After it was established that a magnetic field is created by electric currents, scientists tried to solve the inverse problem - using a magnetic field to create an electric current. This problem was successfully solved in 1831 by M. Faraday, who discovered the phenomenon electromagnetic induction. The essence of this phenomenon is that in a closed conducting circuit, with any change in the magnetic flux penetrating this circuit, an electrical current arises, which is called induction. A diagram of some of Faraday's experiments is shown in Fig. 3.12.
When the position of the permanent magnet changed relative to the coil closed to the galvanometer, an electric current arose in the latter, and the direction of the current turned out to be different - depending on the direction of movement of the permanent magnet. A similar result was achieved when moving another coil through which an electric current flowed. Moreover, a current arose in the large coil even when the position of the smaller coil remained unchanged, but when the current in it changed.
Based on similar experiments, M. Faraday came to the conclusion that an electric current always arises in a coil when the magnetic flux coupled to this coil changes. The magnitude of the current depends on the rate of change of the magnetic flux. We now formulate Faraday's discoveries in the form law of electromagnetic induction: with any change in the magnetic flux associated with a conducting closed circuit, a induced emf, which is defined as
The “-” sign in expression (3.53) means that with an increase in magnetic flux, the magnetic field created by the induction current is directed against the external magnetic field. If the magnetic flux decreases in magnitude, then the magnetic field of the induced current coincides in direction with the external magnetic field. The Russian scientist H. Lenz thus determined the appearance of the minus sign in expression (3.53) - the induction current in the circuit always has such a direction that the magnetic field it creates has such a direction that it prevents the change in the magnetic flux that caused the induction current.
Let's give another formulation law of electromagnetic induction: The induced emf in a closed conducting circuit is equal to the rate of change of the magnetic flux passing through this circuit, taken with the opposite sign.
The German physicist Helmholtz showed that the law of electromagnetic induction can be derived from the law of conservation of energy. In fact, the energy of the EMF source for moving a conductor with current in a magnetic field (see Fig. 3.37) will be spent both on Joule heating of the conductor with resistance R, and on the work of moving the conductor:
Then it immediately follows from equation (3.54) that
The numerator of expression (3.55) contains the algebraic sum of the emfs acting in the circuit. Hence,
What is the physical reason for the occurrence of EMF? The charges in the conductor AB are affected by the Lorentz force when the conductor moves along the x axis. Under the influence of this force, positive charges will shift upward, resulting in electric field in the conductor will be weakened. In other words, an induced emf will appear in the conductor. Consequently, in the case we have considered, the physical cause of the occurrence of EMF is the Lorentz force. However, as we have already noted, even in motionless closed loop An induced emf may appear if the magnetic field penetrating this circuit changes.
In this case, the charges can be considered stationary, and the Lorentz force does not act on stationary charges. To explain the occurrence of EMF in this case, Maxwell suggested that any changing magnetic field generates a changing electric field in the conductor, which is the cause of the occurrence of induced EMF. The circulation of the voltage vector acting in this circuit will thus be equal to the induced emf acting in the circuit:
. (3.56)
The phenomenon of electromagnetic induction is used to convert mechanical rotational energy into electrical energy - in generators electric current. Reverse process- transformation electrical energy into mechanical, based on the torque acting on a frame with current in a magnetic field, used in electric motors.
Let's consider the principle of operation of an electric current generator (Fig. 3.13). Let us have a conducting frame rotating between the poles of a magnet (it could also be an electromagnet) with a frequency w. Then the angle between the normal to the plane of the frame and the direction of the magnetic field changes according to the law a = wt. In this case, the magnetic flux coupled to the frame will change in accordance with the formula
where S is the contour area. In accordance with the law of electromagnetic induction, an emf will be induced in the frame
With e max = BSw. Thus, if a conducting frame rotates in a magnetic field at a constant angular velocity, then an emf will be induced in it, varying according to a harmonic law. In real generators, many turns connected in series are rotated, and in electromagnets, to increase magnetic induction, cores with high magnetic permeability are used m..
Induction currents can also arise in the thickness of conducting bodies placed in an alternating magnetic field. In this case, these currents are called Foucault currents. These currents cause heating of massive conductors. This phenomenon is used in vacuum induction furnaces, where strong currents heat the metal until it melts. Since metals are heated in a vacuum, this makes it possible to obtain especially pure materials.
The most important law of electrical engineering is Ohm's law
Joule-Lenz law
Joule-Lenz law
In verbal formulation it sounds like this - The power of heat released per unit volume of the medium during the flow of electric current is proportional to the product of the electric current density by the value electric field
Where w- heat generation power per unit volume, - electric current density, - electric field strength, σ
- conductivity of the medium.
The law can also be formulated in integral form for the case of current flow in thin wires:
The amount of heat released per unit time in the section of the circuit under consideration is proportional to the product of the square of the current in this section and the resistance of the section
In mathematical form, this law looks like:
Where dQ- the amount of heat released over a period of time dt,I- current strength, R- resistance, Q- the total amount of heat released during the period of time from t1 before t2.
In the case of constant current and resistance:
Kirchhoff's laws
Kirchhoff's laws (or Kirchhoff's rules) are the relationships that are satisfied between currents and voltages in sections of any electrical circuit. Kirchhoff's rules allow you to calculate any electrical circuits of direct and quasi-stationary current. Have special meaning in electrical engineering because of its versatility, as it is suitable for solving any electrical problems. Application of Kirchhoff's rules to the circuit allows us to obtain the system linear equations relative to the currents, and accordingly, find the value of the currents on all branches of the circuit.
To formulate Kirchhoff's laws, nodes are distinguished in an electrical circuit - connection points of three or more conductors and contours - closed paths of conductors. In this case, each conductor can be included in several circuits.
In this case, the laws are formulated as follows.
First Law(ZTK, Kirchhoff's Law of Currents) states that the algebraic sum of currents in any node of any circuit is equal to zero (the values of the flowing currents are taken with the opposite sign):
In other words, as much current flows into a node, as much flows out of it. This law follows from the law of conservation of charge. If the chain contains p nodes, then it is described p − 1 current equations. This law may apply to others as well. physical phenomena(for example, water pipes), where there is a law of conservation of quantity and a flow of this quantity.
Second Law(ZNK, Kirchhoff's Stress Law) states that the algebraic sum of the voltage drops along any closed contour of the circuit is equal to the algebraic sum of the emf acting along the same contour. If there is no EMF in the circuit, then the total voltage drop is zero:
for constant voltages: 
For alternating voltages:
In other words, when going around the circuit along the circuit, the potential, changing, returns to its original value. If a circuit contains branches, of which the branches contain current sources in the amount of , then it is described by voltage equations. A special case of the second rule for a circuit consisting of one circuit is Ohm's law for this circuit.
Kirchhoff's laws are valid for linear and nonlinear circuits for any type of change in currents and voltages over time.
In this figure, for each conductor, the current flowing through it is indicated (the letter “I”) and the voltage between the nodes it connects (the letter “U”)
For example, for the circuit shown in the figure, in accordance with the first law, the following relationships are satisfied:
Note that for each node the positive direction must be chosen, for example here, currents flowing into a node are considered positive and currents flowing out are considered negative.
In accordance with the second law, the following relations are valid:
If the direction of the current coincides with the direction of bypassing the circuit (which is chosen arbitrarily), the voltage drop is considered positive, otherwise - negative.
Kirchhoff's laws, written for the nodes and circuits of a circuit, provide a complete system of linear equations that allows one to find all currents and voltages.
There is an opinion according to which “Kirchhoff’s Laws” should be called “Kirchhoff’s Rules”, because they do not reflect the fundamental essences of nature (and are not a generalization large quantity experimental data), but can be deduced from other provisions and assumptions.
LAW OF TOTAL CURRENT
LAW OF TOTAL CURRENT one of the fundamental laws electromagnetic field. Establishes the relationship between magnetic force and the amount of current passing through a surface. The total current is understood as the algebraic sum of currents penetrating a surface bounded by a closed loop.
The magnetizing force along a contour is equal to the total current passing through the surface bounded by this contour. In general, the field strength is various areas magnetic line may have different meanings, and then the magnetizing force will be equal to the sum of the magnetizing forces of each line.
Joule-Lenz law
Joule-Lenz law- a physical law that gives a quantitative estimate thermal action electric current. Discovered in 1840 independently by James Joule and Emilius Lenz.
In verbal formulation it sounds like this:
The power of heat released per unit volume of a medium during the flow of electric current is proportional to the product of the electric current density and the electric field value
Mathematically can be expressed in the following form:
Where w- power of heat release per unit volume, - electric current density, - electric field strength, σ - conductivity of the medium.
LAW OF ELECTROMAGNETIC INDUCTION, Faraday's law is a law that establishes the relationship between magnetic and electrical phenomena. The EMF of electromagnetic induction in a circuit is numerically equal and opposite in sign to the rate of change of magnetic flux through the surface bounded by this circuit. The magnitude of the EMF field depends on the rate of change of the magnetic flux.
FARADAY'S LAWS(named after the English physicist M. Faraday (1791-1867)) – the basic laws of electrolysis.
A relationship is established between the amount of electricity passing through an electrically conductive solution (electrolyte) and the amount of substance released at the electrodes.
When passed through an electrolyte direct current I within a second q = It, m = kIt.
Faraday's second law: the electrochemical equivalents of elements are directly proportional to their chemical equivalents.
Gimlet rule
Gimlet's rule(also, rule right hand) - a mnemonic rule for determining the direction of the angular velocity vector, characterizing the speed of rotation of the body, as well as the magnetic induction vector B or to determine the direction of the induction current.
Right hand rule
Right hand rule
Gimlet rule: "If the direction forward motion gimlet (screw) coincides with the direction of the current in the conductor, then the direction of rotation of the gimlet handle coincides with the direction of the magnetic induction vector.”
Determines the direction of induced current in a conductor moving in a magnetic field
Right hand rule: “If the palm of the right hand is positioned so that it includes power lines magnetic field, and direct the bent thumb along the movement of the conductor, then four extended fingers will indicate the direction of the induction current.”
For solenoid it is formulated as follows: “If you clasp the solenoid with the palm of your right hand so that four fingers are directed along the current in the turns, then the extended thumb will show the direction of the magnetic field lines inside the solenoid.”
Left hand rule
Left hand rule
If the charge is moving and the magnet is at rest, then the left-hand rule applies to determine the force: “If left hand positioned so that the magnetic field induction lines enter the palm perpendicular to it, and the four fingers are directed along the current (along the movement of a positively charged particle or against the movement of a negatively charged one), then the thumb set at 90° will show the direction of the acting Lorentz or Ampere force.”
Electricity has the ability to generate a magnetic field. In 1831, M. Faraday introduced the concept of electromagnetic induction. He was able to get in closed system conductors electricity, which appears when the magnetic flux changes. The formula of Faraday's law gave impetus to the development of electrodynamics.
History of development
After the proof of the law of electromagnetic induction by the English scientist M. Faraday, Russian scientists E. Lenz and B. Jacobi worked on the discovery. Thanks to their work, today the developed principle forms the basis for the functioning of many devices and mechanisms.
The main units in which Faraday's law of electromagnetic induction is applied are a motor, a transformer and many other devices.
Induction is the electromagnetic name given to the induction of electric current in a closed conducting system. This phenomenon becomes possible when physically moving through a magnetic field conductor system. Mechanical action entails the appearance of electricity. It is usually called induction. Before the discovery of Faraday's law, humanity did not know about other methods of creating electricity other than galvanization.
If a magnetic field is passed through a conductor, an induced emf will arise in it. It is also called electromotive force. With the help of this discovery it is possible to quantify the indicator.
Experimental proof
Carrying out his research, the English scientist found that induced current is obtained in one of two ways. In the first experiment, it appears when the frame moves in a magnetic field created by a stationary coil. The second method involves a fixed position of the frame. In this experiment, only the field of the coil changes when it moves or the current in it changes.
Faraday's experiments led the researcher to the conclusion that when an induction current is generated, it is provoked by an increase or decrease in the magnetic flux in the system. Also, Faraday's experiments made it possible to assert that the value of electricity obtained experimentally does not depend on the methodology by which the flow of magnetic induction was changed. The indicator is affected only by the speed of such change.
Quantitative expression
Faraday's law allows us to establish the quantitative value of the phenomenon of electromagnetic induction. It states that the EMF determined in the system changes its value in proportion to the speed of flow in the conductor. The formula will look like this:
A negative sign indicates that the EMF prevents changes from occurring within the circuit. To solve some problems, a negative sign is not used in the formula. In this case, the result is written as a module.
The system may include several turns. Their number is indicated by the Latin letter N. All elements of the circuit are penetrated by a single magnetic flux. The induced emf will be calculated as follows:
A clear example of the creation of electricity in a conductor is a coil through which a permanent magnet moves.
Work by E. Lenz
The direction of the induction current makes it possible to determine Lenz's rule. The brief formulation sounds quite simple. The current that appears when the field parameters of the conductor circuit change, thanks to its magnetic field, prevents such a change.
If a magnet is gradually introduced into the coil, the level of magnetic flux in it increases. According to Lenz's rule, the magnetic field will be in the opposite direction to the increase in the magnet's field. To understand this orientation, you need to look at the magnet from the north side. From here the gimlet will be screwed in towards the north pole. The current will move in a clockwise direction.
If a magnet is removed from the system, the magnetic flux in it will decrease. To establish the direction of the current, a gimlet is unscrewed. The rotation will be directed towards reverse side moving the dial clockwise.
Lenz's formulations become great importance for a system with a closed loop and no resistance. It is usually called the ideal contour. According to Lenz's rule, it is impossible to increase or decrease the magnetic flux in it.
The concept of self-induction
The generation of induction in an ideal system, which occurs when electricity in a conductor decreases or increases, is called self-induction.
Faraday's law for self-induction is expressed by equality when no other changes occur when electricity changes:
where e is the emf, L is the inductance of the closed coil, ΔI/Δt is the speed at which changes in current occur.
Inductance
The relationship that shows the proportionality between categories such as current strength in a conducting system and magnetic flux is called inductance. The indicator is influenced by the physical dimensions of the coil and the magnetic characteristics of the environment. The relationship is described by the formula:
Electricity moving in the circuit provokes the appearance of a magnetic field. It penetrates its own conductor and causes its own flow to appear through the circuit. Moreover, its own flow is proportional to the electricity that generates it:
The inductance value is also formed from Faraday's law.
Real estate system
The Lorentz force explains the occurrence of EMF when the system moves in a field with a constant value. Induction EMF also has the ability to arise when a stationary conducting system is in an alternating magnetic field. The Lorentz force in this example is not able to explain the appearance of the induced emf.
Maxwell proposed using a special equation for stationary conducting systems. It explains the occurrence of EMF in such systems. The main principle of the Faraday-Maxwell law is the fact that an alternating field creates an electric field in the space around it. It acts as a factor provoking the appearance of induction current in a fixed system. The movement of the vector (E) along stationary contours (L) is the EMF:
In the presence of a current of variable value, Faraday's laws are translated into Maxwell's equations. Moreover, they can be presented both in differential form and in the form of integrals.
Works in the field of electrolysis
When using Faraday's laws, the patterns that exist during electrolysis are described. This process involves the transformation of substances with a variety of different characteristics. This occurs when electricity moves through the electrolyte.
These patterns were proven by M. Faraday in 1834. The first statement states that the mass of the substance that is formed on the electrode changes according to the charge moved through the electrolyte.
The second statement states that the equivalents of components with different characteristics are proportional to the chemical equivalents of these components.
Both presented statements are combined into the combined Faraday law. It follows from it that the Faraday number will be equal to the electricity capable of releasing 1 mole of a substance on the electrolyte. It is calculated per unit of valence. It was according to the combined formula that the charge of an electron was calculated back in 1874.
The laws of electrolysis established by Faraday were tested at different meaning current, temperature, pressure, as well as with the simultaneous release of two or more substances. Electrolysis was also carried out in different melts and solvents. The electrolyte concentration also differed between experiments. At the same time, slight deviations from Faraday's law were sometimes observed. They are explained by the electronic conductivity of electrolytes, which is determined on a par with ionic conductivity.
The discoveries made by the English physicist M. Faraday made it possible to describe many phenomena. Its laws are the basis of modern electrodynamics. Various modern equipment operates on this principle.
What better way to read about the basics on a Monday evening? electrodynamics. That's right, you can find many things that are better. However, we still suggest you read this article. It doesn't take much time, but helpful information will remain in the subconscious. For example, during an exam, under stress, it will be possible to successfully extract Faraday’s law from the depths of memory. Since there are several Faraday laws, let us clarify that here we are talking about Faraday’s law of induction.
Electrodynamics– a branch of physics that studies the electromagnetic field in all its manifestations.
This includes the interaction of electric and magnetic fields, electric current, electromagnetic radiation, and the influence of the field on charged bodies.
Here we do not aim to consider all electrodynamics. God forbid! Let's take a better look at one of its basic laws, which is called Faraday's law of electromagnetic induction.
History and definition
Faraday, in parallel with Henry, discovered the phenomenon of electromagnetic induction in 1831. True, I managed to publish the results earlier. Faraday's law is widely used in technology, in electric motors, transformers, generators and chokes. What is the essence of Faraday's law for electromagnetic induction, simply put? Here's the thing!
When the magnetic flux changes through a closed conducting loop, an electric current arises in the loop. That is, if we twist a frame out of wire and place it in a changing magnetic field (take a magnet and twist it around the frame), current will flow through the frame!
Faraday called this current induction, and the phenomenon itself was dubbed electromagnetic induction.
Electromagnetic induction– the occurrence of an electric current in a closed circuit when the magnetic flux passing through the circuit changes.
The formulation of the basic law of electrodynamics - Faraday's law of electromagnetic induction, looks and sounds as follows:
EMF, arising in the circuit, is proportional to the rate of change of magnetic flux F through the circuit.
Where does the minus come from in the formula, you ask? To explain the minus sign in this formula there is a special Lenz's rule. It says that the minus sign in in this case, indicates the direction of the emerging EMF. The fact is that the magnetic field created by the induction current is directed in such a way that it prevents the change in the magnetic flux that caused the induction current.
Examples of problem solving
That seems to be all. The significance of Faraday's law is fundamental, because the basis of almost the entire electrical industry is built on the use of this law. To help you understand faster, let’s look at an example of solving a problem using Faraday’s law.
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