The phenomenon of self-induction is the inductance of the energy of a magnetic field. Vortex electric field

An electric current passing through a circuit creates a magnetic field around it. The magnetic flux Φ through the circuit of this conductor (it is called own magnetic flux) is proportional to the induction modulus B of the magnetic field inside the circuit \(\left(\Phi \sim B \right)\), and the magnetic field induction, in turn, is proportional to the current strength in the circuit \(\left(B\sim I \right)\ ).

Thus, the intrinsic magnetic flux is directly proportional to the current in the circuit \(\left(\Phi \sim I \right)\). This dependence can be represented mathematically as follows:

\(\Phi = L \cdot I,\)

Where L is the coefficient of proportionality, which is called loop inductance.

• Loop inductance- a scalar physical quantity numerically equal to the ratio of its own magnetic flux penetrating the circuit to the current strength in it:

\(~L = \dfrac(\Phi)(I).\)

The SI unit for inductance is the henry (H):

1 H = 1 Wb / (1 A).

• The inductance of the circuit is 1 H if, with a direct current of 1 A, the magnetic flux through the circuit is 1 Wb.

The inductance of the circuit depends on the size and shape of the circuit, on the magnetic properties of the medium in which the circuit is located, but does not depend on the strength of the current in the conductor. So, the inductance of the solenoid can be calculated by the formula

\(~L = \mu \cdot \mu_0 \cdot N^2 \cdot \dfrac(S)(l),\)

Where μ is the magnetic permeability of the core, μ 0 is the magnetic constant, N- number of turns of the solenoid, S- coil area, l is the length of the solenoid.

With the shape and dimensions of the fixed circuit unchanged, the intrinsic magnetic flux through this circuit can only change when the current strength in it changes, i.e.

\(\Delta \Phi =L \cdot \Delta I.\) (1)

The phenomenon of self-induction

If a direct current passes in the circuit, then there is a constant magnetic field around the circuit, and the own magnetic flux penetrating the circuit does not change over time.

If the current passing in the circuit changes with time, then the correspondingly changing own magnetic flux, and, according to the law of electromagnetic induction, creates an EMF in the circuit.

• The occurrence of an EMF of induction in a circuit, which is caused by a change in the current strength in this circuit, is called phenomenon of self-induction. Self-induction was discovered by the American physicist J. Henry in 1832.

EMF appearing at the same time - EMF of self-induction E si . EMF of self-induction creates a self-induction current in the circuit I si.

The direction of the self-induction current is determined by Lenz's rule: the self-induction current is always directed in such a way that it counteracts the change in the main current. If the main current increases, then the self-induction current is directed against the direction of the main current, if it decreases, then the directions of the main current and the self-induction current coincide.

Using the law of electromagnetic induction for a circuit with an inductance L and equation (1), we obtain the expression for the EMF of self-induction:

\(E_(si) =-\dfrac(\Delta \Phi )(\Delta t)=-L\cdot \dfrac(\Delta I)(\Delta t).\)

• The self-induction emf is directly proportional to the rate of change in the current strength in the circuit, taken with the opposite sign. This formula can only be applied with a uniform change in current strength. With increasing current (Δ I> 0), negative EMF (E si< 0), т.е. индукционный ток направлен в противоположную сторону тока источника. При уменьшении тока (ΔI < 0), ЭДС положительная (E si >0), i.e. the induction current is directed in the same direction as the source current.

From the resulting formula it follows that

\(L=-E_(si) \cdot \dfrac(\Delta t)(\Delta I).\)

• Inductance- this is a physical quantity numerically equal to the EMF of self-induction that occurs in the circuit when the current strength changes by 1 A in 1 s.

The phenomenon of self-induction can be observed in simple experiments. Figure 1 shows a diagram of the parallel connection of two identical lamps. One of them is connected to the source through a resistor R, and the other in series with the coil L. When the key is closed, the first lamp flashes almost immediately, and the second - with a noticeable delay. This is explained by the fact that in the section of the circuit with a lamp 1 there is no inductance, so there will be no self-induction current, and the current in this lamp almost instantly reaches its maximum value. In the area with a lamp 2 when the current in the circuit increases (from zero to maximum), a self-induction current appears I si, which prevents the rapid increase in current in the lamp. Figure 2 shows an approximate graph of the change in current in the lamp 2 when the circuit is closed.

When the key is opened, the current in the lamp 2 will also decay slowly (Fig. 3, a). If the inductance of the coil is large enough, then immediately after opening the key, even a slight increase in current is possible (the lamp 2 flashes stronger), and only then the current begins to decrease (Fig. 3, b).

Rice. 3

The phenomenon of self-induction creates a spark at the point where the circuit opens. If there are powerful electromagnets in the circuit, then the spark can go into an arc discharge and ruin the switch. To open such circuits at power plants, special switches are used.

Magnetic field energy

The energy of the magnetic field of the inductor circuit L with current I

\(~W_m = \dfrac(L \cdot I^2)(2).\)

Since \(~\Phi = L \cdot I\), then the energy of the magnetic field of the current (coil) can be calculated knowing any two of the three values ​​( Φ, L, I):

\(~W_m = \dfrac(L \cdot I^2)(2) = \dfrac(\Phi \cdot I)(2)=\dfrac(\Phi^2)(2L).\)

The energy of a magnetic field contained in a unit volume of space occupied by the field is called volumetric energy density magnetic field:

\(\omega_m = \dfrac(W_m)(V).\)

*Derivation of the formula

1 conclusion.

Let's connect a conducting circuit with an inductance to the current source L. Let the current increase uniformly from zero to a certain value in a short time interval Δt I (Δ I = I). EMF of self-induction will be equal to

\(E_(si) =-L \cdot \dfrac(\Delta I)(\Delta t) = -L \cdot \dfrac(I)(\Delta t).\)

For a given period of time Δ t charge is transferred through the circuit

\(\Delta q = \left\langle I \right \rangle \cdot \Delta t,\)

where \(\left \langle I \right \rangle = \dfrac(I)(2)\) is the average value of the current over time Δ t with a uniform increase from zero to I.

Current in a circuit with inductance L reaches its value not instantly, but during some finite time interval Δ t. In this case, an EMF of self-induction E si arises in the circuit, which prevents the increase in current strength. Consequently, the current source, when closed, does work against the EMF of self-induction, i.e.

\(A = -E_(si) \cdot \Delta q.\)

The work expended by the source on creating a current in the circuit (excluding heat losses) determines the energy of the magnetic field stored by the current-carrying circuit. So

\(W_m = A = L \cdot \dfrac(I)(\Delta t) \cdot \dfrac(I)(2) \cdot \Delta t = \dfrac(L \cdot I^2)(2).\ )

2 conclusion.

If the magnetic field is created by the current passing in the solenoid, then the inductance and the magnetic field induction modulus of the coil are equal

\(~L = \mu \cdot \mu_0 \cdot \dfrac (N^2)(l) \cdot S, \,\,\, ~B = \dfrac (\mu \cdot \mu_0 \cdot N \cdot I)(l)\)

\(I = \dfrac (B \cdot l)(\mu \cdot \mu_0 \cdot N).\)

Substituting the obtained expressions into the formula for the magnetic field energy, we obtain

\(~W_m = \dfrac (1)(2) \cdot \mu \cdot \mu_0 \cdot \dfrac (N^2)(l) \cdot S \cdot \dfrac (B^2 \cdot l^2) ((\mu \cdot \mu_0)^2 \cdot N^2) = \dfrac (1)(2) \cdot \dfrac (B^2)(\mu \cdot \mu_0) \cdot S \cdot l. \)

Since \(~S \cdot l = V\) is the volume of the coil, the energy density of the magnetic field is

\(\omega_m = \dfrac (B^2)(2\mu \cdot \mu_0),\)

where AT- modulus of magnetic field induction, μ - magnetic permeability of the medium, μ 0 - magnetic constant.

Literature

1. Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 351-355, 432-434.
2. Zhilko V.V. Physics: textbook. allowance for the 11th grade. general education institutions with Russian. lang. Education with a 12-year term of study (basic and advanced levels) / V.V. Zhilko, L.G. Markovich. - Mn.: Nar. asveta, 2008. - S. 183-188.
3. Myakishev, G.Ya. Physics: Electrodynamics. 10-11 cells. : studies. for in-depth study of physics / G.Ya. Myakishev, A.3. Sinyakov, V.A. Slobodskov. - M.: Bustard, 2005. - S. 417-424.

« Physics - Grade 11 "

Self-induction.

If an alternating current flows through the coil, then:
the magnetic flux penetrating the coil changes with time,
and an induction emf occurs in the coil.
This phenomenon is called self-induction.

According to Lenz's rule, as the current increases, the intensity of the eddy electric field is directed against the current, i.e. the vortex field prevents the current from rising.
When the current decreases, the intensity of the vortex electric field and the current are directed in the same way, i.e. the vortex field maintains the current.

The phenomenon of self-induction is similar to the phenomenon of inertia in mechanics.

In mechanics:
Inertia leads to the fact that under the action of force the body acquires a certain speed gradually.
The body cannot be instantly slowed down, no matter how great the braking force.

In electrodynamics:
When the circuit is closed due to self-induction, the current strength increases gradually.
When the circuit is opened, self-induction maintains the current for some time, despite the resistance of the circuit.

The phenomenon of self-induction plays a very important role in electrical and radio engineering.

The energy of the magnetic field current

According to the law of conservation of energy magnetic field energy, created by the current, is equal to the energy that the current source (for example, a galvanic cell) must expend to create the current.
When the circuit is opened, this energy is converted into other forms of energy.

When closing circuit current increases.
A vortex electric field appears in the conductor, acting against the electric field created by the current source.
In order for the current to become equal to I, the current source must do work against the forces of the vortex field.
This work goes to increase the energy of the magnetic field of the current.

When opening circuit current disappears.
The vortex field does positive work.
The energy stored by the current is released.
This is revealed, for example, by a powerful spark that occurs when a circuit with a large inductance is opened.

The energy of the magnetic field created by the current passing through the section of the circuit with inductance L is determined by the formula

The magnetic field created by an electric current has an energy that is directly proportional to the square of the current strength.

The energy density of the magnetic field (i.e., the energy per unit volume) is proportional to the square of the magnetic induction: w m ~ B 2,
similarly to how the energy density of the electric field is proportional to the square of the electric field w e ~ E 2 .

STATE AUTONOMOUS PROFESSIONAL EDUCATIONAL INSTITUTION

NOVOSIBIRSK REGION

"BARABINSKY MEDICAL COLLEGE"

Considered at the meeting

CMK OGSED

Protocol No. ___________

dated ____________ 2018

CMC Chairman

Khritankova N. Yu.

______________________

(signature)

METHODOLOGICAL DEVELOPMENT

COMBINED LESSON FOR THE TEACHER

Specialty 34.02.01 Nursing (with basic training)

Discipline: "Physics"

Section 3 Electrodynamics. Vibrations and waves. Optics

Developer - teacher Vashurina T.V.

Methodical sheet
Approximate lesson timeline
Raw material
Annex No. 1 Control of knowledge on the previous topic
Appendix No. 2 Tasks for consolidating and systematizing new knowledge
Appendix No. 3 Tasks for preliminary control of knowledge
Appendix No. 4 Control material
Task for independent extracurricular work of students
List of sources used

Extract from the work program of the discipline "Physics"

for the specialty 34.02.01 Nursing (with basic training)

Name of sections and topics		Watch Volume
Topic 3.14 Self-induction. Inductance. EMF of self-induction. The energy of the magnetic field.
	Concepts: self-induction, inductance. Magnetic field induction. Formula for calculating the energy of the magnetic field. Practicing the ability to confidently use physical terminology and symbols.
	Laboratory work
	Practical lesson
	Test
	Independent work of students: Work with the electronic supplement to the textbook "Physics 10"; Working with a textbook, doing exercises; Work with lecture notes.

METHODOLOGICAL SHEET

Lesson type: combined lesson.

Class type: conversation, explanation with demonstration of visual aids, problem solving.

Duration: 90 minutes.

LESSON OBJECTIVES

Learning goals: to form ideas about the role and place of physics in the modern scientific picture of the world; understanding the physical essence of phenomena observed in the Universe through the study of the concept of self-induction, inductance, self-induction EMF, magnetic field energy; to promote the formation of the ability to master fundamental physical concepts, confidently use physical terminology and symbols. To contribute to the formation of the ability to organize one's own activities, to choose typical methods and ways of performing exercises (OK 2).

Development goals: to develop interest in the future profession, understanding the essence and social significance (OK 1), to promote the formation of the ability to solve physical problems.

Educational goals: promote the development of communication skills; create conditions for the development of the speed of perception and processing of information, culture of speech; to form the ability to work in a team and team (OK 6).

Teaching methods: explanatory and illustrative using information technology, reproductive.

Location: college auditorium.

MOTIVATION

Topic 3.14 “Self-induction. Inductance. EMF of self-induction. Energy of the Magnetic Field" is included in the program for the discipline "Physics" and occupies a significant place, because the knowledge gained in the study of this topic is necessary for the study of many topics both within the framework of the program in physics and in the study of related disciplines (chemistry, mathematics). The danger of working with electrical appliances lies in the fact that the current, the magnetic field of the current and the voltage do not have external signs that would allow a person with the help of the senses (vision, hearing, smell) to detect the impending danger and take precautions.

There are 2 class hours for this lesson. During the combined lesson, knowledge is updated in the form of an oral survey in order to check the residual knowledge that is necessary when studying new material; direct study of new material; primary consolidation of new material by solving problems on this topic. Control of the level of assimilation of new material is carried out in the form of testing students. Every educated person needs to continuously replenish their knowledge in the field of physics, develop interest in their future profession, understand the essence and social significance (GC 1), learn how to organize their activities, be able to choose methods and ways of performing tasks and further evaluate their quality (GC 2), and it is also necessary for the future medical worker to learn how to work in a team and team (OK6).

EXAMPLE TIMELINE OF A COMBINED LESSON

	Stage name	Time	Purpose of the stage	Activity		Equipment
				teacher	students
	Organizational stage		Organization of the beginning of classes, the formation of the ability to organize their own activities (OK 2).	Greetings. Checking the readiness of the audience. Marks absent students in the journal.	The headman calls the absent students. Students adjust the appearance, prepare jobs.	Journal, notebooks for abstracts.
	Control of knowledge on the previous topic		Evaluation of the level of knowledge formation on the previous topic. Development of competent speech of students, self-control of their knowledge.	Instructs and conducts knowledge control.	Repeat homework, answer orally.	Questions for oral survey. Appendix 1.
	Motivational stage and goal setting		Development of interest in the future profession, understanding of the essence and social significance (GC 1), setting priorities in the study of the topic.	Explains to students the importance of studying this topic, voices the objectives of the lesson.	They listen, ask questions, write down a new topic in a notebook.	Methodical development of a combined lesson, multimedia presentation.
	Statement of background information		Formation of knowledge, understanding of the essence and social significance of their future profession (OK 1), Formation of ideas about the role and place of physics in the modern scientific picture of the world; understanding the physical essence of phenomena observed in the Universe through the study of the concept of self-induction, inductance, self-induction EMF, magnetic field energy; to promote the formation of the ability to master fundamental physical concepts, confidently use physical terminology and symbols.	Presents new material, demonstrates a presentation.	Listen, read material on slides, write down.	Methodological development (source material), multimedia equipment, multimedia presentation.
	Completing tasks to consolidate knowledge		Consolidation, systematization, generalization of new knowledge. Develop problem solving skills. Organization of own activities, selection of typical methods and methods for solving problems, evaluation of their implementation (OK2).	Instructs and controls the execution of tasks, discusses the correctness of answers, answers students' questions.	Perform tasks, listen to the correct answers after completion, make adjustments, ask questions.
	Preliminary control of new knowledge		Evaluation of the effectiveness of the lesson and identification of shortcomings in new knowledge.	Instructs and supervises.	Orally answer questions.	Questions for preliminary control of knowledge. Appendix 3
	Final control. Mutual check		Consolidation of the material, the formation of the ability to draw conclusions, generalize. Formation of the ability to work in a team (OK6). Monitoring the assimilation of knowledge and skills of students.	Controls the progress of work. Controls the mutual check, explains the evaluation criteria.	Work in small groups, solve problems according to the model (in writing). They provide the completed task, compare the answers with the standards, give marks.	control material. Appendix 4 Presentation slide with sample answers and mark criteria.
	Summing up the lesson		Development of emotional stability, discipline, objectivity in assessing one's actions, the ability to work in a team and team (OK6).	Evaluates the work of the group as a whole. Announces grades, motivates students, highlights the most prepared.	Listen, participate in the discussion, ask questions.	Group journal.
	Task for independent extracurricular work of students			Gives a task for independent extracurricular work of students, instructs on the correct implementation, evaluation criteria.	Write down the task.	Presentation slide with homework.

RAW MATERIAL

Plan for presenting educational material on the topic

"Self-induction. Inductance. EMF of self-induction. Energy of the magnetic field.

Self-induction.

Inductance.

EMF of self-induction.

The energy of the magnetic field.

1. Self-induction- the phenomenon of the occurrence of induction EMF in a conducting circuit when the current strength changes in it. The resulting emf is called EMF of self-induction.

Manifestation of the phenomenon of self-induction.

Closing the circuit. When a circuit is closed, the current increases, which causes an increase in the magnetic flux in the coil, a vortex electric field arises, directed against the current, i.e. an EMF of self-induction occurs in the coil, which prevents the current from rising in the circuit (the vortex field slows down the electrons).

As a result, L1 lights up later than L2.

Opening the circuit.

When the electrical circuit is opened, the current decreases, there is a decrease in the magnetic flux in the coil, a vortex electric field appears, directed like a current (tending to maintain the same current strength), i.e. A self-inductive emf appears in the coil, which maintains the current in the circuit. As a result, L flashes brightly when turned off.

2.Inductance, or coefficient of self-induction - a parameter of an electrical circuit that determines the EMF of self-induction induced in the circuit when the current flowing through it changes and (and) its deformation. The term "inductance" also refers to a self-induction coil, which determines the inductive properties of the circuit.

Inductance- a physical quantity numerically equal to the EMF of self-induction that occurs in the circuit when the current strength changes by 1 A in 1 s.

Ф - magnetic flux through the circuit, I - current strength in the circuit.

SI unit of inductance Henry(H): [L] = [ ] = []= Hn; 1 Hn = 1
.

Inductance, like capacitance, depends on the geometry of the conductor - its size and shape, but does not depend on the current strength in the conductor. In addition, inductance depends on the magnetic properties of the medium in which the conductor is located.

Coil inductance depends on:

− number of turns,

− dimensions and shape of the coil;

− on the relative magnetic permeability of the medium (possible core).

Closing and opening currents.

With any switching on and off of the current in the circuit, the so-called extracurrents of self-induction (extracurrents of closing and opening), arising in the circuit due to the phenomenon of self-induction and preventing (according to Lenz's rule) the increase or decrease in current in the circuit. Inductance characterizes the inertia of a circuit with respect to a change in the current in it, and it can be considered as an electrodynamic analogue of the mass of a body in mechanics, which is a measure of the inertia of a body. In this case, the current strength I plays the role of the speed of the body.

3. EMF of self-induction.

self induction - the occurrence of induction EMF in a conducting circuit when the current strength changes in it. The induction emf occurs when the magnetic flux changes. If this change is caused by its own current, then one speaks of EMF self-induction :

ε is =–
= -L ,

where L- the inductance of the circuit, or its coefficient of self-induction.

4. Energy of the magnetic field of the current.

Find the energy possessed by the electric current in the conductor. According to the law of conservation of energy, the energy of the magnetic field created by the current is equal to the energy that the current source (galvanic cell, generator at a power plant, etc.) must expend to create current. When the current is interrupted, this energy is released in one form or another.

Let us find out why it is necessary to expend energy to create a current, i.e., it is necessary to do work. This is explained by the fact that when the circuit is closed, when the current begins to increase, a vortex electric field appears in the conductor, acting against the electric field that is created in the conductor due to the current source. In order for the current to become equal to I, the current source must do work against the forces of the vortex field. This work goes to increase the energy of the magnetic field of the current.

When the circuit is opened, the current disappears and the vortex field does positive work. The energy stored by the current is released. This is detected by a powerful spark that occurs when a circuit with a large inductance is opened.

You can write an expression for the energy of the current I flowing through a circuit with inductance L (i.e., for the energy of the magnetic field of the current), based on the analogy between inertia and self-induction, which was mentioned above.

If self-induction is analogous to inertia, then the inductance in the process of creating a current should play the same role as the mass when increasing the speed of a body in mechanics. The role of the body velocity in electrodynamics is played by the current strength I as a quantity that characterizes the movement of electric charges.

If so, then the energy of the current W m can be considered a value similar to the kinetic energy of the body
in mechanics, and write as W m =
(**).

It is this expression for the current energy that is obtained as a result of calculations.

The energy of the current (**) is expressed through the geometric characteristic of the conductor L, and the strength of the current in it I. But the same energy can also be expressed through the characteristics of the field. Calculations show that the energy density of a magnetic field (i.e., the energy per unit volume) is proportional to the square of the magnetic induction, just as the energy density of an electric field is proportional to the square of the electric field strength.

The magnetic field created by an electric current has an energy that is directly proportional to the square of the current strength.

Basic formulas:

Faraday's Law(by the law of electromagnetic induction): ε = –
, where ΔФ is the change in the magnetic flux, Δt is the time interval during which this change occurred.

The phenomenon of self-induction is in that when the current changes in the circuit, an EMF arises that opposes this change.

Magnetic flux F through the surface bounded by the contour, is directly proportional to the current strength I in the circuit: Ф \u003d LI,

where L - coefficient of proportionality, called inductance.

EMF self-induction is expressed through the change in current strength in the circuit ΔI by the following formula:

ε = -
=-L where Δt is the time during which this change occurred.

Magnetic field energy W is expressed by the formula: W=

APPENDIX №1

CONTROL OF KNOWLEDGE ON THE PREVIOUS TOPIC (oral)

Lenz's rule. Eddy currents. Maxwell's Electromagnetic Theory"

Lenz's rule.

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

This formula is called Faraday's law.

Experience shows that the induction current excited in a closed circuit when the magnetic flux changes is always directed in such a way that the magnetic field it creates prevents a change in the magnetic flux that causes the inductive current. This statement, formulated in 1833, is called Lenz's rule.

Rice. 1 illustrates Lenz's rule on the example of a fixed conducting circuit, which is in a uniform magnetic field, the modulus of induction of which increases with time.

Lenz's rule reflects the experimental fact that and always have opposite signs (the minus sign in Faraday's formula). Lenz's rule has a deep physical meaning - it expresses the law of conservation of energy.

Lenz's rule (Lenz's law) was established by E. X. Lenz in 1834. It specifies the law of electromagnetic induction, discovered in 1831 by M. Faraday. Lenz's rule determines the direction of the induction current in a closed circuit when it moves in an external magnetic field.

The direction of the induction current is always such that the forces experienced by it from the side of the magnetic field oppose the movement of the circuit, and the magnetic flux created by this current Fi seeks to compensate for changes in the external magnetic flux Fe.

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

Lenz's rule is illustrated by the figure:

If a permanent magnet is pushed into a coil closed to a galvanometer, the induction current in the coil will have such a direction that will create a magnetic field with vector AT", directed opposite to the magnetic field induction vector AT, i.e., will push the magnet out of the coil or prevent its movement. When pulling the magnet out of the coil, on the contrary, the field created by the inductive current will attract the coil, i.e. again prevent its movement.

Describe the algorithm for applying the Lenz rule in practice.

Answer: To apply the Lenz rule to determine the direction of the inductive current Ie in the circuit, you must follow these recommendations:

1. Set the direction of the lines of magnetic induction of the external magnetic field.

2. Find out if the magnetic induction flux of this field increases through the surface bounded by the contour ( ΔF 0), or decreases ( ΔF

3. Set the direction of the lines of magnetic induction of the magnetic field of the induction current Ii. These lines should be directed, according to Lenz's rule, opposite to the lines if ΔF 0, and have the same direction as them if ΔF

4. Knowing the direction of the lines of magnetic induction, determine the direction of the induction current Ii, using gimlet rule.

3. What are the reasons for the change in the magnetic flux (2 people answer).

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

1. The magnetic flux changes due to the movement of the circuit or its parts in a magnetic field constant in time. 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.

Consider, as an example, the occurrence of induction EMF in a rectangular circuit placed in a uniform magnetic field perpendicular to the plane of the circuit. Let one of the sides of a contour of length l slide along the other two sides with a speed (Fig. 2).

Lorentz force acts on free charges in this section of the contour. One of the components of this force, associated with the transfer velocity of the charges, is directed along the conductor. This component is shown in Fig. 1.20.3. She plays the role of an external force. Its modulus is

According to the definition of EMF

In other fixed parts of the contour, the external force is zero. The ratio for ind can be given a familiar form. During the time Δt, the contour area changes by ΔS = lυΔt. The change in the magnetic flux during this time is equal to ΔΦ = BlυΔt. Hence,

In order to set the sign in the formula connecting and, you need to choose the direction of the normal and the positive direction of the contour traversal that are consistent with each other according to the rule of the right gimlet, as is done in Fig. 1.20.1 and 1.20.2. If this is done, then it is easy to come to the Faraday formula.

If the resistance of the entire circuit is R, then an inductive current equal to will flow through it. During the time Δt, Joule heat will be released on the resistance R

The question arises: where does this energy come from, because the Lorentz force does no work! This paradox arose because we took into account the work of only one component of the Lorentz force. When an inductive current flows through a conductor in a magnetic field, free charges are affected by another component of the Lorentz force, associated with the relative velocity of the charges along the conductor. This component is responsible for the appearance of the ampere force. For the case shown in Fig. 1.20.3, Ampère's force modulus is equal to FA = I B l. The Ampere force is directed towards the movement of the conductor; therefore, it performs negative mechanical work. During the time Δt, this work Amex is equal to

A conductor moving in a magnetic field, through which an induction current flows, experiences magnetic braking. The total work of the Lorentz force is zero. Joule heat is released in the circuit either due to the work of an external force that keeps the speed of the conductor unchanged, or due to a decrease in the kinetic energy of the conductor.

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. In this case, the occurrence of the induction EMF can no longer be explained by the action of the Lorentz force. Electrons in a fixed conductor can only be set in motion by an electric field. This electric field is generated by a time-varying magnetic field. The work of this field when moving a single positive charge along a closed circuit is equal to the induction EMF in a stationary conductor. Therefore, the electric field generated by the changing magnetic field is not potential. It is called the vortex electric field. The idea of ​​a vortex electric field was introduced into physics by the great English physicist James Maxwell in 1861.

4. Describe the occurrence of electromagnetic induction in fixed conductors.

Answer: The phenomenon of electromagnetic induction in fixed conductors, which occurs when the surrounding magnetic field changes, is also described by the Faraday formula. Thus, the phenomena of induction in moving and stationary conductors proceed in the same way, but the physical cause of the occurrence of the inductive current turns out to be different in these two cases: in the case of moving conductors, the induction EMF is due to the Lorentz force; in the case of fixed conductors, the induction EMF is a consequence of the action on free charges of the vortex electric field that occurs when the magnetic field changes.

5. Describe the use of eddy currents using the example of the operation of various devices.

Answer:

In Russia.

In the electric motor, when current is passed, a torque appears

The first electric motor was designed by Jacobi (1836).

Closed currents that occur in continuous conductive media are called eddy currents or Foucault currents named after the French scientist who discovered them. Foucault currents can be both harmful (in the cores of transformers, rotating parts of generators and motors, Foucault currents cause useless heating) and beneficial (in induction furnaces for melting metals or cooking). In this case, the conductive body (metal or food) actually plays the role of a core. It is placed inside a coil through which a high frequency alternating current is passed, generating an alternating magnetic field inside the coil. And then the law of electromagnetic induction "works". An alternating magnetic field causes the appearance of Foucault induction currents, which heat up the conducting body.

6. Describe the main provisions of Maxwell's electromagnetic theory.

Answer: Maxwell's theory is a consistent theory of a single electromagnetic field, which is created by an arbitrary system of electric charges and currents. In Maxwell's theory, the main problem of electrodynamics is solved: according to a given distribution of charges and currents, the characteristics of the electric and magnetic fields created by them are calculated. Maxwell's theory is a generalization of the most important laws describing electrical and magnetic phenomena: the Gauss theorem, the law of total current, the law of electromagnetic induction.

This theory does not consider the internal mechanism of phenomena occurring in the environment and causing the appearance of electric and magnetic fields. The medium is described using three quantities that define its electrical and magnetic properties: relative permittivity, relative magnetic permeability, and electrical conductivity.

Macroscopic fields are considered, which are created by macroscopic charges and currents concentrated in volumes, much larger volumes of atoms and molecules. The distances from the sources of fields to the considered points in space are much larger than the linear dimensions of atoms and molecules. Therefore macroscopic fields change appreciably only at distances much larger than the dimensions of the atoms.

Macroscopic charges and currents are sets of microscopic charges and currents that create their own electric and magnetic microfields. These microfields are continuously changing over time at every point in space. Macroscopic fields are averaged microfields.

Maxwell's theory is a theory of short-range action, according to which electrical and magnetic interactions are carried out by means of an electromagnetic field and propagate at a finite speed equal to the speed of light in a given medium.

Criteria for evaluation:

Rating "5" - the student gave a full detailed answer to the question posed and answered an additional question;

Rating "4" - the student gave a full detailed answer to the question posed, but did not answer the additional question;

Grade "3" - the student gave an incomplete answer to the question posed and could not answer the additional question;

Rating "2" - did not answer to the question posed.

APPENDIX №2

TASKS FOR CONSOLIDATION AND SYSTEMATIZATION OF NEW KNOWLEDGE(written, not graded)

Physics 11 Multi-level independent and control work A. Kirik p. 10 average level No. 1-6.

Sample answers to tasks for consolidation and systematization

Level /No.
Middle level

APPENDIX No. 3

TASKS FOR PRELIMINARY CONTROL OF KNOWLEDGE

(Oral, not assessed. Sample answers to questions for preliminary control of knowledge are contained in the source material)

Define self-induction.

Describe the occurrence of this phenomenon.

Formulate the definition of inductance.

What is the unit of measure for inductance?

On what parameters does this value depend?

What is the formula for calculating the energy of a magnetic field?

APPENDIX №4

CONTROL MATERIAL (in writing)

Test

What phenomenon is called self-induction?

A) the phenomenon of the occurrence of induction EMF in a conducting circuit

B) a physical quantity numerically equal to the EMF of self-induction

C) the phenomenon of the occurrence of an EMF of induction in a conducting circuit when the current strength changes in it

D) the phenomenon of the occurrence of an electric current in a conducting circuit

What is the value of inductance?

A) the flux of magnetic induction through a surface bounded by a contour

B) a physical quantity numerically equal to the EMF of self-induction that occurs in the circuit when the current strength changes by 1 A in 1 s.

C) a physical quantity numerically equal to the EMF of self-induction

3. What is the unit of measure for magnetic inductance called?

4. What is the formula for calculating the energy of a magnetic field?

A) W=

B) ε = –
,

How will the energy of the magnetic field change if the current in the circuit is doubled?

A) will not change

B) doubled

B) will increase by 4 times

How will the energy of the magnetic field change if the inductance of the circuit is doubled?

A) will decrease by 4 times

B) will double

B) will not change

D) doubled

Sample answers to the tasks of the control material:

Job number

Criteria for evaluation:

for 4 correct answers - "3" points;

for 5 correct answers - "4" points;

for 6 correct answers - "5" points.

TASK FOR INDEPENDENT EXTRACURRICULAR WORK OF STUDENTS

Target: Determine the amount of information for the student's independent work, pay attention to significant points.

Time to complete the task: 45 minutes.

G. Ya. Myakishev, B. B. Bukhovtsev, N. N. Sotsky, Phys. Grade 11. Textbook for educational institutions (with an application on electronic media). Basic and profile levels - M .: Education, 2011, p. 43-48, paragraphs 15-17 read, learn the synopsis; with. 50 ex. 2 (4).

Criteria for evaluation:

the student learned the abstract - "3" points;

the student read the paragraphs and learned the abstract, owns the information from the textbook - "4" points;

the student has learned the abstract, owns the information from the textbook, completed the task - "5" points.

LIST OF USED SOURCES

Info-lesson Development of an open lesson

Inductance
Unit of inductance
self induction
Magnetic field energy

Inductance. An electric current passing through a conductor creates a magnetic field around it. magnetic flux F through the circuit from this conductor is proportional to the modulus of the magnetic field induction inside the circuit, and the magnetic field induction, in turn, is proportional to the current strength in the conductor. Therefore, the magnetic flux through the circuit is directly proportional to the current strength in the circuit:

Ф = LI. (55.1)

Proportionality factor L between current strength I in loop and magnetic flux F generated by this current is called inductance. The inductance depends on the size and shape of the conductor, on the magnetic properties of the medium in which the conductor is located.

Unit of inductance. The unit of inductance in the International system is taken Henry(GN). This unit is determined based on formula (55.1):

The inductance of the circuit is 1 H if, with a DC current of 1 A, the magnetic flux through the circuit is 1 Wb:

Self-induction. When the current strength in the coil changes, the magnetic flux created by this current changes. A change in the magnetic flux penetrating the coil should cause the appearance of an induction emf in the coil. The phenomenon of the occurrence of induction EMF in an electrical circuit as a result of a change in the current strength in this circuit is called self-induction.
In accordance with the Lenz rule, the EMF of self-induction prevents the increase in current strength when the circuit is turned on and the decrease in current strength when the circuit is turned off.
The phenomenon of self-induction can be observed by assembling an electrical circuit from a coil with a large inductance, a resistor, two identical incandescent lamps and a current source (Fig. 197).

The resistor must have the same electrical resistance as the coil wire. Experience shows that when the circuit is closed, an electric lamp connected in series with a coil lights up somewhat later than a lamp connected in series with a resistor. The increase in current in the coil circuit upon closing is prevented by the self-induction EMF that occurs with an increase in the magnetic flux in the coil. When the power source is turned off, both lamps flash. In this case, the current in the circuit is supported by the EMF of self-induction, which occurs when the magnetic flux in the coil decreases.
EMF of self-induction, arising in a coil with inductance L, according to the law of electromagnetic induction is equal to

The EMF of self-induction is directly proportional to the inductance of the coil and the rate of change of the current strength in the coil.
Using expression (55.3), we can give the second definition of the unit of inductance: an element of an electrical circuit has an inductance of 1 H, if, with a uniform change in the current strength in the circuit by 1 A for 1 s, an EMF of self-induction of 1 V occurs in it.

The energy of the magnetic field. When the inductor is disconnected from the current source, an incandescent lamp connected in parallel with the coil gives a short flash. The current in the circuit arises under the action of self-induction EMF. The source of energy released in this case in the electrical circuit is the magnetic field of the coil.
The energy of the magnetic field of an inductor can be calculated in the following way. To simplify the calculation, consider the case when, after disconnecting the coil from the source, the current in the circuit decreases with time according to a linear law. In this case, the EMF of self-induction has a constant value equal to

where t- the time interval during which the current in the circuit decreases from the initial value I to 0.
During t with a linear decrease in current strength from I to 0 in the circuit passes an electric charge:

so the work done by the electric current is

This work is done due to the energy of the magnetic field of the coil.
The energy of the magnetic field of an inductor is equal to half the product of its inductance and the square of the current in it:

(Based on the materials of the manual "Physics - reference materials" Kabardin O.F.)

Plan - lesson summary

« self induction . And inductance . Magnetic field energy current"

Completed by a 5th year student

group FM-112

full-time education

physical and mathematical education

Kezhutina Olga Vladislavovna

Date: 09/23/16

Vladimir 2016

Lesson topic: self induction . And inductance .

Class: "11b"

Lesson type : learning lesson.

Type of lesson: lesson-lecture.

Target : form the idea that a change in the current strength in a conductor creates a vortex wave, which can either accelerate or decelerate moving electrons; form an idea of ​​​​the energy that an electric current has in a conductor and the energy of a magnetic field created by a current.

Tasks:

Educational: Repeat students' knowledge about the phenomenon of electromagnetic induction, deepen them; on this basis to study the phenomenon of self-induction. Learn to use the law of electromagnetic induction to explain phenomena.Introduce a formula for calculating the energy of the magnetic field of the current and the concept of an electromagnetic field.

Educational: To cultivate interest in the subject, diligence and the ability to carefully evaluate the answers of comrades, the ability to work collectively and in pairs.

Developing: The development of the physical thinking of students, the expansion of the conceptual apparatus of students, the formation of skills to analyze information, draw conclusions from observations and experiments.

Equipment:

During the classes:

organizational stage.

11.20 – 11.21

Hello guys, sit down.

The students are getting ready for the lesson.

Knowledge update.

11.22-11.28

Checking homework, if students have questions, then we sort them out.

Front poll:

What field is called a vortex electric field?

What is the source of the vortex field?

What are Foucault currents? Give examples of their use.

What determines the EMF of induction that occurs in a conductor that moves in a time-varying magnetic field?

Students check their homework and answer the following questions:

The field that generatestime-varying magnetic field.

Time-varying magnetic field.

Induction currents reaching a large numerical value in massive conductors, due to the fact that their resistance is small.

On the speed of the conductor in a uniform magnetic field.

Sample leading questions:

4. Remember the formula by which you can find the EMF of induction in moving conductors.

motivational stage.

11.29-11.31

The foundations of electrodynamics were laid by Ampère in 1820. Ampere's work inspired many engineers to design various technical devices, such as an electric motor (designer B.S. Jacobi), a telegraph (S. Morse), an electromagnet, which was designed by the famous American scientist Henry.

Joseph Henry became famous thanks to the creation of a series of unique powerful electromagnets with a lifting force of 30 to 1500 kg with a dead weight of a magnet of 10 kg. Creating various electromagnets, in 1832 the scientist discovered a new phenomenon in electromagnetism - the phenomenon of self-induction. This lesson is devoted to this phenomenon.

Write the topic on the board: " self induction . And inductance . The energy of the magnetic field current ».

Learning new material.

11.32-11.45

Henry invented flat copper strip coils, with which he achieved force effects that were more pronounced than with wire solenoids. The scientist noticed that when a powerful coil is in the circuit, the current in this circuit reaches its maximum value much more slowly than without a coil.

Experience: The figure shows the electrical circuit of the experimental setup, on the basis of which it is possible to demonstrate the phenomenon of self-induction. The electrical circuit consists of two parallel-connected light bulbs connected through a key to a DC source. A coil is connected in series with one of the bulbs. After the circuit is closed, it can be seen that the bulb, which is connected in series with the coil, lights up more slowly than the second bulb.

When the source is turned off, the light bulb connected in series with the coil goes out more slowly than the second light bulb.

Consider the processes occurring in this circuit when the key is closed and opened.

1. Closing the key.

There is a conductive loop in the circuit. Let the current in this coil flow counterclockwise. Then the magnetic field will be directed upwards.

Thus, the coil is in the space of its own magnetic field. With an increase in current, the coil will be in the space of a changing magnetic field of its own current. If the current increases, then the magnetic flux created by this current also increases. As you know, with an increase in the magnetic flux penetrating the plane of the circuit, an electromotive force of induction arises in this circuit and, as a result, an induction current. According to Lenz's rule, this current will be directed in such a way that its magnetic field prevents a change in the magnetic flux penetrating the plane of the circuit.

That is, for the coil considered in Figure 4, the inductive current must be directed clockwise, thereby preventing the increase in the coil's own current. Consequently, when the key is closed, the current in the circuit does not increase instantly, due to the fact that a braking induction current appears in this circuit, directed in the opposite direction.

2. Opening the key.

When the key is opened, the current in the circuit decreases, which leads to a decrease in the magnetic flux through the plane of the coil. A decrease in the magnetic flux leads to the appearance of an EMF of induction and an induction current. In this case, the induction current is directed in the same direction as the loop's own current. This leads to a slower decrease in the intrinsic current.

Conclusion: when the current in the conductor changes, electromagnetic induction occurs in the same conductor, which generates an induction current directed in such a way as to prevent any change in the intrinsic current in the conductor. This is the essence of the phenomenon of self-induction. Self-induction is a special case of electromagnetic induction.

self induction - this is the phenomenon of the occurrence of electromagnetic induction in a conductor when the strength of the current flowing through this conductor changes.

Inductance. The modulus of the induction vector B of the magnetic field created by the current is proportional to the strength of the current. Since the magnetic flux Ф is proportional to B, then Ф ~ V ~ I.

It can therefore be argued that

F \u003d LI,

where L is the coefficient of proportionality between the current in the conductive circuit and the magnetic flux.

The value L is called the inductance of the circuit, or its coefficient of self-induction.

Using the law of electromagnetic induction and the resulting expression, we obtain the equality

It follows from the formula thatinductance is a physical quantity numerically equal to the EMF of self-induction that occurs in the circuit when the current strength in it changes by 1 A in 1 s.

Inductance, like electrical capacitance, depends on geometric factors: the size of the conductor and its shape, but does not depend directly on the current strength in the conductor. In addition to the geometry of the conductor, the inductance depends on the magnetic properties of the medium in which the conductor is located.

Obviously, the inductance of one wire turn is less than that of a coil (solenoid) consisting of N of the same turns, since the magnetic flux of the coil increases N times.

The SI unit of inductance is called the henry (denoted H). The inductance of the conductor is 1 H, if in it, with a uniform change in the current strength of 1 A for 1 s, an EMF of self-induction of 1 V occurs:

A person encounters the phenomenon of self-induction every day. Each time we turn on or off the light, we thereby close or open the circuit, while exciting induction currents. Sometimes these currents can reach such high values ​​that a spark jumps inside the switch, which we can see.

Analogy between self-induction and inertia. The phenomenon of self-induction is similar to the phenomenon of inertia in mechanics. So, inertia leads to the fact that under the action of force the body does not instantly acquire a certain speed, but gradually. The body cannot be instantly slowed down, no matter how great the braking force. In the same way, due to self-induction, when the circuit is closed, the current strength does not immediately acquire a certain value, but increases gradually. Turning off the source, we do not stop the current immediately. Self-induction maintains it for some time, despite the resistance of the circuit.

To create an electric current, and hence its magnetic field, work must be done against the forces of the eddy electric field. This work (according to the law of conservation of energy) is equal to the energy of the electric current or the energy of the magnetic field of the current.

Write down the expression for the energy of the currentI, flowing through the circuit with inductanceL, i.e. for the energy of the magnetic field of the current, it is possible on the basis of the analogy between inertia and self-induction.

If self-induction is analogous to inertia, then inductance plays the same role in the process of creating current as mass does in mechanics when speed increases. The role of the speed of a body in electrodynamics is played by the current strength as a quantity that characterizes the movement of electric charges.

Then the energy of the current can be considered the value of a similar kinetic energy in mechanics:

The energy of the magnetic field of the current.

Answer questions, engage in discussion, draw conclusions, make notes in notebooks.

Consolidation of the studied material

11.46-11.56

Offers to solve the problem:

Solve problems at the board and in the field.

Summarizing. Homework.

11.57-11.58

Marking and substantiation. Writing and discussing homework.

D/Z: §14-16, nos. 932, 934, 938.

Write down homework

Reflection

11.59-12.00

A conversation is organized with the aim of understanding the participants of the lesson of their own actions during the lesson.

Questions:

1. What new did you learn for yourself in the lesson?

2. Was the lesson material clear?

3. Did you like the lesson?

Take part in the conversation

№931. What is the inductance of the circuit if, at a current strength of 5 A, a magnetic flux of 0.5 mWb occurs in it?

№933. Find the inductance of the conductor, in which, with a uniform change in the current strength of 2 A for 0.25 s, an EMF of self-induction of 20 mV is excited.

№937. In a coil with an inductance of 0.6 H, the current strength is 20 A. What is the energy of the magnetic field of this coil? How will the field energy change if the current is halved?

№939. Find the energy of the magnetic field of the solenoid, in which, at a current of 10 A, a magnetic flux of 0.5 Wb arises.

№932. What magnetic flux occurs in a circuit with an inductance of 0.2 mH at a current strength of 10 A?

№934. What EMF of self-induction is excited in the winding of an electromagnet with an inductance of 0.4 H with a uniform change in the current strength in it by 5 A in 0.02 s?

№938. What should be the current strength in the inductor winding with an inductance of 0.5 Gn so that the field energy is equal to 1 J?