The session is approaching, and it’s time for us to move from theory to practice. Over the weekend we sat down and thought that many students would benefit from having a collection of basic physics formulas at their fingertips. Dry formulas with explanation: short, concise, nothing superfluous. A very useful thing when solving problems, you know. And during an exam, when exactly what was memorized the day before might “jump out” of your head, such a selection will serve an excellent purpose.

The most problems are usually asked in the three most popular sections of physics. This Mechanics, thermodynamics And Molecular physics, electricity. Let's take them!

Basic formulas in physics dynamics, kinematics, statics

Let's start with the simplest. The good old favorite straight and uniform movement.

Kinematics formulas:

Of course, let's not forget about motion in a circle, and then we'll move on to dynamics and Newton's laws.

After dynamics, it’s time to consider the conditions of equilibrium of bodies and liquids, i.e. statics and hydrostatics

Now we present the basic formulas on the topic “Work and Energy”. Where would we be without them?

Basic formulas of molecular physics and thermodynamics

Let's finish the mechanics section with formulas for oscillations and waves and move on to molecular physics and thermodynamics.

The efficiency factor, the Gay-Lussac law, the Clapeyron-Mendeleev equation - all these formulas dear to the heart are collected below.

By the way! There is now a discount for all our readers 10% on .

Basic formulas in physics: electricity

It's time to move on to electricity, even though it is less popular than thermodynamics. Let's start with electrostatics.

And, to the beat of the drum, we end with formulas for Ohm’s law, electromagnetic induction and electromagnetic oscillations.

That's all. Of course, a whole mountain of formulas could be cited, but this is of no use. When there are too many formulas, you can easily get confused and even melt your brain. We hope our cheat sheet of basic physics formulas will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or haven’t found the right formula: ask the experts student service. Our authors keep hundreds of formulas in their heads and crack problems like nuts. Contact us, and soon any task will be up to you.

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

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 involved in the study of 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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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 is a long solenoid ($l>>d$) and a short one ($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 prevent 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 prevent 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.

The physics of electricity is something that each of us has to deal with. In this article we will look at the basic concepts associated with it.

What is electricity? For the uninitiated, it is associated with a flash of lightning or with the energy that powers a TV and washing machine. He knows that electric trains are used. What else can he tell you? Power lines remind him of our dependence on electricity. Someone can give several other examples.

However, there are many other, not so obvious, but everyday phenomena associated with electricity. Physics introduces us to all of them. We begin to study electricity (problems, definitions and formulas) at school. And we learn a lot of interesting things. It turns out that a beating heart, a running athlete, a sleeping child and a swimming fish all produce electrical energy.

Electrons and protons

Let's define the basic concepts. From a scientist's point of view, the physics of electricity is concerned with the movement of electrons and other charged particles in various substances. Therefore, scientific understanding of the nature of the phenomenon that interests us depends on the level of knowledge about atoms and their constituent subatomic particles. The key to this understanding is the tiny electron. Atoms of any substance contain one or more electrons, moving in different orbits around the nucleus, just as the planets revolve around the Sun. Usually equal to the number of protons in the nucleus in an atom. However, protons, being much heavier than electrons, can be considered as if fixed at the center of the atom. This extremely simplified model of the atom is quite enough to explain the basics of such a phenomenon as the physics of electricity.

What else do you need to know? Electrons and protons have the same size (but different signs), so they attract each other. The charge of a proton is positive and that of an electron is negative. An atom that has more or fewer electrons than normal is called an ion. If there are not enough of them in an atom, then it is called a positive ion. If it contains an excess of them, then it is called a negative ion.

When an electron leaves an atom, it acquires some positive charge. An electron, deprived of its opposite, a proton, either moves to another atom or returns to the previous one.

Why do electrons leave atoms?

This is due to several reasons. The most general one is that under the influence of a pulse of light or some external electron, an electron moving in an atom can be knocked out of its orbit. Heat causes atoms to vibrate faster. This means that electrons can escape from their atom. During chemical reactions they also move from atom to atom.

A good example of the relationship between chemical and electrical activity is provided by muscles. Their fibers contract when exposed to an electrical signal coming from the nervous system. Electric current stimulates chemical reactions. They lead to muscle contraction. External electrical signals are often used to artificially stimulate muscle activity.

Conductivity

In some substances, electrons move more freely under the influence of an external electric field than in others. Such substances are said to have good conductivity. They are called conductors. These include most metals, heated gases and some liquids. Air, rubber, oil, polyethylene and glass are poor conductors of electricity. They are called dielectrics and are used to insulate good conductors. There are no ideal insulators (absolutely non-conducting current). Under certain conditions, electrons can be removed from any atom. However, these conditions are usually so difficult to satisfy that, from a practical point of view, such substances can be considered non-conducting.

Getting acquainted with such a science as “Electricity”), we learn that there is a special group of substances. These are semiconductors. They behave partly as dielectrics and partly as conductors. These include, in particular: germanium, silicon, copper oxide. Due to its properties, semiconductors have many applications. For example, it can serve as an electrical valve: like the valve on a bicycle tire, it allows charges to move in only one direction. Such devices are called rectifiers. They are used in both miniature radios and large power plants to convert alternating current to direct current.

Heat is a chaotic form of movement of molecules or atoms, and temperature is a measure of the intensity of this movement (for most metals, as the temperature decreases, the movement of electrons becomes more free). This means that the resistance to the free movement of electrons decreases with decreasing temperature. In other words, the conductivity of metals increases.

Superconductivity

In some substances at very low temperatures, resistance to the flow of electrons disappears completely, and electrons, having begun to move, continue to move indefinitely. This phenomenon is called superconductivity. At temperatures several degrees above absolute zero (-273 °C) it is observed in metals such as tin, lead, aluminum and niobium.

Van de Graaff generators

The school curriculum includes various experiments with electricity. There are many types of generators, one of which we would like to talk about in more detail. The Van de Graaff generator is used to produce ultra-high voltages. If an object containing an excess of positive ions is placed inside a container, then electrons will appear on the inner surface of the latter, and the same number of positive ions will appear on the outer surface. If you now touch the inner surface with a charged object, then all the free electrons will transfer to it. On the outside, positive charges will remain.

The positive ions from the source are applied to a conveyor belt running inside a metal sphere. The tape is connected to the inner surface of the sphere using a conductor in the form of a ridge. Electrons flow from the inner surface of the sphere. Positive ions appear on its outer side. The effect can be enhanced by using two generators.

Electricity

The school physics course also includes such a concept as electric current. What is it? Electric current is caused by the movement of electric charges. When an electric lamp connected to a battery is turned on, current flows through a wire from one pole of the battery to the lamp, then through the hair, causing it to glow, and back through the second wire to the other pole of the battery. If you turn the switch, the circuit opens - the current flow stops and the lamp goes out.

Electron movement

Current in most cases is the ordered movement of electrons in a metal that serves as a conductor. In all conductors and some other substances, some random movement always occurs, even if no current flows. Electrons in a substance can be relatively free or strongly bound. Good conductors have free electrons that can move around. But in poor conductors, or insulators, most of these particles are quite tightly bound to the atoms, which prevents their movement.

Sometimes, naturally or artificially, a movement of electrons in a conductor is created in a certain direction. This flow is called electric current. It is measured in amperes (A). Current carriers can also be ions (in gases or solutions) and “holes” (lack of electrons in some types of semiconductors. The latter behave like positively charged electric current carriers. To make electrons move in one direction or another, a certain force is needed. In nature its sources can be: exposure to sunlight, magnetic effects and chemical reactions. Some of them are used to produce electric current. Typically, a generator using magnetic effects and an element (battery), the action of which is determined by chemical reactions, are used for this purpose. , creating force electrons to move in one direction along the circuit. The magnitude of the emf is measured in volts (V). These are the basic units of measurement of electricity.

The magnitude of the EMF and the strength of the current are related to each other, like pressure and flow in a liquid. Water pipes are always filled with water at a certain pressure, but water begins to flow only when the tap is opened.

Similarly, it can be connected to a source of emf, but current will not flow in it until a path is created along which electrons can move. It could be, say, an electric lamp or a vacuum cleaner; the switch here plays the role of a faucet, “releasing” the current.

Relationship between current and voltage

As the voltage in the circuit increases, so does the current. While studying a physics course, we learn that electrical circuits consist of several different sections: usually a switch, conductors and a device that consumes electricity. All of them, connected together, create resistance to electric current, which (assuming constant temperature) for these components does not change over time, but is different for each of them. Therefore, if the same voltage is applied to a light bulb and to an iron, then the flow of electrons in each of the devices will be different, since their resistances are different. Consequently, the strength of the current flowing through a certain section of the circuit is determined not only by the voltage, but also by the resistance of the conductors and devices.

Ohm's law

The amount of electrical resistance is measured in ohms (ohms) in the science of physics. Electricity (formulas, definitions, experiments) is a broad topic. We will not derive complex formulas. For the first acquaintance with the topic, what was said above is enough. However, one formula is still worth deducing. It's not complicated at all. For any conductor or system of conductors and devices, the relationship between voltage, current and resistance is given by the formula: voltage = current x resistance. This is a mathematical expression of Ohm's law, named after Georg Ohm (1787-1854), who was the first to establish the relationship between these three parameters.

The physics of electricity is a very interesting branch of science. We have considered only the basic concepts associated with it. You learned what electricity is and how it is formed. We hope you find this information useful.