it is played by the dielectric separating the conductive plates; established the identity of atmospheric and friction-generated electricity and provided proof electrical nature of lightning; established that metal points connected to the ground remove electrical charges from charged bodies even without contact with them and proposed in 1752 lightning rod project.
Proposed an idea electric motor and demonstrated an “electric wheel” rotating under the influence of electrostatic forces; first used electric spark for the explosion of gunpowder...
David Martin(David Martin; 04/01/1737–12/30/1797) - British painter and engraver.

Electrification of bodies

Task No. 1
Why does a spark occasionally jump between the belt and the pulley on which it is worn during operation?

Task No. 2
For what purpose in explosive production should drive belts be treated with antistatic (conductive) paste and the pulleys grounded?

Task No. 3
In a belt drive, can only the belt be electrified and the pulley remain uncharged? Why? Assume that the pulley is not grounded.

Task No. 4
In textile factories, threads often stick to the combs of carding machines, become tangled and break. To combat this phenomenon, high humidity is artificially created in workshops. Explain the physical essence of this measure.

Problem #5
Why do two oppositely charged balls suspended on threads attract each other, but immediately repel each other after contact?

ATMOSPHERIC ELECTRICITY
Lightning over an erupting volcano

The occurrence of lightning over an erupting volcano is caused by: seismological processes, as well as the processes occurring in the clouds during ordinary thunderstorms. Electric charges can arise due to piezoelectric, triboelectric and similar phenomena during faults and movements of rock layers accompanying a volcanic eruption.
Charges also arise during friction between ash particles flying out of the crater of a volcano.. In ordinary thunderstorms, the potential difference, which is then discharged into lightning, occurs because heavier droplets or pieces of ice, due to their weight, accumulate in the lower layers of the thundercloud, and small, light ones are lifted by rising air currents to the upper part. They accumulate opposite charges, which, after a certain voltage, penetrate the air layer. The sum of these not yet fully studied “earthly” and “heavenly” phenomena and summons lightning over an erupting volcano.

Vesuvius opened its mouth - smoke poured out in a cloud - flames Widely developed as a battle flag. The earth is agitated - from the shaky columns Idols fall! A people driven by fear Under the stone rain, under the inflamed ashes, Crowds, old and young, are running out of the city. August–September 1834, Alexander Sergeevich Pushkin The last day of Pompeii Bryullov Karl Pavlovich, 1830–1833

It has been known for almost 2000 years that volcanic eruptions are sometimes accompanied by lightning strikes. In 79 AD Pliny the Younger, watching eruption of Vesuvius, recorded that dark clouds gathered over the crater and lightning flashed.

Bryullov Karl Pavlovich(12/23/1799–06/23/1852) - Russian painter, monumentalist, prominent representative of academicism.
Pompeii- an ancient Roman city near Naples, buried under a layer of volcanic ash as a result Vesuvius eruption August 24, 79 AD.

Problem #6
Why do electricians, when working to repair electrical networks and installations, wear rubber gloves, rubber shoes, stand on rubber mats, and use tools with plastic handles?

Problem No. 7
Printing shop workers rolling rolls of paper wear rubber gloves and rubber boots. Explain why.

Problem No. 8
We cannot see, hear, touch, etc. the electric field, since it does not directly affect the senses. How can one detect the existence of an electric field?

For the curious: Term electricity(“amber”: ancient Greek ηλεκτρον – electron, "amber", English electron) was introduced in 1600 by an English naturalist William Gilbert in his essay “On the Magnet, Magnetic Bodies and the Great Magnet – the Earth,” which explains the action of a magnetic compass and describes some experiments with electrified bodies.

Problem No. 9
When stroking the cat's fur with your palm, you can notice in the dark small sparks appearing between the hand and the fur. What is the cause of sparks?

Problem No. 10
Apply a friction-electrified comb to a thin stream of water. Record what you observe in the form of a drawing and accompany it with a comment.

Problem No. 11
A question for neat and attentive housewives;-) Where does dust accumulate the fastest in your home? Why?

Problem No. 12
Why, when combing your hair with a plastic comb, does your hair seem to “stick” to it (sometimes you can hear a slight crackling sound; small sparks appear in the dark)?

Problem No. 14
Why do the smallest droplets that make up the fragrant stream of cologne, perfume, or hairspray, obtained using a spray bottle, become electrified?

Problem No. 15
Raindrops and snowflakes are almost always electrically charged. Why?

Conductors and dielectrics. Electricity

Problem No. 16
Why is it possible to electrify a glass rod by friction while holding it in your hand, but not a metal rod?

Problem No. 17
What should you do to electrify a metal object, such as a spoon?

Problem No. 18
Why can connecting to a water tap serve as a method of grounding?

Problem No. 19
Why is wet hair not electrified when combed?

Problem No. 20
Why do electrical experiments most often fail in damp weather or when indoor humidity is high?

One experience I value more than a thousand opinions,
born only from imagination...
Mikhail Vasilievich Lomonosov

Fedorov Ivan Kuzmich(1853–1915?) – Russian historical painter, genre painter.

In June 1764, Catherine II visited the house Mikhail Lomonosov and for two hours looked at “works of mosaic art, newly invented physical instruments by Lomonosov and some physical and chemical experiments».
In the picture Ivan Kuzmich Fedorov standing in front of Empress Catherine II electrostatic machine with a glass cylinder rotated by a pedal mechanism and rubbed with leather pads pressed against the glass using springs. The pads were trimmed with horsehair and connected to the ground with wire. The machine produced sparks so strong that they could ignite the ether.

Problem No. 21
Experiments have shown that black cotton thread conducts current better than white! How can you comment on this fact?

...Thunder struck. The cup of heaven is split.
The dense clouds were torn apart.
On light gold pendants
The heavenly lamps began to sway...
"Heroic whistle." Sergei Alexandrovich Yesenin

Problem No. 22
Is lightning occurring between a cloud and the Earth an electric current? between the clouds? Why can lightning cause a fire?

Problem No. 23
Lightning most often strikes trees that have large roots that penetrate deep into the soil. Why?

George Morland(George Morland; 06/26/1763–10/29/1804) - English artist.

Problem No. 24
Explain why when lightning strikes sandy soil, so-called fulgurites are formed - irregularly shaped pieces of fused quartz (sand).

For the curious: The current in a lightning discharge reaches 10–500 thousand amperes, the voltage ranges from tens of millions to billions of volts. The channel temperature during the main discharge can exceed 20000–30000°C. Lightning has also been recorded on Venus, Jupiter, Saturn and Uranus...

...You recently hugged the sky,
And lightning wrapped around you menacingly;
And you made mysterious thunder
And watered the greedy land with rain...
"Cloud". Alexander Sergeevich Pushkin

For the curious: Thunder arises as a result sudden expansion of air with a rapid increase in temperature in the lightning discharge channel. Flash of lightning we see almost as an instantaneous flash and at the same moment when the discharge occurs; after all light travels at speed 3 10 8 m/s. As for sound, it travels much slower. In the air the speed of sound is 330 m/s. That's why we hear thunder after lightning has flashed. The farther the lightning is from us, the longer the pause between the flash of light and the thunder, and, in addition, the weaker the thunder. By measuring the duration of these pauses, we can roughly estimate how far is the thunderstorm from us at the moment? how quickly it approaches us, or, on the contrary, moves away from us. Thunder from very distant lightning does not reach at all - the sound energy is dissipated and absorbed along the way. Such lightning is called lightning. Note also that the reflection of sound from the clouds explains the sometimes increased sound volume at the end of thunderclaps. However, not only the reflection of sound from clouds is explained thunderclaps ;-)

Alexander Column(Alexandrian Pillar) is one of the most famous monuments in St. Petersburg. Erected in the Empire style in 1834 in the center of Palace Square by the architect Auguste Montferrand by order of Emperor Nicholas I in memory of the victory of his elder brother Alexander I over Napoleon.
Raev Vasily Egorovich(1808–1871) – Russian painter, teacher.

Problem No. 26
The appearance of thunderstorms in the atmosphere makes it difficult to use a magnetic compass. Explain this.

Problem No. 27
During a thunderstorm, the antennas of radios and televisions should be grounded, especially those that are installed high above the ground (for example, the roofs of high-rise buildings). How, and for what purpose, is this done?

For the curious: In 1785, the Dutch physicist Van Marum Martin by the characteristic smell of freshness, as well as the oxidative properties that air acquires after passing through it electrical sparks, discovered ozone– O 3 (from ancient Greek οζω - I smell) However, it was not described as a new substance; Van Marum believed that it was formed special "electric matter". Term ozone, for its odor :-) was proposed by the German chemist Christian Friedrich Schönbein in 1840.

Problem No. 28
"Terrible revenge, 1832,
Nikolai Vasilyevich Gogol
“...When blue clouds roll across the sky like mountains, the black forest staggers to its roots, the oak trees crack and lightning, breaking between the clouds, illuminates the whole world at once - then the Dnieper is terrible!”
Observations show that lightning most often strikes wet ground near the shores of lakes, rivers, and swamps. How to explain this?

Vasnetsov Apollinariy Mikhailovich(06.08.1856–23.01.1933) – Russian artist, master of historical painting, art critic.

Problem No. 29
Why does lightning rarely strike open oil storage facilities (“oil lakes”)?

Problem #30
Why does the lower end of the lightning rod need to be buried deeper, where the layers of the earth are always wet?

Perun(Old Russian Perun) – thunder god in Slavic mythology, the patron saint of the prince and squad in the ancient Russian pagan pantheon. After the spread of Christianity in Rus', many elements of the image of Perun were transferred to the image of Elijah the Prophet ( Ilya Gromovnik). The name of Perun heads the list of gods in the pantheon of Prince Vladimir in The Tale of Bygone Years.

Shishkin Ivan Ivanovich(01/25/1832–03/20/1898) - Russian landscape painter, one of the founding members of the Partnership of the Wanderers.
Savrasov Alexey Kondratievich(05/12/1830–09/26/1897) - Russian landscape painter, one of the founding members of the Partnership of the Wanderers.

For the curious:
Is it true that lightning prefers to strike oak trees?
If the tree is wet, the lightning current passes through the water and the tree remains unharmed. In a dry tree, current can pass into the trunk and flow through the tree sap into the ground. In this case, the sap can heat up, evaporate and, expanding, “explode” the tree. Oak suffers from lightning more often than other trees because its bark is very uneven. If lightning strikes an oak tree at the beginning of a thunderstorm, it may be that only the top of the tree gets wet, whereas a tree with smooth bark quickly becomes wet from top to bottom. Therefore, when struck by lightning, an oak tree can “explode”, but a tree with smooth bark can remain intact. A forest fire occurs in cases where several discharges occur in the lightning channel, but in the intervals between the main discharges, current continues to flow in the channel.

Before the storm Vasiliev Fedor Alexandrovich 1870		After the thunderstorm Vasiliev Fedor Alexandrovich 1868

Vasiliev Fedor Alexandrovich(02/22/1850–10/06/1873) - Russian landscape painter.

Children running from a thunderstorm Makovsky Konstantin Egorovich 1767

For the curious: Thunderstorm - an atmospheric phenomenon, in which inside the clouds or between the cloud and the earth's surface there are electrical discharges - lightning accompanied by thunder. Typically, a thunderstorm forms in powerful cumulonimbus clouds and is associated with heavy rain, hail and strong winds. At the same time, about one and a half thousand thunderstorms are active on Earth, the average intensity of discharges is estimated as 46 lightning per second.
Thunderstorms are distributed unevenly across the planet's surface. There are approximately ten times fewer thunderstorms over the ocean than over the continents.
The intensity of thunderstorms follows the sun: Maximum thunderstorms (in mid-latitudes) occur during summer time and afternoon daylight hours. The minimum of recorded thunderstorms occurs before sunrise. Thunderstorms are also influenced by geographic features of the area: strong thunderstorm centers are located in the mountainous regions of the Himalayas and Cordilleras.

Makovsky Konstantin Egorovich(06/20/1839–09/30/1915) - Russian painter, one of the early participants in the Association of Itinerants.

Problem No. 31
Will we get a galvanic cell if we put two plates of the same metal (for example, zinc) into an aqueous solution of some acid or salt?

Problem No. 32
Why does a galvanometer indicate the presence of current if steel and aluminum wires are connected to its terminals, the other ends of which are stuck into a lemon or a fresh apple?

For the curious: Italian physicist, chemist and physiologist - Alexandro Volta, during the study "animal electricity", repeating and developing experiments Luigi Galvani, found that electric current can be “tasted” - when electric current flows through a copper wire, the tongue feels a sour taste, and the greater the current, the stronger the feeling of acid; it turns out that our language can act as a very unique ammeter;-) In 1800, Volta built the first electric current generator - “voltaic pole”. This invention brought him worldwide fame.

Problem No. 33
They say that in the Arctic in winter, when the air temperature is -50°C, the world there becomes “terribly electric.” Explain or refute this.

Problem No. 34
Why is it possible for a person to get an electric shock in very damp rooms even when touching the glass container of a light bulb?

Problem No. 35
Using the chemical action of current, it is possible to coat with a metal layer a product not only made of conductive materials, but also of dielectrics - wax, plastic, plaster, wood, plasticine, etc. How to do this?

BIOLOGICAL ELECTRICITY
Electric fish

More to the ancient Greeks it was known that stingrays have an amazing ability to hit small fish, crabs, and octopuses swimming nearby at a distance. Having accidentally found themselves close to a stingray, they suddenly began to twitch convulsively and immediately froze. They were killed electrical discharges, which generated special organs of stingrays. U common stingrays these organs are located in the tail, and in those living in warm seas electric stingrays- in the area of ​​the head and gills. Common stingrays create voltage near 5 V, electric before 50 V. Ancient Greeks used electrogenic properties of electric stingrays for pain relief during operations and childbirth.

IN 1775 British physicist and chemist Henry Cavendish invited seven eminent scientists to demonstrate the artificial electric stingray, and let everyone feel electrical discharge, absolutely identical to what real stingray paralyzes its victims. Electric ramp model, was “powered” by battery Leyden jars and immersed in salted water. At the end of the show Henry Cavendish, ahead of his contemporaries Galvani And Volta, solemnly announced to the invitees that it was this, demonstrated by him new power some day revolutionizes the whole world!

Electric ramps(lat. Torpediniformes) - a detachment of cartilaginous fish with kidney-shaped electrical organs. They do not, however, have the weak electrical organs present on either side of the tail in the rhomboid family. sea ​​fox, or spiny stingray (lat. Raja clavata) is the most common European species of stingrays (family: Diamondback; genus: Diamondback).

Pierre Moulin du Coudray La Blanchere(1821–1880) – French naturalist, illustrator.
Wilhelm Richard Paul Flanderky(1872–1937) – German illustrator.

Electric catfish(lat. Malapterurus electricus) is a species of bottom-dwelling freshwater fish that lives in tropical and subtropical waters of Africa. The electric catfish electrical organs located over the entire surface of the body, directly under the skin. They make up 1/4 of the catfish's body weight. Depending on the size, electric catfish capable of producing voltage, reaching 350–450 V, at current strength 0.1–0.5 A.
In many electric fish (electric eel; gymnarchus; gnatonemus - elephant fish; apteronotus - knife fish), the tail is charged negatively, the head is positively charged, but in electric catfish, on the contrary, the tail is charged positively, head negative.

Electric catfish(Malapterurus electricus),
Nile multi-feather, or bishir(Polypterus bichir),
Electric pike(Mormyrus oxyrhynchus).

Friedrich Wilhelm Kunert(Friedrich Wilhelm Kuhnert; 1865–1926) – German painter, writer and illustrator.

Fish with electrical properties They use these properties not only for attack, but also to find potential prey, identify dangerous opponents, and navigate unlit or murky water. Electric field around the electric fish also leads to electrolysis of water, which results in enrichment of water with oxygen, which attracts fish and frogs, thereby making it easier for electric fish to find prey.

Not all fish have electrical properties. The number of living beings that have special organs for generation and perception of electric fields, not that big. Nevertheless, in any living organism and even in individual living cells, electrical voltages; they are called biopotentials. "Biological electricity" is an integral property of all living matter. It occurs during the functioning of the nervous system, during the work of glands and muscles. So, working heart muscle creates on the surface of the body rhythmically changing electrical potentials. The change in these potentials over time can be recorded in the form electrocardiograms, allowing the specialist to judge the work of the heart.

We continue to solve problems ;-)

Current strength. Voltage. Resistance

Problem No. 36
Two dissimilar metal plates immersed in an aqueous solution of salt, alkali or acid always form a galvanic cell. Is it possible to obtain a galvanic cell from two identical metal plates, but immersed in different solutions?

Problem No. 37
A lamp and an ammeter were connected in series with the battery and this circuit was closed with the ends of conductors dipped in a solution of copper sulfate. Will the ammeter reading change if the solution is heated?

Problem No. 38
When zinc is dissolved in an aqueous solution of sulfuric acid, the solution becomes very hot. Why is the dissolution of zinc in a Volta galvanic cell closed in an external circuit not accompanied by strong heating of the electrolyte?

Problem No. 39
Is it possible to make an electric current source using mercury, an aqueous solution of sulfuric acid, a knife and a piece of insulated aluminum wire?

Problem No. 40
At your disposal are: table salt, a bar of soap, water, pieces of insulated copper wire, a knife, a wooden stick, an aluminum pan and a large glass vessel. The length of the stick is slightly larger than the diameter of the vessel. Show how using these materials you can make a source of electric current (galvanic cell). Avoid direct contact between copper and aluminum.

PHYSICS AND MILITARY EQUIPMENT
Galvanic impact mine model 1908

“Under Water”, 1915, Alexey Nikolaevich Tolstoy
“...Andrei Nikolaevich drummed his fingers on the glass. It was impossible to remain under water; appearing on the surface meant giving yourself away and being subject to fire. Still, this was the only way to determine the exact location. He commanded a slow rise and returned to the porthole. The shadows went down. The water became noticeably brighter. And suddenly a dark ball began to descend from above, towards me. “Mina... Now let’s touch...” thought Andrei Nikolaevich and, overcoming the numbness that was pressing on his brain, he shouted: “To the left, as far to the left as possible!” The ball moved away, and a second one was approaching from the left. Without getting up, we moved forward. But even there, in the greenish twilight, cast iron balls appeared, waiting for the steel plating of the boat to touch them. "Kat" got lost in the minefields..."
How does a naval galvanic impact mine work?

In the minds of the vast majority of people, a sea mine is a large and scary horned black ball, floating freely on the waves or attached to an anchor cable under water. If a passing ship touches one of the “horns” of such a mine, an explosion will occur and the ship, along with its entire crew, will go to the bottom of the sea. Horned black balls are the most common mines are anchored galvanic impact mines.

1 – heating device; 2 – galvanic shock cap; 3 – ignition cartridge; 4 – ignition glass; 5 – anchor foot; 6 – rollers; 7 – view with minrep; 8 BB charge; 9 – weight with pin; 10 – safety device.

How does a naval galvanic impact mine work?

This mine was a further development of the galvanic impact mines of the 1898 and 1906 models. In a galvanic impact mine, the fuse was located in the cover of the only mounting neck on top of the mine, a spring buffer softened the jerks of the mine, five galvanic lead caps - the “horns” of the mine - were placed around the perimeter of its body. Each horn-cap contained a dry carbon-zinc battery with an electrolyte in a glass ampoule - a “flask”.
When the ship hit a mine, the lead cap was crushed, the “flask” broke and the electrolyte activated the battery. Current from the battery was supplied to the ignition device and ignited the detonator.
TNT was used as an explosive instead of pyroxylin, the anchor was installed on 4 rollers, and rail grips were provided to hold the mine while rolling. The mine was equipped with anti-mine cartridges - mine protectors designed by P.P. Kitkina.
To place the mine on a given recess, an automatic rod-load method was used. The procedure for preparing the mine for placement consisted of two stages. Preliminary stage: installation of galvanic shock caps, “flasks” with electrolyte, a safety device, extension of conductors and checking of all electrical circuits. The final stage involved only the installation of the ignition accessory.

Design of galvanic shock mine turned out to be so successful that, after minor modernization in 1939, under the code “model 1908/39.” it remained in service with the Russian fleet until the mid-60s.

Bordachev Ivan Vasilievich(08/13/1920...) Member of the Union of Artists of the USSR since 1957. Participant of the Great Patriotic War. Awarded the Order of the Red Star, the Order of the Patriotic War, II degree, and the medal “For the victory over Germany in the Great Patriotic War of 1941–1945.” and other medals of the USSR.

From the first days of its existence, the Russian fleet became a real forge of all kinds of new products and advanced innovations. This was most clearly manifested in the field of mine weapons. Russian sailors have priority in the creation of a sea mine, an anti-mine trawl, surface and underwater mine layers and a minesweeper. The first experiments in this area in Russia began at the beginning of the 19th century, and already on June 20, 1855, four ships of the Anglo-French squadron were blown up by sea mines placed near Kronstadt. In memory of this event, June 20 has been celebrated since 1997 as Day of specialists of the mine and torpedo service of the Russian Navy.

We continue to solve problems ;-)

Current strength. Voltage. Resistance

Problem No. 41
A student mistakenly turned on a voltmeter instead of an ammeter when measuring the current in a lamp. What will happen to the glow of the lamp filament?

Problem No. 42
It is required to halve the current in this conductor. What do I need to do?

Problem No. 43
A piece of wire was torn in half and the halves were twisted together, how did the resistance of the conductor change?

Problem No. 44
The wire was passed through a drawing machine, as a result of which its cross-section was halved (the volume did not change). How did the resistance of the wire change?

Problem No. 45
Why are copper wires not used to make rheostats?

Problem No. 46
Why is copper or aluminum wire usually used to make electrical wires?

Problem No. 47
For what purpose are wires covered with a layer of rubber, plastic, varnish, etc.? or wrapped with paper yarn soaked in paraffin?

Problem No. 48
How can you determine the length of a copper wire in plastic insulation, rolled into a large coil, without unwinding it?

Problem No. 49
Why doesn't it electrocute a bird that lands on one of the high voltage wires?

Problem #50
Why is painting small objects by spraying paint economically profitable and also harmless to the health of the worker if high voltage is created between the spray gun and the object?

An important and completely logical step on the path to studying electrical phenomena there was a transition from qualitative observations towards establishing quantitative connections and patterns, to the development basic theory of electricity. The most significant contribution to the solution of these problems was made by St. Petersburg academicians Mikhail Vasilievich Lomonosov, Georg Wilhelm Richman and American scientist Benjamin Franklin.
§ Virtual physical laboratory “Principles of Electronics”: Issue No. 1
Solving calculation problems in physics.
+ Program installation file "Virtual laboratory of the BEGINNING OF ELECTRONICS"(with file verification Dr.WEB antivirus)
+ Exciting experiments on the virtual editing table;-)
…
§ Virtual physical laboratory “Principles of Electronics”: Group C

I wish you success in making your own decision
quality problems in physics!

Literature:
§ Lukashik V.I. Physics Olympiad
Moscow: Prosveshchenie Publishing House, 1987
§ Tarasov L.V. Physics in nature
Moscow: Prosveshchenie Publishing House, 1988
§ Perelman Ya.I. Do you know physics?
Domodedovo: publishing house "VAP", 1994
§ Zolotov V.A. Questions and tasks in physics grades 6-7
Moscow: Prosveshchenie Publishing House, 1971
§ Tulchinsky M.E. Qualitative problems in physics
Moscow: Prosveshchenie Publishing House, 1972
§ Kirillova I.G. Reading book on physics grades 6-7
Moscow: Prosveshchenie Publishing House, 1978
§ Erdavletov S.R., Rutkovsky O.O. Interesting geography of Kazakhstan
Alma-Ata: Mektep Publishing House, 1989.

Electricity and magnetism (electrodynamics) study electromagnetic interactions. The carrier of these interactions is the electromagnetic field; it is a combination of two interconnected fields: magnetic and electric.

The teachings about electricity today are based on Maxwell's equations, they determine fields through their vortices and source.

Electrical Facts in History

Electrical phenomena have been known since ancient times, among them the following facts can be distinguished:

1. Around 500 BC e. Thales of Miletus discovered that amber rubbed with wool easily attracts light fluff. Even his daughter, when cleaning an amber spindle with wool, saw this effect. The word “electron” is translated from Greek as “amber”, hence the term “electricity”. This concept was introduced by V. 16th century English physician Gilbert. After a series of experiments, he discovered that a number of substances become electrified.
2. Clay vessels were discovered in Babylon (4000 years ago) containing copper and iron rods. At the bottom there was bitumen, which insulates the material. The rods were separated by acetic or citric acid, that is, this find is reminiscent of a galvanic cell. Gold on Babylonian jewelry was applied by electroplating.

Electromagnetic field

Definition 1

An electromagnetic field is a type of matter through which electromagnetic interaction is produced between particles with an electric charge. This is a type of matter that transmits the actions of electromagnetic forces.

Electricity is the concept of an electromagnetic field. It is worth remembering that the term “field” in physics is used to designate a number of concepts that are different in content, which include the following:

1. The word “field” fully characterizes the distribution of any physical quantity, scalar or vector. When studying, for example, the thermal state at different points of the medium, a scalar temperature field is reported. When considering the process of mechanical vibrations in an elastic medium, we are talking about a mechanical wave field. In these examples, the concept of “field” describes the physical state of the material environment being studied.
2. A special type of matter is also called a field. The term field (as a type of matter) appeared due to the general problem of interaction. The theory where the action of forces is transmitted through a common void instantly is called the theory of long-range action. The theory that states that the action of forces is transmitted at a finite speed through an intermediate material medium is called the theory of short-range action.

Electric and magnetic fields are usually considered separately, although in reality there are no “purely” magnetic or “purely” electrical phenomena. There is only one single electromagnetic process. The division of electromagnetic interaction into magnetic and electric, as well as the division of unified electromagnetic forces into magnetic and electric, is conditional, and such a conditionality can be easily proven. The terminology – “magnetic”, “electric” forces – is just as conventional.

Electric charge

Definition 2

Electric charge is an inherent property that is inherent in some of the “simplest” particles of matter – “elementary” particles. Electric charge with energy, mass, etc. creates a “complex” of fundamental properties of particles.

Of the known elementary particles, only positrons, electrons, antiprotons, protons, some hyperons and mesons and their antiparticles have an electric charge. At the same time, neutrinos, neutrons, neutral hyperons and mesons and their antiparticles, as well as photons do not have an electric charge.

Only two types of electric charges are known, conventionally called negative and positive (the concepts of “negative” and “positive” electricity were first introduced by W. Franklin (USA) in the 18th century).

Direct determination of the value of the elementary charge was carried out in 1909 - 1904. A.F. Ioffe (Russia), as well as R.E. Milliken (USA). After the experiments of Ioffe and Millikan, the hypothesis about the existence of subelectrons, i.e. charges that are less than the charge of the electron.

Such a charge cannot be separated from the particles to which it belongs. The general indestructibility of matter entails the indestructibility of electric charge. To the laws of momentum, conservation of mass, energy, and angular momentum that are popular in theoretical mechanics, we must add the law of conservation of electric charge: in a closed system of particles or bodies, the algebraic sum of charges has a constant value, no matter what processes occur in this system. The general law of charge conservation was established experimentally by M. Faraday (England) and F. Epinus (Russia).

The presence of an electromagnetic microfield is associated with the movement of each elementary charge. It is worth noting that the electric and magnetic fields studied by macroscopic and electrostatics, electrodynamics, have become averaged: they all represent a superposition or superposition of microfields, which creates a large collection of moving elementary charges. As experience shows, the averaged electric field can also be completely different from zero only when its “source” - the macrocharge - is completely stationary, and also when it is in motion.

Electric field strength

Electric field strength is a vector characteristic of the field, a force acting on a unit electric charge at rest in a given reference frame.

Tension is determined by the formula:

$E↖(→)=(F↖(→))/(q)$

where $E↖(→)$ is the field strength; $F↖(→)$ is the force acting on the charge $q$ placed at a given point in the field. The direction of the vector $E↖(→)$ coincides with the direction of the force acting on the positive charge and is opposite to the direction of the force acting on the negative charge.

The SI unit of voltage is volt per meter (V/m).

Field strength of a point charge. According to Coulomb's law, a point charge $q_0$ acts on another charge $q$ with a force equal to

$F=k(|q_0||q|)/(r^2)$

The modulus of the field strength of a point charge $q_0$ at a distance $r$ from it is equal to

$E=(F)/(q)=k(|q_0|)/(r^2)$

The intensity vector at any point of the electric field is directed along the straight line connecting this point and the charge.

Electric field lines

The electric field in space is usually represented by lines of force. The concept of lines of force was introduced by M. Faraday while studying magnetism. This concept was then developed by J. Maxwell in his research on electromagnetism.

A line of force, or electric field strength line, is a line whose tangent at each point coincides with the direction of the force acting on a positive point charge located at that point in the field.

Tension lines of a positively charged ball;

Tension lines of two oppositely charged balls;

Tension lines of two similarly charged balls

Tension lines of two plates charged with charges of different signs, but equal in absolute value.

The tension lines in the last figure are almost parallel in the space between the plates, and their density is the same. This suggests that the field in this region of space is uniform. An electric field is called homogeneous if its strength is the same at all points in space.

In an electrostatic field, the lines of force are not closed; they always begin on positive charges and end on negative charges. They do not intersect anywhere; the intersection of the field lines would indicate the uncertainty of the direction of the field strength at the intersection point. The density of field lines is greater near charged bodies, where the field strength is greater.

Field of a charged ball. The field strength of a charged conducting ball at a distance from the center of the ball exceeding its radius $r≥R$ is determined by the same formula as the fields of a point charge. This is evidenced by the distribution of field lines, similar to the distribution of intensity lines of a point charge.

The charge of the ball is distributed evenly over its surface. Inside the conducting ball, the field strength is zero.

A magnetic field. Magnet interaction

The phenomenon of interaction between permanent magnets (the establishment of a magnetic needle along the Earth’s magnetic meridian, the attraction of unlike poles, the repulsion of like poles) has been known since ancient times and was systematically studied by W. Gilbert (the results were published in 1600 in his treatise “On the Magnet, Magnetic Bodies and the Great Magnet - Earth").

Natural (natural) magnets

The magnetic properties of some natural minerals were known already in ancient times. Thus, there is written evidence from more than 2000 years ago about the use of natural permanent magnets as compasses in China. The attraction and repulsion of magnets and the magnetization of iron filings by them is mentioned in the works of ancient Greek and Roman scientists (for example, in the poem “On the Nature of Things” by Lucretius Cara).

Natural magnets are pieces of magnetic iron ore (magnetite), consisting of $FeO$ (31%) and $Fe_2O$ (69%). If such a piece of mineral is brought close to small iron objects - nails, sawdust, a thin blade, etc., they will be attracted to it.

Artificial permanent magnets

Permanent magnet- this is a product made of a material that is an autonomous (independent, isolated) source of a constant magnetic field.

Artificial permanent magnets are made from special alloys, which include iron, nickel, cobalt, etc. These metals acquire magnetic properties (magnetize) if they are brought close to permanent magnets. Therefore, in order to make permanent magnets from them, they are specially kept in strong magnetic fields, after which they themselves become sources of a constant magnetic field and are able to retain magnetic properties for a long time.

The figure shows an arc and strip magnets.

In Fig. pictures of the magnetic fields of these magnets are given, obtained by the method that M. Faraday first used in his research: with the help of iron filings scattered on a sheet of paper on which the magnet lies. Each magnet has two poles - these are the places of greatest concentration of magnetic field lines (they are also called magnetic field lines, or lines of magnetic induction field). These are the places that iron filings are most attracted to. One of the poles is usually called northern(($N$), other - southern($S$). If you bring two magnets close to each other with like poles, you can see that they repel, and if they have opposite poles, they attract.

In Fig. it is clearly seen that the magnetic lines of the magnet are closed lines. The magnetic field lines of two magnets facing each other with like and unlike poles are shown. The central part of these paintings resembles patterns of electric fields of two charges (opposite and like). However, a significant difference between electric and magnetic fields is that electric field lines begin and end at charges. Magnetic charges do not exist in nature. The magnetic field lines leave the north pole of the magnet and enter the south; they continue in the body of the magnet, i.e., as mentioned above, they are closed lines. Fields whose field lines are closed are called vortex. A magnetic field is a vortex field (this is its difference from an electric one).

Application of magnets

The most ancient magnetic device is the well-known compass. In modern technology, magnets are used very widely: in electric motors, in radio engineering, in electrical measuring equipment, etc.

Earth's magnetic field

The globe is a magnet. Like any magnet, it has its own magnetic field and its own magnetic poles. That is why the compass needle is oriented in a certain direction. It is clear where exactly the north pole of the magnetic needle should point, because opposite poles attract. Therefore, the north pole of the magnetic needle points to the south magnetic pole of the Earth. This pole is located in the north of the globe, somewhat away from the north geographic pole (on Prince of Wales Island - about $75°$ north latitude and $99°$ west longitude, at a distance of approximately $2100$ km from the north geographic pole).

When approaching the north geographic pole, the lines of force of the Earth's magnetic field increasingly tilt toward the horizon at a greater angle, and in the region of the south magnetic pole they become vertical.

The Earth's north magnetic pole is located near the south geographic pole, namely at $66.5°$ south latitude and $140°$ east longitude. Here the magnetic field lines exit the Earth.

In other words, the Earth's magnetic poles do not coincide with its geographic poles. Therefore, the direction of the magnetic needle does not coincide with the direction of the geographic meridian, and the magnetic needle of the compass only approximately shows the direction to the north.

The compass needle can also be influenced by some natural phenomena, for example, magnetic storms, which are temporary changes in the Earth's magnetic field associated with solar activity. Solar activity is accompanied by the emission of streams of charged particles, in particular electrons and protons, from the surface of the Sun. These streams, moving at high speed, create their own magnetic field that interacts with the Earth's magnetic field.

On the globe (except for short-term changes in the magnetic field) there are areas in which there is a constant deviation in the direction of the magnetic needle from the direction of the Earth's magnetic line. These are the areas magnetic anomaly(from the Greek anomalia - deviation, abnormality). One of the largest such areas is the Kursk magnetic anomaly. The anomalies are caused by huge deposits of iron ore at a relatively shallow depth.

The Earth's magnetic field reliably protects the Earth's surface from cosmic radiation, the effect of which on living organisms is destructive.

Flights of interplanetary space stations and ships have made it possible to establish that the Moon and the planet Venus have no magnetic field, while the planet Mars has a very weak one.

Experiments by Oerstedai ​​Ampere. Magnetic field induction

In 1820, the Danish scientist G. H. Oersted discovered that a magnetic needle placed near a conductor through which current flows rotates, tending to be perpendicular to the conductor.

The diagram of G. H. Oersted's experiment is shown in the figure. The conductor included in the current source circuit is located above the magnetic needle parallel to its axis. When the circuit is closed, the magnetic needle deviates from its original position. When the circuit is opened, the magnetic needle returns to its original position. It follows that the current-carrying conductor and the magnetic needle interact with each other. Based on this experiment, we can conclude that there is a magnetic field associated with the flow of current in a conductor and the vortex nature of this field. The described experiment and its results were Oersted's most important scientific achievement.

In the same year, the French physicist Ampere, who was interested in Oersted's experiments, discovered the interaction of two straight conductors with current. It turned out that if the currents in the conductors flow in one direction, i.e., they are parallel, then the conductors attract, if in opposite directions (i.e., they are antiparallel), then they repel.

Interactions between current-carrying conductors, i.e., interactions between moving electric charges, are called magnetic, and the forces with which current-carrying conductors act on each other are called magnetic forces.

According to the theory of short-range action, which M. Faraday adhered to, the current in one of the conductors cannot directly affect the current in the other conductor. Similar to the case with stationary electric charges around which there is an electric field, it was concluded that in the space surrounding the currents, there is a magnetic field, which acts with some force on another current-carrying conductor placed in this field, or on a permanent magnet. In turn, the magnetic field created by the second current-carrying conductor acts on the current in the first conductor.

Just as an electric field is detected by its effect on a test charge introduced into this field, a magnetic field can be detected by the orienting effect of a magnetic field on a frame with a current of small (compared to the distances at which the magnetic field changes noticeably) dimensions.

The wires supplying current to the frame should be intertwined (or placed close to each other), then the resulting force exerted by the magnetic field on these wires will be zero. The forces acting on such a current-carrying frame will rotate it so that its plane becomes perpendicular to the magnetic field induction lines. In the example, the frame will rotate so that the current-carrying conductor is in the plane of the frame. When the direction of current in the conductor changes, the frame will rotate $180°$. In the field between the poles of a permanent magnet, the frame will turn with a plane perpendicular to the magnetic lines of force of the magnet.

Magnetic induction

Magnetic induction ($B↖(→)$) is a vector physical quantity that characterizes the magnetic field.

The direction of the magnetic induction vector $B↖(→)$ is taken to be:

1) the direction from the south pole $S$ to the north pole $N$ of a magnetic needle freely positioned in a magnetic field, or

2) the direction of the positive normal to a closed circuit with current on a flexible suspension, freely installed in a magnetic field. The normal directed towards the movement of the tip of the gimlet (with a right-hand thread), the handle of which is rotated in the direction of the current in the frame, is considered positive.

It is clear that directions 1) and 2) coincide, which was established by Ampere’s experiments.

As for the magnitude of magnetic induction (i.e., its modulus) $B$, which could characterize the strength of the field, experiments have established that the maximum force $F$ with which the field acts on a current-carrying conductor (placed perpendicular to the induction lines magnetic field), depends on the current $I$ in the conductor and on its length $∆l$ (proportional to them). However, the force acting on a current element (of unit length and current strength) depends only on the field itself, i.e. the ratio $(F)/(I∆l)$ for a given field is a constant value (similar to the ratio of force to charge for electric field). This value is determined as magnetic induction.

The magnetic field induction at a given point is equal to the ratio of the maximum force acting on a current-carrying conductor to the length of the conductor and the current strength in the conductor placed at this point.

The greater the magnetic induction at a given point in the field, the greater the force the field at that point will act on a magnetic needle or a moving electric charge.

The SI unit of magnetic induction is tesla(Tl), named after the Serbian electrical engineer Nikola Tesla. As can be seen from the formula, $1$ T $=l(H)/(A m)$

If there are several different sources of magnetic field, the induction vectors of which at a given point in space are equal to $(В_1)↖(→), (В_2)↖(→), (В_3)↖(→),...$, then, according to the principle of field superposition, the magnetic field induction at this point is equal to the sum of the magnetic field induction vectors created every source.

$В↖(→)=(В_1)↖(→)+(В_2)↖(→)+(В_3)↖(→)+...$

Magnetic induction lines

To visualize the magnetic field, M. Faraday introduced the concept magnetic lines of force, which he repeatedly demonstrated in his experiments. A picture of the field lines can easily be obtained using iron filings sprinkled on cardboard. The figure shows: lines of magnetic induction of direct current, solenoid, circular current, direct magnet.

Magnetic induction lines, or magnetic lines of force, or simply magnetic lines are called lines whose tangents at any point coincide with the direction of the magnetic induction vector $B↖(→)$ at this point in the field.

If, instead of iron filings, small magnetic needles are placed around a long straight conductor carrying current, then you can see not only the configuration of the field lines (concentric circles), but also the direction of the field lines (the north pole of the magnetic needle indicates the direction of the induction vector at a given point).

The direction of the forward current magnetic field can be determined by right gimlet rule.

If you rotate the handle of the gimlet so that the translational movement of the tip of the gimlet indicates the direction of the current, then the direction of rotation of the handle of the gimlet will indicate the direction of the magnetic field lines of the current.

The direction of the forward current magnetic field can also be determined using first rule of the right hand.

If you grasp the conductor with your right hand, pointing the bent thumb in the direction of the current, then the tips of the remaining fingers at each point will show the direction of the induction vector at that point.

Vortex field

Magnetic induction lines are closed, which indicates that there are no magnetic charges in nature. Fields whose field lines are closed are called vortex fields. That is, the magnetic field is a vortex field. This differs from the electric field created by charges.

Solenoid

A solenoid is a coil of wire carrying current.

The solenoid is characterized by the number of turns per unit length $n$, length $l$ and diameter $d$. The thickness of the wire in the solenoid and the pitch of the helix (helical line) are small compared to its diameter $d$ and length $l$. The term “solenoid” is also used in a broader sense - this is the name given to coils with an arbitrary cross-section (square solenoid, rectangular solenoid), and not necessarily cylindrical in shape (toroidal solenoid). There are long solenoid ($l>>d$) and short ($l

The solenoid was invented in 1820 by A. Ampere to enhance the magnetic action of current discovered by X. Oersted and used by D. Arago in experiments on the magnetization of steel rods. The magnetic properties of a solenoid were experimentally studied by Ampere in 1822 (at the same time he introduced the term “solenoid”). The equivalence of the solenoid to permanent natural magnets was established, which was a confirmation of Ampere’s electrodynamic theory, which explained magnetism by the interaction of ring molecular currents hidden in bodies.

The magnetic field lines of the solenoid are shown in the figure. The direction of these lines is determined using second rule of the right hand.

If you clasp the solenoid with the palm of your right hand, directing four fingers along the current in the turns, then the extended thumb will indicate the direction of the magnetic lines inside the solenoid.

Comparing the magnetic field of a solenoid with the field of a permanent magnet, you can see that they are very similar. Like a magnet, a solenoid has two poles - north ($N$) and south ($S$). The North Pole is the one from which magnetic lines emerge; the south pole is the one they enter. The north pole of the solenoid is always located on the side that the thumb of the palm points to when it is positioned in accordance with the second rule of the right hand.

A solenoid in the form of a coil with a large number of turns is used as a magnet.

Studies of the magnetic field of a solenoid show that the magnetic effect of the solenoid increases with increasing current and the number of turns in the solenoid. In addition, the magnetic action of a solenoid or current-carrying coil is enhanced by introducing an iron rod into it, which is called core

Electromagnets

A solenoid with an iron core inside is called electromagnet.

Electromagnets can contain not one, but several coils (windings) and have cores of different shapes.

Such an electromagnet was first constructed by the English inventor W. Sturgeon in 1825. With a mass of $0.2$ kg, W. Sturgeon’s electromagnet held a load weighing $36$ N. In the same year, J. Joule increased the lifting force of the electromagnet to $200$ N, and six years later American scientist J. Henry built an electromagnet weighing $300$ kg, capable of holding a load weighing $1$ t!

Modern electromagnets can lift loads weighing several tens of tons. They are used in factories when moving heavy iron and steel products. Electromagnets are also used in agriculture to clean the grains of a number of plants from weeds and in other industries.

Ampere power

A straight section of conductor $∆l$, through which current $I$ flows, is acted upon by a force $F$ in a magnetic field with induction $B$.

To calculate this force, use the expression:

$F=B|I|∆lsinα$

where $α$ is the angle between the vector $B↖(→)$ and the direction of the conductor segment with current (current element); The direction of the current element is taken to be the direction in which the current flows through the conductor. The force $F$ is called Ampere force in honor of the French physicist A. M. Ampere, who was the first to discover the effect of a magnetic field on a current-carrying conductor. (In fact, Ampere established a law for the force of interaction between two elements of current-carrying conductors. He was a proponent of the theory of long-range action and did not use the concept of field.

However, according to tradition and in memory of the scientist’s merits, the expression for the force acting on a current-carrying conductor from a magnetic field is also called Ampere’s law.)

The direction of Ampere's force is determined using the left-hand rule.

If you position the palm of your left hand so that the magnetic field lines enter it perpendicularly, and the four extended fingers indicate the direction of the current in the conductor, then the outstretched thumb will indicate the direction of the force acting on the current-carrying conductor. Thus, the Ampere force is always perpendicular to both the magnetic field induction vector and the direction of the current in the conductor, i.e., perpendicular to the plane in which these two vectors lie.

The consequence of the Ampere force is the rotation of the current-carrying frame in a constant magnetic field. This finds practical application in many devices, e.g. electrical measuring instruments- galvanometers, ammeters, where a movable frame with current rotates in the field of a permanent magnet and by the angle of deflection of a pointer fixedly connected to the frame, one can judge the amount of current flowing in the circuit.

Thanks to the rotating effect of the magnetic field on the current-carrying frame, it also became possible to create and use electric motors- machines in which electrical energy is converted into mechanical energy.

Lorentz force

The Lorentz force is a force acting on a moving point electric charge in an external magnetic field.

Dutch physicist H. A. Lorenz at the end of the 19th century. established that the force exerted by a magnetic field on a moving charged particle is always perpendicular to the direction of motion of the particle 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 position the palm of your left hand so that the four extended fingers indicate the direction of movement of the charge, and the vector of the magnetic induction field enters the palm, then the extended thumb 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 modulus of the Lorentz force is easily determined from Ampere's law and is:

where $q$ is the charge of the particle, $υ$ is the speed of its movement, $α$ is the angle between the velocity and magnetic field induction vectors.

If, in addition to the magnetic field, there is also an electric field that acts on the charge with a force $(F_(el))↖(→)=qE↖(→)$, then the total force acting on the charge is equal to:

$F↖(→)=(F_(el))↖(→)+(F_l)↖(→)$

Often this total force is called the Lorentz force, and the force expressed by the formula $F=|q|υBsinα$ is called 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 no work), but can only change the direction of its motion, i.e., bend the trajectory.

This curvature of the trajectory of electrons in a TV picture tube is easy to observe if you bring a permanent magnet to its screen: the image will be distorted.

Motion of a charged particle in a uniform magnetic field. Let a charged particle fly with a speed $υ$ into a uniform magnetic field perpendicular to the tension lines. 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 expression for centripetal acceleration and the formula $F=|q|υBsinα$:

$(mυ^2)/(r)=|q|υB$

From here we get

$r=(mυ)/(|q|B)$

where $m$ is the particle mass.

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 by their specific charges, i.e., by the ratio of the charge of a particle to its mass, and from the results obtained to accurately determine the masses of the particles.

The vacuum chamber of the device is placed in a field (the induction vector $B↖(→)$ is perpendicular to the figure). Charged particles (electrons or ions) accelerated by the electric field, having described an arc, fall on the photographic plate, where they leave a trace that allows the radius of the trajectory $r$ to be measured with great accuracy. This radius determines the specific charge of the ion. Knowing the charge of an ion, it is easy to calculate its mass.

Magnetic properties of substances

In order to explain the existence of the magnetic field of permanent magnets, Ampere suggested that microscopic circular currents exist in a substance with magnetic properties (they were called molecular). This idea was subsequently, after the discovery of the electron and the structure of the atom, brilliantly confirmed: these currents are created by the movement of electrons around the nucleus and, being oriented in the same way, in total create a field around and inside the magnet.

In Fig. the planes in which elementary electric currents are located are randomly oriented due to the chaotic thermal motion of atoms, and the substance does not exhibit magnetic properties. In a magnetized state (under the influence, for example, of an external magnetic field), these planes are oriented identically, and their actions add up.

Magnetic permeability. The reaction of the medium to the influence of an external magnetic field with induction $B_0$ (field in a vacuum) is determined by the magnetic susceptibility $μ$:

where $B$ is the magnetic field induction in the substance. Magnetic permeability is similar to dielectric constant $ε$.

Based on their magnetic properties, substances are divided into Diamagnets, paramagnets and ferromagnets. For diamagnetic materials, the coefficient $μ$, which characterizes the magnetic properties of the medium, is less than $1$ (for example, for bismuth $μ = 0.999824$); for paramagnets $μ > 1$ (for platinum $μ = 1.00036$); for ferromagnets $μ >> 1$ (iron, nickel, cobalt).

Diamagnets are repelled by a magnet, paramagnetic materials are attracted. By these characteristics they can be distinguished from each other. For most substances, the magnetic permeability practically does not differ from unity, only for ferromagnets it greatly exceeds it, reaching several tens of thousands of units.

Ferromagnets. Ferromagnets exhibit the strongest magnetic properties. The magnetic fields created by ferromagnets are much stronger than the external magnetizing field. True, the magnetic fields of ferromagnets are not created as a result of the rotation of electrons around the nuclei - orbital magnetic moment, and due to the electron’s own rotation - its own magnetic moment, called spin.

The Curie temperature ($T_c$) is the temperature above which ferromagnetic materials lose their magnetic properties. It is different for each ferromagnet. For example, for iron $Т_с = 753°$С, for nickel $Т_с = 365°$С, for cobalt $Т_с = 1000°$ С. There are ferromagnetic alloys with $Т_с

The first detailed studies of the magnetic properties of ferromagnets were carried out by the outstanding Russian physicist A. G. Stoletov (1839-1896).

Ferromagnets are used very widely: as permanent magnets (in electrical measuring instruments, loudspeakers, telephones, etc.), steel cores in transformers, generators, electric motors (to enhance the magnetic field and save electricity). Magnetic tapes made from ferromagnetic materials record sound and images for tape recorders and video recorders. Information is recorded on thin magnetic films for storage devices in electronic computers.

Lenz's rule

Lenz's rule (Lenz's law) was established by E. H. Lenz in 1834. It refines the law of electromagnetic induction, discovered in 1831 by M. Faraday. Lenz's rule determines the direction of the induced current in a closed loop as it moves in an external magnetic field.

The direction of the induction current is always such that the forces it experiences from the magnetic field counteract the movement of the circuit, and the magnetic flux $Ф_1$ created by this current tends to compensate for changes in the external magnetic flux $Ф_e$.

Lenz's law is an expression of the law of conservation of energy for electromagnetic phenomena. Indeed, when a closed loop moves in a magnetic field due to external forces, it is necessary to perform some work against the forces arising as a result of the interaction of the induced current with the magnetic field and directed in the direction opposite to the movement.

Lenz's rule is illustrated in the figure. If a permanent magnet is moved into a coil closed to a galvanometer, the induced current in the coil will have a direction that will create a magnetic field with vector $B"$ directed opposite to the induction vector of the magnet's field $B$, i.e. it will push the magnet out of the coil or interfere with its movement.When a magnet is pulled out of the coil, on the contrary, the field created by the induction current will attract the coil, i.e. again impede its movement.

To apply Lenz's rule to determine the direction of the induced current $I_e$ in the circuit, you must follow these recommendations.

1. Set the direction of the magnetic induction lines $B↖(→)$ of the external magnetic field.
2. Find out whether the flux of magnetic induction of this field through the surface bounded by the contour ($∆Ф > 0$) increases or decreases ($∆Ф
3. Set the direction of the magnetic induction lines $В"↖(→)$ of the magnetic field of the induced current $I_i$. These lines should be directed, according to Lenz's rule, opposite to the lines $В↖(→)$, if $∆Ф > 0$, and have the same direction as them if $∆Ф
4. Knowing the direction of the magnetic induction lines $B"↖(→)$, determine the direction of the induction current $I_i$ using gimlet rule.

Modern life cannot be imagined without electricity; this type of energy is used most fully by humanity. However, not all adults are able to remember the definition of electric current from a school physics course (this is a directed flow of elementary particles with a charge), very few people understand what it is.

What is electricity

The presence of electricity as a phenomenon is explained by one of the main properties of physical matter - the ability to have an electric charge. They can be positive and negative, while objects with oppositely polar signs are attracted to each other, and “equivalent” ones, on the contrary, repel. Moving particles are also the source of a magnetic field, which once again proves the connection between electricity and magnetism.

At the atomic level, the existence of electricity can be explained as follows. The molecules that make up all bodies contain atoms made up of nuclei and electrons circulating around them. These electrons can, under certain conditions, break away from the “mother” nuclei and move to other orbits. As a result, some atoms become “understaffed” with electrons, and some have an excess of them.

Since the nature of electrons is such that they flow to where there is a shortage of them, the constant movement of electrons from one substance to another constitutes electric current (from the word “to flow”). It is known that electricity flows from the minus pole to the plus pole. Therefore, a substance with a lack of electrons is considered to be positively charged, and with an excess - negatively, and it is called “ions”. If we are talking about the contacts of electrical wires, then the positively charged one is called “zero”, and the negatively charged one is called “phase”.

In different substances, the distance between atoms is different. If they are very small, the electron shells literally touch each other, so electrons easily and quickly move from one nucleus to another and back, thereby creating the movement of an electric current. Substances such as metals are called conductors.

In other substances, interatomic distances are relatively large, so they are dielectrics, i.e. do not conduct electricity. First of all, it's rubber.

Additional Information. When the nuclei of a substance emit electrons and move, energy is generated that heats the conductor. This property of electricity is called “power” and is measured in watts. This energy can also be converted into light or another form.

For the continuous flow of electricity through the network, the potentials at the end points of the conductors (from power lines to house wiring) must be different.

History of the discovery of electricity

What electricity is, where it comes from, and its other characteristics are fundamentally studied by the science of thermodynamics with related sciences: quantum thermodynamics and electronics.

To say that any scientist invented electric current would be wrong, because since ancient times many researchers and scientists have been studying it. The term “electricity” itself was introduced into use by the Greek mathematician Thales; this word means “amber”, since it was in experiments with an amber stick and wool that Thales was able to generate static electricity and describe this phenomenon.

The Roman Pliny also studied the electrical properties of resin, and Aristotle studied electric eels.

At a later time, the first person to thoroughly study the properties of electric current was V. Gilbert, the physician to the Queen of England. The German burgomaster from Magdeburg O.f. Gericke is considered the creator of the first light bulb made from a grated sulfur ball. And the great Newton proved the existence of static electricity.

At the very beginning of the 18th century, the English physicist S. Gray divided substances into conductors and non-conductors, and the Dutch scientist Pieter van Musschenbroek invented a Leyden jar capable of accumulating an electric charge, i.e. it was the first capacitor. The American scientist and politician B. Franklin was the first to develop the theory of electricity in scientific terms.

The entire 18th century was rich in discoveries in the field of electricity: the electrical nature of lightning was established, an artificial magnetic field was constructed, the existence of two types of charges (“plus” and “minus”) and, as a consequence, two poles was revealed (US naturalist R. Simmer) , Coulomb discovered the law of interaction between point electric charges.

In the next century, batteries were invented (by the Italian scientist Volta), an arc lamp (by the Englishman Davey), and also a prototype of the first dynamo. 1820 is considered the year of the birth of electrodynamic science, the Frenchman Ampere did this, for which his name was assigned to the unit for indicating the strength of electric current, and the Scotsman Maxwell deduced the light theory of electromagnetism. Russian Lodygin invented an incandescent lamp with a coal core - the progenitor of modern light bulbs. A little over a hundred years ago, the neon lamp was invented (by the French scientist Georges Claude).

To this day, research and discoveries in the field of electricity continue, for example, the theory of quantum electrodynamics and the interaction of weak electric waves. Among all the scientists who researched electricity, Nikola Tesla holds a special place - many of his inventions and theories about how electricity works are still not fully appreciated.

Natural electricity

For a long time it was believed that electricity “by itself” does not exist in nature. This misconception was dispelled by B. Franklin, who proved the electrical nature of lightning. It was they, according to one version of scientists, that contributed to the synthesis of the first amino acids on Earth.

Electricity is also generated inside living organisms, which generates nerve impulses that provide motor, respiratory and other vital functions.

Interesting. Many scientists consider the human body to be an autonomous electrical system that is endowed with self-regulatory functions.

Representatives of the animal world also have their own electricity. For example, some breeds of fish (eels, lampreys, stingrays, anglerfish and others) use it for protection, hunting, obtaining food and orientation in underwater space. A special organ in the body of these fish generates electricity and stores it, like in a capacitor, its frequency is hundreds of hertz, and its voltage is 4-5 volts.

Getting and using electricity

Electricity in our time is the basis of a comfortable life, so humanity needs its constant production. For these purposes, various types of power plants are being built (hydroelectric power plants, thermal, nuclear, wind, tidal and solar), capable of generating megawatts of electricity with the help of generators. This process is based on the conversion of mechanical (energy of falling water at hydroelectric power plants), thermal (combustion of carbon fuel - hard and brown coal, peat at thermal power plants) or interatomic energy (atomic decay of radioactive uranium and plutonium at nuclear power plants) into electrical energy.

Much scientific research is devoted to the electrical forces of the Earth, all of which seek to harness atmospheric electricity for the benefit of humanity - generating electricity.

Scientists have proposed many interesting current generator devices that make it possible to produce electricity from a magnet. They use the ability of permanent magnets to perform useful work in the form of torque. It arises as a result of repulsion between similarly charged magnetic fields on the stator and rotor devices.

Electricity is more popular than all other energy sources because it has many advantages:

• easy movement to the consumer;
• rapid conversion to thermal or mechanical energy;
• new areas of its application are possible (electric vehicles);
• discovery of new properties (superconductivity).

Electricity is the movement of differently charged ions inside a conductor. This is a great gift from nature, which people have been cognizing since ancient times, and this process is not yet completed, although humanity has already learned to extract it in huge quantities. Electricity plays a huge role in the development of modern society. We can say that without it, the lives of most of our contemporaries will simply stop, because it’s not for nothing that when the electricity goes out, people say that they “turned off the lights.”

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