Ohm's law for electromagnetic induction. The phenomenon of electromagnetic induction. Magnetic flux. Law of electromagnetic induction. Lenz's rule

In 1831, the world first learned about the concept electromagnetic induction. It was then that Michael Faraday discovered this phenomenon, which ultimately became the most important discovery in electrodynamics.

History of development and experiments of Faraday

Before mid-19th centuries, it was believed that the electric and magnetic fields have no connection, and the nature of their existence is different. But M. Faraday was confident in the unified nature of these fields and their properties. The phenomenon of electromagnetic induction, discovered by him, subsequently became the foundation for the design of generators of all power plants. Thanks to this discovery, humanity's knowledge of electromagnetism has made great strides forward.

Faraday performed the following experiment: he closed a circuit in coil I and the magnetic field around it increased. Further, the induction lines of this magnetic field crossed coil II, in which an induced current arose.

Rice. 1. Scheme of Faraday's experiment

In fact, simultaneously with Faraday, but independently of him, another scientist, Joseph Henry, discovered this phenomenon. However, Faraday published his research earlier. Thus, the author of the law of electromagnetic induction was Michael Faraday.

No matter how many experiments Faraday conducted, one condition remained unchanged: for the formation of an induction current, it is important to change the magnetic flux penetrating a closed conducting circuit (coil).

Faraday's law

The phenomenon of electromagnetic induction is determined by the occurrence electric current in a closed electrically conducting circuit when the magnetic flux changes through the area of this circuit.

Faraday's basic law is that electromotive force (EMF) is directly proportional to the rate of change of magnetic flux.

The formula for Faraday's law of electromagnetic induction is as follows:

Rice. 2. Formula for the law of electromagnetic induction

And if the formula itself, based on the above explanations, does not raise questions, then the “-” sign may raise doubts. It turns out that there is a rule by Lenz, a Russian scientist who conducted his research based on Faraday’s postulates. According to Lenz, the “-” sign indicates the direction of the emerging EMF, i.e. the induced current is directed in such a way that the magnetic flux it creates, through the area bounded by the circuit, tends to oppose the change in flux that the current causes.

Faraday-Maxwell law

In 1873, J.C. Maxwell presented the theory in a new way electromagnetic field. The equations he derived formed the basis of modern radio engineering and electrical engineering. They are expressed as follows:

Edl = -dФ/dt– electromotive force equation
Hdl = -dN/dt– equation of magnetomotive force.

Where E– electric field strength in the area dl; H– magnetic field strength in the area dl; N– flow of electrical induction, t- time.

The symmetrical nature of these equations establishes a connection between electrical and magnetic phenomena, as well as magnetic and electrical. the physical meaning that defines these equations can be expressed by the following provisions:

If electric field changes, then this change is always accompanied by a magnetic field.
if the magnetic field changes, then this change is always accompanied by an electric field.

Rice. 3. Emergence of a vortex magnetic field

Maxwell also established that the propagation of the electromagnetic field is equal to the speed of propagation of light.

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Today we will reveal such a physics phenomenon as the “law of electromagnetic induction”. We will tell you why Faraday conducted the experiments, give the formula and explain the importance of the phenomenon for everyday life.

Ancient Gods and Physics

Ancient people worshiped the unknown. And now man is afraid of the abyss of the sea and the depths of space. But science can explain why. Submarines are documenting the incredible life of the oceans at depths of more than a kilometer, and space telescopes are studying objects that existed only a few million years after the big bang.

But then people deified everything that fascinated and worried them:

Sunrise;
awakening of plants in spring;
rain;
birth and death.

In every object and phenomenon lived unknown forces that ruled the world. Until now, children tend to humanize furniture and toys. Left without adult supervision, they fantasize: a blanket will hug you, a stool will fit, a window will open on its own.

Perhaps the first evolutionary step of humanity was the ability to maintain a fire. Anthropologists suggest that the earliest fires were lit by a tree struck by lightning.

Thus, electricity has played a huge role in the life of mankind. The first lightning gave impetus to the development of culture, the basic law of electromagnetic induction led humanity to the modern state.

From vinegar to a nuclear reactor

Strange ceramic vessels were found in the Cheops pyramid: the neck was sealed with wax, and a metal cylinder was hidden in the depths. Residues of vinegar or sour wine. Scientists have come to a sensational conclusion: this artifact is a battery, a source of electricity.

But until 1600, no one undertook to study this phenomenon. Before moving electrons, the nature of static electricity was studied. The ancient Greeks knew that amber produces shocks when rubbed against fur. The color of this stone reminded them of the light of the star Electra from the Pleiades. And the name of the mineral became, in turn, a reason to christen a physical phenomenon.

The first primitive direct current source was built in 1800

Naturally, as soon as a sufficiently powerful capacitor appeared, scientists began to study the properties of the conductor connected to it. In 1820, the Danish scientist Hans Christian Oersted discovered that the magnetic needle deviates near a conductor connected to the network. This fact gave impetus to the discovery of the law of electromagnetic induction by Faraday (the formula will be given below), which allowed humanity to produce electricity from water, wind and nuclear fuel.

Primitive but modern

The physical basis for Max Faraday's experiments was laid by Oersted. If a switched-on conductor affects a magnet, then the reverse is also true: the magnetized conductor must cause a current.

The structure of the experiment, which helped to derive the law of electromagnetic induction (we will consider EMF as a concept a little later), was very simple. The wire wound into a spring was connected to a device that records the current. The scientist brought a large magnet to the coils. While the magnet moved next to the circuit, the device recorded the flow of electrons.

Since then, the technology has improved, but the basic principle of creating electricity at huge stations is still the same: a moving magnet excites a current in a conductor wound by a spring.

Development of the idea

The very first experiment convinced Faraday that electric and magnetic fields are interconnected. But it was necessary to find out exactly how. Does a magnetic field also arise around a current-carrying conductor, or are they simply capable of influencing each other? Therefore, the scientist went further. He wound one wire, supplied a current to it, and pushed this coil into another spring. And I also received electricity. This experiment proved that moving electrons create not only an electric, but also a magnetic field. Later, scientists figured out how they are located in space relative to each other. The electromagnetic field is also the reason why light exists.

By experimenting with different options for the interaction of live conductors, Faraday found out that current is transmitted best if both the first and second coils are wound on one common metal core. The formula expressing the law of electromagnetic induction was derived precisely on this device.

Formula and its components

Now that the history of the study of electricity has been brought to Faraday’s experiment, it’s time to write the formula:

Let's decipher:

ε is electromotive force (abbreviated emf). Depending on the value of ε, electrons move more intensely or weakly in the conductor. The EMF is affected by the power of the source, and it is influenced by the strength of the electromagnetic field.

Φ is the magnitude of the magnetic flux that is currently passing through a given area. Faraday rolled the wire into a spring because he needed a certain space through which the conductor would pass. Of course, it would be possible to make a very thick conductor, but this would be expensive. The scientist chose the shape of a circle because this flat figure has the greatest ratio of surface area to surface length. This is the most energy efficient form. Therefore, water droplets on a flat surface become round. In addition, a spring with a round cross-section is much easier to obtain: you just need to wind the wire around some round object.

t is the time during which the flow passed through the circuit.

The prefix d in the formula for the law of electromagnetic induction means that the quantity is differential. That is, a small magnetic flux must be differentiated over short periods of time in order to obtain the final result. This mathematical operation requires some preparation from people. To better understand the formula, we strongly encourage the reader to review differentiation and integration.

Consequences from the law

Immediately after the discovery, they began to study the phenomenon of electromagnetic induction. Lenz's law, for example, was derived experimentally by a Russian scientist. It was this rule that added a minus to the final formula.

It looks like this: the direction of the induction current is not random; the flow of electrons in the second winding tends to reduce the effect of the current in the first winding. That is, the occurrence of electromagnetic induction is actually the resistance of the second spring to interference in “personal life”.

Lenz's rule has another consequence.

if the current in the first coil increases, then the current of the second spring will also tend to increase;
if the current in the inducing winding drops, then the current in the second winding will also decrease.

According to this rule, the conductor in which the induced current occurs actually tends to compensate for the effect of the changing magnetic flux.

Grain and donkey

People have long sought to use the simplest mechanisms for their own benefit. Grinding flour is a complicated matter. Some tribes grind the grain by hand: placing the wheat on one stone, covering it with another flat and round stone, and turning the millstone. But if you need to grind flour for an entire village, then you can’t do it with muscular labor alone. At first, people thought of tying a draft animal to a millstone. The donkey pulled the rope - the stone rotated. Then people probably thought: “The river flows all the time, it pushes all sorts of things downstream. Why don’t we use it for good?” This is how water mills appeared.

Wheel, water, wind

Of course, the first engineers who built these structures knew nothing about the force of gravity, due to which water always tends downward, or about the force of friction or surface tension. But they saw: if you put a wheel with blades in diameter in a stream or river, it will not only rotate, but will also be able to do useful work.

But this mechanism was also limited: not everywhere there is running water with sufficient current strength. So people moved on. They built mills that were powered by the wind.

Coal, fuel oil, gasoline

When scientists understood the principle of exciting electricity, a technical task was set: to obtain it in industrial scale. At that time (mid-nineteenth century) the world was gripped by machine fever. They tried to entrust all the difficult work to the expanding steam.

But then they could only heat large volumes of water with fossil fuels - coal and fuel oil. Therefore, those that were rich in ancient carbons immediately attracted the attention of investors and workers. And the redistribution of people led to the industrial revolution.

Holland and Texas

However, this state of affairs has a bad impact on the environment. And scientists wondered: how to get energy without destroying nature? The well-forgotten old thing came to the rescue. The mill used torque to directly perform rough mechanical work. Hydroelectric turbines rotate magnets.

Currently, the cleanest electricity comes from wind energy. The engineers who built the first generators in Texas relied on experience from the windmills of Holland.

The emergence of the electromotive force of induction was the most important discovery in the field of physics. It was fundamental for the development of the technical application of this phenomenon.

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Michael Faraday

Story

In the 20s of the 19th century, the Dane Oersted observed the deflection of a magnetic needle when it was placed next to a conductor through which an electric current flowed.

Michael Faraday wanted to explore this phenomenon more closely. With great persistence he pursued his goal of converting magnetism into electricity.

Faraday's first experiments brought him a number of failures, since he initially believed that a significant direct current in one circuit could generate a current in a nearby circuit, provided there was no electrical connection between them.

The researcher modified the experiments, and in 1831 they were crowned with success. Faraday's experiments began with winding copper wire around the paper tube and connecting its ends to the galvanometer. The scientist then placed a magnet inside the coil and noticed that the galvanometer needle gave an instantaneous deflection, indicating that a current had been induced in the coil. After removing the magnet, the arrow deflected in the opposite direction. Soon, in the course of other experiments, he noticed that at the moment of applying and removing voltage from one coil, a current appeared in a nearby coil. Both coils had a common magnetic circuit.

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Faraday's experiments

Faraday's numerous experiments with other coils and magnets were continued, and the researcher found that the strength of the induced current depends on:

number of turns in the coil;
magnet strength;
the speed at which the magnet was immersed in the coil.

The term electromagnetic induction (EMF) refers to the phenomenon that an emf is generated in a conductor by an alternating external magnetic field.

Formulation of the law of electromagnetic induction

Verbal formulation of the law of electromagnetic induction: the induced electromotive force in any closed circuit is equal to the negative time rate of change of the magnetic flux enclosed in the circuit.

This definition is expressed mathematically by the formula:

E = - ΔΦ/ Δt,

where Ф = B x S, with magnetic flux density B and area S, which is crossed perpendicularly by the magnetic flux.

Additional Information. There are two different approaches to induction. The first explains induction using the Lorentz force and its action on a moving electric charge. However, in certain situations, such as magnetic shielding or unipolar induction, problems may arise in understanding the physical process. The second theory uses the methods of field theory and explains the process of induction using variable magnetic fluxes and the associated densities of these fluxes.

The physical meaning of the law of electromagnetic induction is formulated in three provisions:

A change in the external MF in a wire coil induces a voltage in it. When the conducting electrical circuit is closed, the induced current begins to circulate through the conductor;
The magnitude of the induced voltage corresponds to the rate of change of the magnetic flux associated with the coil;
The direction of the induced emf is always opposite to the cause that caused it.

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Law of Electromagnetic Induction

Important! The formula for the law of electromagnetic induction applies in the general case. There is no known form of induction that cannot be explained by a change in magnetic flux.

Induction emf in a conductor

To calculate the induction voltage in a conductor that moves in the MF, another formula is used:

E = - B x l x v x sin α, where:

B – induction;
l is the length of the conductor;
v – speed of its movement;
α is the angle formed by the direction of movement and the vector direction of magnetic induction.

Important! A method of determining where the induction current created in a conductor is directed: by placing right hand palm perpendicular to the entry of the power lines of the MP and, retracted thumb indicating the direction of movement of the conductor, we recognize the direction of the current in it by straightening four fingers.

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Right hand rule

Laws of electrolysis

Faraday's historical experiments in 1833 were also related to electrolysis. He took a test tube with two platinum electrodes immersed in dissolved tin chloride heated with an alcohol lamp. Chlorine was released on the positive electrode, and tin was released on the negative electrode. He then weighed the released tin.

In other experiments, the researcher connected containers with different electrolytes in series and measured the amount of substance deposited.

Based on these experiments, two laws of electrolysis are formulated:

The first of them: the mass of the substance released at the electrode is directly proportional to the amount of electricity passed through the electrolyte. Mathematically it is written like this:

m = K x q, where K is a constant of proportionality, called the electrochemical equivalent.

Formulate its definition as the mass of a substance in g released at the electrode when a current of 1 A passes in 1 s or when 1 C of electricity passes;

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First law of electrolysis

Faraday's Second Law states that if the same amount of electricity is passed through different electrolytes, then the amount of substances released at the corresponding electrodes is directly proportional to their chemical equivalent (the chemical equivalent of a metal is obtained by dividing its molar mass by its valency - M/z).

For the second law of electrolysis, the following notation is used:

HereF – Faraday's constant, which is determined by the charge of 1 mole of electrons:

F = Na (Avogadro's number) x e (elementary electric charge) = 96485 C/mol.

Write another expression for Faraday's second law:

m1/m2 = K1/K2.

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Second Law of Electrolysis

For example, if you take two electrolytic containers connected in series containing a solution of AgNO 3 and CuSO 4 and pass the same amount of electricity through them, then the ratio of the mass of deposited copper on the cathode of one container to the mass of deposited silver on the cathode of the other container will be equal to the ratio of their chemical equivalents. For copper it is Rate this article:

Electricity has the ability to generate a magnetic field. In 1831, M. Faraday introduced the concept of electromagnetic induction. He was able to obtain electricity in a closed system of conductors, which appeared when the magnetic flux changed. 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 produces 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 negative sign is not included 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 in the opposite direction of clockwise movement on the dial.

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 magnetic characteristics 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 valency. It was by using 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.

Fedun V.I. Lecture notes on physics Electromagnetics

Lecture 26.

Electromagnetic induction. Faraday's discovery .

In 1831, M. Faraday made one of the most important fundamental discoveries in electrodynamics - the phenomenon was discovered electromagnetic induction .

In a closed conducting circuit, when the magnetic flux (vector flux) covered by this circuit changes, an electric current arises.

This current is called induction .

The appearance of induction current means that when the magnetic field changes

	flow in the circuit occurs e.m.f. induction (work on transferring a unit charge along a closed circuit). Note that the value completely independent of how the magnetic flux changes , and is determined only by the rate of its change, i.e. size . Changing the sign of the derivative leads to a change in sign e.m.f. induction .
Figure 26.1.

Faraday discovered that an induced current can be produced in two different ways, which can be conveniently explained by means of a diagram.

1st method: moving the frame in the magnetic field of a stationary coil (see Fig. 26.1).

2nd method: changing the magnetic field , created by the coil , due to its movement or due to changes in current strength in it (or both together). Frame while motionless.

In both these cases the galvanometer will indicate the presence of induction current in the frame .

The direction of the induction current and, accordingly, the sign of the emf. induction are determined by Lenz's rule.

Lenz's rule.

Induction current is always directed in such a way as to counteract the cause that causes it. .

Lenz's rule expresses an important physical property - the desire of a system to counteract changes in its state. This property is called electromagnetic inertia .

Law of electromagnetic induction (Faraday's law).

Whatever the reason for the change in the magnetic flux covered by a closed conducting circuit, arising in the emf circuit. induction is given by the formula

The nature of electromagnetic induction.

In order to clarify the physical reasons that lead to the emergence of emf. By induction, we consider two cases successively.

1. The circuit moves in a constant magnetic field.

act force

The electromotive force created by this field is called electromotive force of induction . In our case

The minus sign is placed here because the third-party field directed against the positive bypass of the circuit determined by the right screw rule. Work is the rate of increase in the contour area (increase in area per unit time), therefore

Where
- increment of magnetic flux through the circuit.

The obtained result can be generalized to the case of arbitrary orientation of the magnetic field induction vector relative to the contour plane and to any contour moving (and/or deforming) in an arbitrary manner in a constant non-uniform external magnetic field.

So, the excitation of the emf. induction when the circuit moves in a constant magnetic field is explained by the action of the magnetic component of the Lorentz force, proportional to
, which occurs when the conductor moves.

2. The circuit is at rest in an alternating magnetic field.

The experimentally observed occurrence of an induction current indicates that in this case, extraneous forces appear in the circuit, which are now associated with a time-varying magnetic field. What is their nature? The answer to this fundamental question was given by Maxwell.

Since the conductor is at rest, the speed of the ordered movement of electric charges
and therefore a magnetic force proportional to
, is also equal to zero and can no longer set charges in motion. However, in addition to the magnetic force, the only force that can act on an electric charge is the electric field, equal to . Therefore, it remains to conclude that induced current is caused by the electric field , arising when the external magnetic field changes over time. It is this electric field that is responsible for the appearance of emf. induction in a stationary circuit. According to Maxwell, a time-varying magnetic field generates an electric field in the surrounding space. The occurrence of an electric field is not associated with the presence of a conducting circuit, which only makes it possible to detect the existence of this field by the appearance of an induction current in it.

Formulation law of electromagnetic induction , given by Maxwell, is one of the most important generalizations of electrodynamics.

Any change in the magnetic field over time excites an electric field in the surrounding space .

The mathematical formulation of the law of electromagnetic induction in Maxwell’s understanding is:

Circulation of the tension vector of this field along any fixed closed contour is determined by the expression

Where - magnetic flux penetrating the circuit .

The partial derivative sign used to indicate the rate of change of magnetic flux indicates that the circuit is stationary.

Flow vector through a surface bounded by a contour , is equal
, therefore, the expression of the law of electromagnetic induction can be rewritten as follows:

This is one of the equations in Maxwell's system of equations.

The fact that the circulation of the electric field excited by a time-varying magnetic field is nonzero means that the electric field in question not potential.It, like the magnetic field, is vortex.

In general, the electric field can be represented by the vector sum of the potential (field of static electric charges, the circulation of which is zero) and vortex (due to a time-varying magnetic field) electric fields.

At the basis of the phenomena we have considered, which explain the law of electromagnetic induction, there is no visible general principle that allows us to establish their commonality physical nature. Therefore, these phenomena should be considered as independent, and the law of electromagnetic induction - as the result of their joint action. All the more surprising is the fact that the emf. Induction in a circuit is always equal to the rate of change of magnetic flux through the circuit. In cases where the field also changes and the location or configuration of the circuit in the magnetic field, emf. induction should be calculated using the formula

The expression on the right side of this equality represents the total derivative of the magnetic flux with respect to time: the first term is associated with the change in the magnetic field over time, the second with the movement of the circuit.

We can say that in all cases the induced current is caused by the total Lorentz force

Which part of the induced current is caused by the electric and which magnetic component of the Lorentz force depends on choice of reference system.

On the work of the Lorentz and Ampere forces.

From the very definition of work it follows that a force acting in a magnetic field on an electric charge and perpendicular to its speed cannot do work. However, when a conductor with current moves, carrying charges along with it, the Ampere force still does work. Electric motors are a clear proof of this.

This contradiction disappears if we take into account that the movement of a conductor in a magnetic field is inevitably accompanied by the phenomenon of electromagnetic induction. Therefore, along with the Ampere force, work on electric charges is also performed by the electromotive force of induction that arises in the conductor. Thus, the total work of the magnetic field forces consists of the mechanical work caused by the Ampere force and the work of the emf induced by the movement of the conductor. Both jobs are equal in magnitude and opposite in sign, so their sum is zero. Indeed, the work done by the ampere force during elementary movement of a conductor with current in a magnetic field is equal to
, during the same time emf. induction does work

then full work
.

Ampere forces do work not due to the energy of the external magnetic field, which can remain constant, but due to the emf source that maintains the current in the circuit.