Magnetism for dummies: basic formulas, definition, examples. Electricity

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 do well to have a collection of basic physics formulas handy. Dry formulas with explanation: short, concise, nothing more. A very useful thing when solving problems, you know. Yes, and in the exam, when exactly what was cruelly memorized the day before can “jump out” of my head, such a selection will serve you well.

Most of the tasks are usually given 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. Good old favorite rectilinear and uniform movement.

Kinematic formulas:

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

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

Now we give 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 section of mechanics with formulas for vibrations and waves and move on to molecular physics and thermodynamics.

Efficiency, Gay-Lussac's law, the Clapeyron-Mendeleev equation - all these sweet formulas are collected below.

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

Basic formulas in physics: electricity

It's time to move on to electricity, although thermodynamics loves it less. Let's start with electrostatics.

And, to the drum roll, we finish with the formulas for Ohm's law, electromagnetic induction and electromagnetic oscillations.

That's all. Of course, a whole mountain of formulas could be given, but this is useless. When there are too many formulas, you can easily get confused, and then completely melt the brain. We hope that 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 have not found the formula you need: ask the experts student service. Our authors keep hundreds of formulas in their heads and click tasks like nuts. Contact us, and soon any task will be "too tough" for you.

Charged bodies are capable of creating, in addition to electric, another kind of field. If the charges move, then a special kind of matter is created in the space around them, called magnetic field. Therefore, an electric current, which is an ordered movement of charges, also creates a magnetic field. Like the electric field, the magnetic field is not limited in space, it propagates very quickly, but still with a finite speed. It can only be detected by its effect on moving charged bodies (and, as a result, currents).

To describe the magnetic field, it is necessary to introduce the force characteristic of the field, similar to the intensity vector E electric field. Such a characteristic is the vector B magnetic induction. In the SI system of units, 1 Tesla (T) is taken as a unit of magnetic induction. If in a magnetic field with induction B place the conductor length l with current I, then a force called by the power of Ampere, which is calculated by the formula:

Where: IN– magnetic field induction, I is the current in the conductor, l- its length. The Ampere force is directed perpendicular to the magnetic induction vector and the direction of the current flowing through the conductor.

To determine the direction of the Ampère force, one usually uses left hand rule: if you position your left hand so that the lines of induction enter the palm, and the outstretched fingers are directed along the current, then the retracted thumb will indicate the direction of the Ampère force acting on the conductor (see figure).

If the angle α between the directions of the vector of magnetic induction and the current in the conductor is different from 90 °, then to determine the direction of the Ampère force, it is necessary to take the component of the magnetic field, which is perpendicular to the direction of the current. It is necessary to solve the problems of this topic in the same way as in dynamics or statics, i.e. by writing the forces along the coordinate axes or by adding the forces according to the rules of vector addition.

The moment of forces acting on the loop with current

Let the loop with current be in a magnetic field, and the plane of the loop is perpendicular to the field. The Ampere forces will compress the frame, and their resultant will be equal to zero. If you change the direction of the current, then the Ampere forces will change their direction, and the frame will not shrink, but stretch. If the lines of magnetic induction lie in the plane of the frame, then a torque of the Ampère forces arises. Rotational moment of Ampere forces equals:

Where: S- frame area, α - angle between the normal to the frame and the magnetic induction vector (the normal is a vector perpendicular to the plane of the frame), N- the number of turns, B– magnetic field induction, I- the current strength in the frame.

Lorentz force

Ampere force acting on a piece of conductor of length Δ l with current I located in a magnetic field B can be expressed in terms of the forces acting on individual charge carriers. These forces are called Lorentz forces. Lorentz force acting on a particle with a charge q in a magnetic field B moving at a speed v, is calculated by the following formula:

Corner α in this expression is equal to the angle between the speed and the magnetic induction vector. Direction of the Lorentz force acting on positively a charged particle, as well as the direction of the Ampère force, can be found by the left hand rule or by the gimlet rule (as well as the Ampère force). The vector of magnetic induction must be mentally stuck into the palm of the left hand, four closed fingers should be directed along the speed of the charged particle, and the bent thumb will show the direction of the Lorentz force. If the particle has negative charge, then the direction of the Lorentz force, found by the left hand rule, will need to be replaced by the opposite.

The Lorentz force is directed perpendicular to the velocity and magnetic field induction vectors. When a charged particle moves in a magnetic field Lorentz force does no work. Therefore, the modulus of the velocity vector does not change when the particle moves. If a charged particle moves in a uniform magnetic field under the action of the Lorentz force, and its velocity lies in a plane perpendicular to the magnetic field induction vector, then the particle will move in a circle, the radius of which can be calculated by the following formula:

The Lorentz force in this case plays the role of a centripetal force. The period of revolution of a particle in a uniform magnetic field is:

The last expression shows that for charged particles of a given mass m the period of revolution (and hence the frequency and angular velocity) does not depend on the speed (and hence on the kinetic energy) and the radius of the trajectory R.

Magnetic field theory

If two parallel wires carry current in the same direction, they attract; if in opposite directions, they repel each other. The patterns of this phenomenon were experimentally established by Ampère. The interaction of currents is caused by their magnetic fields: the magnetic field of one current acts by the Ampere force on another current and vice versa. Experiments have shown that the modulus of force acting on a segment of length Δ l each of the conductors, is directly proportional to the strength of the current I 1 and I 2 in conductors, segment length Δ l and inversely proportional to the distance R between them:

Where: μ 0 is a constant value, which is called magnetic constant. The introduction of the magnetic constant into the SI simplifies the writing of a number of formulas. Its numerical value is:

μ 0 = 4π 10 -7 H / A 2 ≈ 1.26 10 -6 H / A 2.

Comparing the expression just given for the force of interaction of two conductors with current and the expression for the Ampère force, it is easy to obtain an expression for induction of the magnetic field created by each of the rectilinear conductors with current on distance R From him:

Where: μ - the magnetic permeability of the substance (more on this below). If current flows in a circular loop, then center of the coil magnetic field induction is determined by the formula:

lines of force The magnetic field is called the lines along the tangents to which the magnetic arrows are located. magnetic needle called a long and thin magnet, its poles are pointed. A magnetic needle suspended on a thread always turns in one direction. At the same time, one end of it is directed towards the north, the other - towards the south. Hence the name of the poles: north ( N) and southern ( S). Magnets always have two poles: north (indicated in blue or the letter N) and southern (in red or letter S). Magnets interact in the same way as charges: like poles repel, and opposite poles attract. It is impossible to get a magnet with one pole. Even if the magnet is broken, each part will have two different poles.

Magnetic induction vector

Magnetic induction vector- a vector physical quantity that is a characteristic of a magnetic field, numerically equal to the force acting on a current element of 1 A and a length of 1 m, if the direction of the field line is perpendicular to the conductor. Denoted IN, unit of measurement - 1 Tesla. 1 T is a very large value, therefore, in real magnetic fields, magnetic induction is measured in mT.

The magnetic induction vector is directed tangentially to the lines of force, i.e. coincides with the direction of the north pole of a magnetic needle placed in a given magnetic field. The direction of the magnetic induction vector does not coincide with the direction of the force acting on the conductor, therefore, the magnetic field lines, strictly speaking, are not force lines.

Magnetic field line of permanent magnets directed with respect to the magnets themselves as shown in the figure:

When magnetic field of electric current to determine the direction of field lines use the rule "Right hand": if you take the conductor in your right hand so that the thumb is directed along the current, then four fingers clasping the conductor show the direction of the lines of force around the conductor:

In the case of direct current, the lines of magnetic induction are circles whose planes are perpendicular to the current. The magnetic induction vectors are directed tangentially to the circle.

Solenoid- a conductor wound on a cylindrical surface, through which an electric current flows I similar to the field of a direct permanent magnet. inside solenoid length l and the number of turns N a uniform magnetic field is created with induction (its direction is also determined by the right hand rule):

Magnetic field lines look like closed lines is a common property of all magnetic lines. Such a field is called a vortex field. In the case of permanent magnets, the lines do not end at the surface, but penetrate inside the magnet and close inside. This difference between electric and magnetic fields is explained by the fact that, unlike electric, magnetic charges do not exist.

Magnetic properties of matter

All substances have magnetic properties. The magnetic properties of a substance are characterized relative magnetic permeability μ , for which the following is true:

This formula expresses the correspondence of the magnetic induction vector of the field in vacuum and in a given medium. In contrast to the electrical interaction, during the magnetic interaction in the medium, one can observe both strengthening and weakening of the interaction compared to vacuum, in which the magnetic permeability μ = 1. diamagnets magnetic permeability μ slightly less than unity. Examples: water, nitrogen, silver, copper, gold. These substances somewhat weaken the magnetic field. Paramagnets- oxygen, platinum, magnesium - somewhat enhance the field, having μ a little more than one. At ferromagnets- iron, nickel, cobalt - μ >> 1. For example, for iron μ ≈ 25000.

magnetic flux. Electromagnetic induction

Phenomenon electromagnetic induction was discovered by the outstanding English physicist M. Faraday in 1831. It consists in the occurrence of an electric current in a closed conducting circuit with a change in time of the magnetic flux penetrating the circuit. magnetic flux Φ across the square S the contour is called the value:

Where: B is the modulus of the magnetic induction vector, α is the angle between the magnetic induction vector B and normal (perpendicular) to the contour plane, S- contour area, N- the number of turns in the circuit. The unit of magnetic flux in the SI system is called Weber (Wb).

Faraday experimentally established that when the magnetic flux changes in a conducting circuit, EMF induction ε ind, equal to the rate of change of the magnetic flux through the surface bounded by the contour, taken with a minus sign:

A change in the magnetic flux penetrating a closed circuit can occur for two possible reasons.

1. The magnetic flux changes due to the movement of the circuit or its parts in a time-constant magnetic field. This is the case when conductors, and with them free charge carriers, move in a magnetic field. The occurrence of the induction EMF is explained by the action of the Lorentz force on free charges in moving conductors. The Lorentz force plays the role of an outside force in this case.
2. The second reason for the change in the magnetic flux penetrating the circuit is the change in time of the magnetic field when the circuit is stationary.

When solving problems, it is important to immediately determine how the magnetic flux changes. Three options are possible:

1. The magnetic field changes.
2. The area of ​​the contour changes.
3. The orientation of the frame relative to the field changes.

In this case, when solving problems, the EMF is usually considered modulo. Let us also pay attention to one particular case in which the phenomenon of electromagnetic induction occurs. So, the maximum value of the induction emf in a circuit consisting of N turns, area S, rotating with angular velocity ω in a magnetic field with induction IN:

Movement of a conductor in a magnetic field

When moving the conductor length l in a magnetic field B with speed v a potential difference arises at its ends, caused by the action of the Lorentz force on free electrons in the conductor. This potential difference (strictly speaking, EMF) is found by the formula:

Where: α - the angle that is measured between the direction of the velocity and the magnetic induction vector. EMF does not occur in the fixed parts of the circuit.

If the rod is long L spins in a magnetic field IN around one of its ends with an angular velocity ω , then at its ends there will be a potential difference (EMF), which can be calculated by the formula:

Inductance. Self-induction. Magnetic field energy

self induction is an important special case of electromagnetic induction, when a changing magnetic flux, causing an EMF of induction, is created by a current in the circuit itself. If the current in the circuit under consideration changes for some reason, then the magnetic field of this current changes, and, consequently, the own magnetic flux penetrating the circuit. In the circuit, an EMF of self-induction occurs, which, according to the Lenz rule, prevents a change in the current in the circuit. Own magnetic flux Φ , penetrating the circuit or coil with current, is proportional to the strength of the current I:

Proportionality factor L in this formula is called the coefficient of self-induction or inductance coils. The SI unit of inductance is the Henry (H).

Remember: the inductance of the circuit does not depend on either the magnetic flux or the strength of the current in it, but is determined only by the shape and size of the circuit, as well as the properties of the environment. Therefore, when the current strength in the circuit changes, the inductance remains unchanged. The inductance of a coil can be calculated using the formula:

Where: n- concentration of turns per unit length of the coil:

EMF self-induction, arising in a coil with a constant value of inductance, according to the Faraday formula is equal to:

So the EMF of self-induction is directly proportional to the inductance of the coil and the rate of change of the current strength in it.

The magnetic field has energy. Just as a charged capacitor has a supply of electrical energy, a coil with current flowing through its coils has a supply of magnetic energy. Energy W m magnetic field coil with inductance L generated by current I, can be calculated by one of the formulas (they follow from each other, taking into account the formula Φ = LI):

By correlating the formula for the energy of the magnetic field of the coil with its geometric dimensions, we can obtain a formula for volumetric energy density of the magnetic field(or energy per unit volume):

Lenz's rule

Inertia- a phenomenon that occurs both in mechanics (when accelerating a car, we lean back, counteracting an increase in speed, and when braking, we lean forward, counteracting a decrease in speed), and in molecular physics (when a liquid is heated, the evaporation rate increases, the fastest molecules leave the liquid, reducing speed heating) and so on. In electromagnetism, inertia manifests itself in opposition to a change in the magnetic flux penetrating the circuit. If the magnetic flux increases, then the induction current arising in the circuit is directed so as to prevent the increase in the magnetic flux, and if the magnetic flux decreases, then the induction current arising in the circuit is directed so as to prevent the magnetic flux from decreasing.

On that website. To do this, you need nothing at all, namely: to devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on various topics and varying complexity. The latter can only be learned by solving thousands of problems.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result on the CT, the maximum of what you are capable of.

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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 exact charges and to calculate the strength of the electric field created by a point charge, one must be able to apply Coulomb's law. To calculate the field strengths created by extended charges (charged thread, plane, etc.), the Gauss theorem is applied. For a system of electric charges, it is necessary to apply the principle

When studying the topic "Direct current" it is necessary to consider in all forms the laws of Ohm and Joule-Lenz 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 we 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 the existence of matter - an electromagnetic field. The basis of the electromagnetic field theory is Maxwell's theory.

Table of basic formulas for electricity and magnetism

In conductors, under certain conditions, a continuous ordered movement of free electric charge carriers can occur. Such a movement is called electric shock. The direction of movement of positive free charges is taken as the direction of the electric current, although in most cases electrons move - negatively charged particles.

The quantitative measure of electric current is the strength of the current I is a scalar physical quantity equal to the charge ratio q, transferred through the cross section of the conductor for a time interval t, to this time interval:

If the current is not constant, then to find the amount of charge passed through the conductor, the area of ​​\u200b\u200bthe figure under the graph of the dependence of the current strength on time is calculated.

If the strength of the current and its direction do not change with time, then such a current is called permanent. The current strength is measured by an ammeter, which is connected in series to the circuit. In the International System of Units SI, current is measured in amperes [A]. 1 A = 1 C/s.

It is found as the ratio of the total charge to the total time (i.e., according to the same principle as the average speed or any other average value in physics):

If the current changes uniformly over time from the value I 1 to value I 2, then the value of the average current can be found as the arithmetic mean of the extreme values:

current density- the current strength per unit cross-section of the conductor is calculated by the formula:

When current flows through a conductor, the current experiences resistance from the conductor. The reason for the resistance is the interaction of charges with the atoms of the substance of the conductor and with each other. The unit of resistance is 1 ohm. Conductor resistance R is determined by the formula:

Where: l- the length of the conductor, S is its cross-sectional area, ρ - resistivity of the conductor material (be careful not to confuse the latter value with the density of the substance), which characterizes the ability of the conductor material to resist the passage of current. That is, this is the same characteristic of a substance as many others: specific heat capacity, density, melting point, etc. The unit of measurement of resistivity is 1 Ohm m. The specific resistance of a substance is a tabular value.

The resistance of a conductor also depends on its temperature:

Where: R 0 – conductor resistance at 0°С, t is the temperature expressed in degrees Celsius, α is the temperature coefficient of resistance. It is equal to the relative change in resistance as the temperature increases by 1°C. For metals, it is always greater than zero, for electrolytes, on the contrary, it is always less than zero.

Diode in DC circuit

Diode- This is a non-linear circuit element, the resistance of which depends on the direction of current flow. The diode is designated as follows:

The arrow in the schematic symbol of a diode shows in which direction it passes current. In this case, its resistance is zero, and the diode can be replaced simply with a conductor with zero resistance. If the current flows through the diode in the opposite direction, then the diode has an infinitely large resistance, that is, it does not pass current at all, and is a break in the circuit. Then the section of the circuit with the diode can simply be crossed out, since the current does not flow through it.

Ohm's law. Series and parallel connection of conductors

The German physicist G. Ohm in 1826 experimentally established that the current strength I, flowing through a homogeneous metal conductor (that is, a conductor in which external forces do not act) with resistance R, proportional to voltage U at the ends of the conductor:

the value R called electrical resistance. A conductor with electrical resistance is called resistor. This ratio expresses Ohm's law for a homogeneous section of the circuit: The strength of the current in a conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor.

Conductors that obey Ohm's law are called linear. Graphic dependence of current strength I from voltage U(such graphs are called current-voltage characteristics, abbreviated VAC) is depicted by a straight line passing through the origin. It should be noted that there are many materials and devices that do not obey Ohm's law, such as a semiconductor diode or a gas discharge lamp. Even for metal conductors at sufficiently high currents, a deviation from Ohm's linear law is observed, since the electrical resistance of metal conductors increases with increasing temperature.

Conductors in electrical circuits can be connected in two ways: series and parallel. Each method has its own patterns.

1. Patterns of serial connection:

The formula for the total resistance of series-connected resistors is valid for any number of conductors. If the circuit is connected in series n same resistance R, then the total resistance R 0 is found by the formula:

2. Patterns of parallel connection:

The formula for the total resistance of resistors connected in parallel is valid for any number of conductors. If the circuit is connected in parallel n same resistance R, then the total resistance R 0 is found by the formula:

Electrical measuring instruments

To measure voltages and currents in DC electrical circuits, special devices are used - voltmeters And ammeters.

Voltmeter designed to measure the potential difference applied to its terminals. It is connected in parallel with the section of the circuit on which the potential difference is measured. Any voltmeter has some internal resistance. R b. In order for the voltmeter not to introduce a noticeable redistribution of currents when connected to the measured circuit, its internal resistance must be large compared to the resistance of the section of the circuit to which it is connected.

Ammeter designed to measure the current in the circuit. The ammeter is connected in series to the break in the electrical circuit so that the entire measured current passes through it. The ammeter also has some internal resistance. R A. Unlike a voltmeter, the internal resistance of an ammeter must be sufficiently small compared to the total resistance of the entire circuit.

EMF. Ohm's law for a complete circuit

For the existence of direct current, it is necessary to have a device in an electrical closed circuit capable of creating and maintaining potential differences in sections of the circuit due to the work of forces of non-electrostatic origin. Such devices are called direct current sources. Forces of non-electrostatic origin acting on free charge carriers from current sources are called outside forces.

The nature of outside forces can be different. In galvanic cells or batteries, they arise as a result of electrochemical processes, in DC generators, external forces arise when conductors move in a magnetic field. Under the action of external forces, electric charges move inside the current source against the forces of the electrostatic field, due to which a constant electric current can be maintained in a closed circuit.

When electric charges move along a DC circuit, external forces acting inside current sources do work. Physical quantity equal to the ratio of work A st external forces when moving charge q from the negative pole of the current source to the positive to the value of this charge, is called source electromotive force (EMF):

Thus, the EMF is determined by the work done by external forces when moving a single positive charge. The electromotive force, like the potential difference, is measured in volts (V).

Ohm's law for a complete (closed) circuit: the current strength in a closed circuit is equal to the electromotive force of the source divided by the total (internal + external) resistance of the circuit:

Resistance r– internal (intrinsic) resistance of the current source (depends on the internal structure of the source). Resistance R– load resistance (external circuit resistance).

Voltage drop in the external circuit while equal (it is also called voltage at the source terminals):

It is important to understand and remember: the EMF and the internal resistance of the current source do not change when different loads are connected.

If the load resistance is zero (the source closes on itself) or much less than the source resistance, then the circuit will flow short circuit current:

Short circuit current - the maximum current that can be obtained from a given source with an electromotive force ε and internal resistance r. For sources with low internal resistance, the short-circuit current can be very large, and cause the destruction of the electrical circuit or source. For example, lead-acid batteries used in automobiles can have a short circuit current of several hundred amperes. Particularly dangerous are short circuits in lighting networks powered by substations (thousands of amperes). To avoid the destructive effect of such high currents, fuses or special circuit breakers are included in the circuit.

Multiple EMF sources in a circuit

If the circuit contains several emfs connected in series, That:

1. With the correct (the positive pole of one source is connected to the negative of the other) connection of sources, the total EMF of all sources and their internal resistance can be found by the formulas:

For example, such a connection of sources is carried out in remote controls, cameras and other household appliances that operate on several batteries.

2. If the sources are connected incorrectly (sources are connected by the same poles), their total EMF and resistance are calculated by the formulas:

In both cases, the total resistance of the sources increases.

At parallel connection it makes sense to connect sources only with the same EMF, otherwise the sources will be discharged into each other. Thus, the total EMF will be the same as the EMF of each source, that is, with a parallel connection, we will not get a battery with a large EMF. This reduces the internal resistance of the battery of sources, which allows you to get more current and power in the circuit:

This is the meaning of the parallel connection of sources. In any case, when solving problems, you first need to find the total EMF and the total internal resistance of the resulting source, and then write Ohm's law for the complete circuit.

Work and current power. Joule-Lenz law

Job A electric current I flowing through a fixed conductor with resistance R, converted to heat Q, which stands out on the conductor. This work can be calculated using one of the formulas (taking into account Ohm's law, they all follow from each other):

The law of converting the work of current into heat was experimentally established independently by J. Joule and E. Lenz and is called Joule–Lenz law. Electric current power equal to the ratio of the work of the current A to the time interval Δ t, for which this work was done, so it can be calculated using the following formulas:

The work of an electric current in SI, as usual, is expressed in joules (J), power - in watts (W).

Closed circuit energy balance

Consider now a complete DC circuit consisting of a source with an electromotive force ε and internal resistance r and an external homogeneous area with resistance R. In this case, the useful power or the power released in the external circuit is:

The maximum possible useful power of the source is achieved if R = r and is equal to:

If, when connected to the same current source of different resistances R 1 and R 2 equal powers are allocated to them, then the internal resistance of this current source can be found by the formula:

Power loss or power inside the current source:

The total power developed by the current source:

Current source efficiency:

Electrolysis

electrolytes It is customary to call conductive media in which the flow of electric current is accompanied by the transfer of matter. Carriers of free charges in electrolytes are positively and negatively charged ions. Electrolytes include many compounds of metals with metalloids in the molten state, as well as some solid substances. However, the main representatives of electrolytes widely used in technology are aqueous solutions of inorganic acids, salts and bases.

The passage of an electric current through the electrolyte is accompanied by the release of a substance on the electrodes. This phenomenon has been named electrolysis.

Electric current in electrolytes is the movement of ions of both signs in opposite directions. Positive ions move towards the negative electrode ( cathode), negative ions - to the positive electrode ( anode). Ions of both signs appear in aqueous solutions of salts, acids and alkalis as a result of the splitting of some neutral molecules. This phenomenon is called electrolytic dissociation.

law of electrolysis was experimentally established by the English physicist M. Faraday in 1833. Faraday's law determines the amount of primary products released on the electrodes during electrolysis. So the mass m substance released at the electrode is directly proportional to the charge Q passed through the electrolyte:

the value k called electrochemical equivalent. It can be calculated using the formula:

Where: n is the valence of the substance, N A is the Avogadro constant, M is the molar mass of the substance, e is the elementary charge. Sometimes the following notation for the Faraday constant is also introduced:

Electric current in gases and in vacuum

Electric current in gases

Under normal conditions, gases do not conduct electricity. This is due to the electrical neutrality of gas molecules and, consequently, the absence of electric charge carriers. In order for a gas to become a conductor, one or more electrons must be stripped from the molecules. Then there will be free charge carriers - electrons and positive ions. This process is called gas ionization.

It is possible to ionize gas molecules by external influence - ionizer. Ionizers can be: a stream of light, X-rays, an electron stream or α -particles. Gas molecules also ionize at high temperature. Ionization leads to the appearance of free charge carriers in gases - electrons, positive ions, negative ions (an electron combined with a neutral molecule).

If an electric field is created in the space occupied by an ionized gas, then the carriers of electric charges will begin to move in an orderly manner - this is how an electric current arises in gases. If the ionizer ceases to operate, then the gas becomes neutral again, since recombination– formation of neutral atoms by ions and electrons.

Electric current in a vacuum

Vacuum is such a degree of rarefaction of a gas at which one can neglect the collision between its molecules and assume that the mean free path exceeds the linear dimensions of the vessel in which the gas is located.

An electric current in a vacuum is called the conductivity of the interelectrode gap in a vacuum state. In this case, there are so few gas molecules that the processes of their ionization cannot provide such a number of electrons and ions that are necessary for ionization. The conductivity of the interelectrode gap in vacuum can be ensured only with the help of charged particles that have arisen due to emission phenomena at the electrodes.

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How to successfully prepare for the CT in Physics and Mathematics?

In order to successfully prepare for the CT in Physics and Mathematics, among other things, three critical conditions must be met:

1. Study all the topics and complete all the tests and tasks given in the study materials on this site. To do this, you need nothing at all, namely: to devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on various topics and varying complexity. The latter can only be learned by solving thousands of problems.
2. Learn all formulas and laws in physics, and formulas and methods in mathematics. In fact, it is also very simple to do this, there are only about 200 necessary formulas in physics, and even a little less in mathematics. In each of these subjects there are about a dozen standard methods for solving problems of a basic level of complexity, which can also be learned, and thus, completely automatically and without difficulty, solve most of the digital transformation at the right time. After that, you will only have to think about the most difficult tasks.
3. Attend all three stages of rehearsal testing in physics and mathematics. Each RT can be visited twice to solve both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and the knowledge of formulas and methods, it is also necessary to be able to properly plan time, distribute forces, and most importantly fill out the answer form correctly, without confusing either the numbers of answers and tasks, or your own name. Also, during the RT, it is important to get used to the style of posing questions in tasks, which may seem very unusual to an unprepared person on the DT.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result on the CT, the maximum of what you are capable of.

Found an error?

If you, as it seems to you, found an error in the training materials, then please write about it by mail. You can also write about the error on the social network (). In the letter, indicate the subject (physics or mathematics), the name or number of the topic or test, the number of the task, or the place in the text (page) where, in your opinion, there is an error. Also describe what the alleged error is. Your letter will not go unnoticed, the error will either be corrected, or you will be explained why it is not a mistake.

It often happens that the problem cannot be solved due to the fact that the necessary formula is not at hand. Deriving a formula from the very beginning is not the fastest thing, and every minute counts.

Below we have collected together the basic formulas on the topic "Electricity and Magnetism". Now, when solving problems, you can use this material as a reference, so as not to waste time searching for the necessary information.

Magnetism: definition

Magnetism is the interaction of moving electric charges that occurs through a magnetic field.

Field is a special form of matter. Within the framework of the standard model, there are electric, magnetic, electromagnetic fields, the field of nuclear forces, the gravitational field, and the Higgs field. Perhaps there are other hypothetical fields that we can only guess about or not guess at all. Today we are interested in the magnetic field.

Magnetic induction

Just as charged bodies create an electric field around them, moving charged bodies generate a magnetic field. The magnetic field is not only created by moving charges (electric current), but also acts on them. In fact, a magnetic field can only be detected by its effect on moving charges. And it acts on them with a force called the Ampere force, which will be discussed later.

Before we begin to give specific formulas, we need to talk about magnetic induction.

Magnetic induction is a power vector characteristic of a magnetic field.

It is marked with the letter B and measured in Tesla (Tl) . By analogy with the strength for the electric field E magnetic induction shows how strong the magnetic field acts on the charge.

By the way, you will find many interesting facts on this topic in our article about.

How to determine the direction of the magnetic induction vector? Here we are interested in the practical side of the issue. The most common case in problems is a magnetic field created by a conductor with current, which can be either straight, or in the form of a circle or coil.

To determine the direction of the magnetic induction vector, there is right hand rule. Get ready to use abstract and spatial thinking!

If you take the conductor in your right hand so that the thumb points in the direction of the current, then the fingers bent around the conductor will show the direction of the magnetic field lines around the conductor. The vector of magnetic induction at each point will be directed tangentially to the lines of force.

Amp power

Imagine that there is a magnetic field with induction B. If we place a conductor of length l , through which current flows I , then the field will act on the conductor with the force:

That's what it is ampere power . Corner alpha is the angle between the direction of the magnetic induction vector and the direction of the current in the conductor.

The direction of the Ampère force is determined by the rule of the left hand: if you place your left hand so that the lines of magnetic induction enter the palm, and the outstretched fingers indicate the direction of the current, the thumb set aside will indicate the direction of the Ampère force.

Lorentz force

We found out that the field acts on a conductor with current. But if this is so, then initially it acts separately on each moving charge. The force with which a magnetic field acts on an electric charge moving in it is called Lorentz force . It is important to note here the word "moving", so the magnetic field does not act on stationary charges.

So, a particle with a charge q moves in a magnetic field with induction IN with speed v , A alpha is the angle between the particle velocity vector and the magnetic induction vector. Then the force acting on the particle is:

How to determine the direction of the Lorentz force? Left hand rule. If the induction vector enters the palm, and the fingers point in the direction of the velocity, then the bent thumb will show the direction of the Lorentz force. Note that this is how the direction is determined for positively charged particles. For negative charges, the resulting direction must be reversed.

If a particle of mass m flies into the field perpendicular to the lines of induction, then it will move in a circle, and the Lorentz force will play the role of a centripetal force. The radius of the circle and the period of revolution of a particle in a uniform magnetic field can be found by the formulas:

Interaction of currents

Let's consider two cases. First, current flows in a straight wire. The second is in a circular loop. As we know, current creates a magnetic field.

In the first case, the magnetic induction of a wire with current I on distance R from it is calculated by the formula:

Mu is the magnetic permeability of the substance, mu with index zero is the magnetic constant.

In the second case, the magnetic induction at the center of a circular loop with current is:

Also, when solving problems, the formula for the magnetic field inside the solenoid can be useful. - this is a coil, that is, a set of circular turns with current.

Let their number be N , and the length of the solenoil itself is l . Then the field inside the solenoid is calculated by the formula:

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Magnetic flux and EMF

If magnetic induction is a vector characteristic of a magnetic field, then magnetic flux is a scalar value, which is also one of the most important characteristics of the field. Let's imagine that we have some kind of frame or contour that has a certain area. The magnetic flux shows how many lines of force pass through a unit area, that is, it characterizes the intensity of the field. measured in Weberach (Wb) and denoted F .

S - contour area, alpha is the angle between the normal (perpendicular) to the contour plane and the vector IN .

When changing the magnetic flux through the circuit, the circuit is induced EMF , equal to the rate of change of the magnetic flux through the circuit. By the way, you can read more about what electromotive force is in another of our articles.

In essence, the formula above is the formula for Faraday's law of electromagnetic induction. We remind you that the rate of change of any quantity is nothing but its derivative with respect to time.

The reverse is also true for magnetic flux and induction EMF. A change in the current in the circuit leads to a change in the magnetic field and, accordingly, to a change in the magnetic flux. In this case, an EMF of self-induction arises, which prevents a change in the current in the circuit. The magnetic flux that permeates the circuit with current is called its own magnetic flux, is proportional to the strength of the current in the circuit and is calculated by the formula:

L is a proportionality factor called inductance, which is measured in Henry (Gn) . Inductance is affected by the shape of the circuit and the properties of the medium. For coil length l and with the number of turns N inductance is calculated by the formula:

The formula for the EMF of self-induction:

Magnetic field energy

Electricity, nuclear energy, kinetic energy. Magnetic energy is one form of energy. In physical problems, it is most often necessary to calculate the energy of the coil's magnetic field. Magnetic energy coil with current I and inductance L is equal to:

Volumetric field energy density:

Of course, these are not all the basic formulas of the physics section. « electricity and magnetism » , however, they can often help in solving standard problems and calculations. If you come across a problem with an asterisk, and you just can’t find the key to it, simplify your life and contact the