Presentation of a generalizing lesson on the topic of electromagnetic induction. Electromagnetic induction. The law of electromagnetic induction. Opening and closing currents

The phenomenon of electromagnetic induction

"A happy accident falls on only one share of the prepared mind."

L. Pasternak

The experience of the Danish scientist Oersted

1820 year

1777 - 1851

Michael Faraday

1791 - 1867, English physicist,

Honorary Member of the Petersburg

Academy of Sciences (1830),

The founder of the doctrine of the electromagnetic field; introduced the concepts of "electric" and "magnetic field";

expressed the idea of \u200b\u200bexistence

electromagnetic waves .

1821 year: "Convert magnetism to electricity."

1931 year - received an electric current using a magnetic field

"Electromagnetic induction" -

latin word means “ guidance "

M. Faraday's experience

“Copper wire 203 feet long was wound around a wide wooden spool, and a wire of the same length was wound between the turns, isolated from the first cotton thread.

One of these coils was connected to a galvanometer, the other to a strong battery ...

When the circuit was closed, a sudden but extremely weak action was observed on the galvanometer, and the same action was observed when the current was cut off.

With the continuous passage of current through one of the spirals, it was not possible to detect the deflection of the galvanometer needle ...

What do we see?

Conclusion from the experience seen :

• The current arising in the coil (closed loop) is called

induction.

• The difference between the obtained current and the one known to us earlier is that to get it no current source needed.

Faraday's general conclusion

An induction current in a closed loop occurs when the magnetic flux changes through the area bounded by the loop.

Electromagnetic induction - This is a physical phenomenon, consisting in the appearance of an electric current in a conducting circuit, which either rests in a time-varying magnetic field, or moves in a constant magnetic field in such a way that the number of magnetic induction lines penetrating the circuit changes.

The resulting current is called induction .

What is the reason for the occurrence induction current in the coil?

Consider a magnet:

What can you say about a magnet?

When we bring a magnet into the closed loop of the coil, what does it change?

How to determine the direction of the induction current?

We see that the direction of the induction current is different in these experiments.

Based on the law of conservation of energy, the Russian scientist Lenz proposed the rule , which determines the direction of the induction current.

Russian physicist Emil Lenz

1804 - 1865

0, if extends, then ∆Ф 0). 3. Determine the direction of the induction lines of the magnetic field B ′ created by the induction current (if ∆Ф 0, then the lines B and B ′ are directed in opposite directions; if ∆Ф 0, then the lines B and B ′ are co-directed). 4. Using the rule of the gimbal (right hand), determine the direction of the induction current. ∆ Ф is characterized by a change in the number of lines of magnetic induction B penetrating the contour "width \u003d" 640 "

1. Determine the direction of the lines of induction of the external field B (leave N and are included in S ).

2. Determine whether the magnetic flux through the circuit increases or decreases (if the magnet slides into the ring, then ∆Ф 0, if it is extended, then ∆Ф 0).

3. Determine the direction of the induction lines of the magnetic field B ′ created by the induction current (if ∆Ф 0, then lines B and B 'are directed in opposite directions; if ∆Ф 0, then lines B and B 'are co-directed).

4. Using the rule of the gimbal (right hand), determine the direction of the induction current.

∆ F

characterized by a change

the number of lines of magnetic induction B,

piercing the contour

Mathematical formula for the law of electromagnetic induction

ε =  - ΔΦ/Δ t 

ΔΦ/Δ t - the rate of change of the magnetic flux (units Vb / s )

The EMF of induction in a closed loop is equal in magnitude to the rate of change of the magnetic flux through the surface bounded by the loop.

Electromagnetic law induction

EMF of electromagnetic induction in a closed loop is numerically equal and opposite in sign to the rate of change of the magnetic flux through the surface bounded by this loop.

The current in the loop has a positive direction when the external magnetic flux decreases.

Computer hard drive.

Electromagnetic induction in the modern world

Video recorder.

Police detector.

Airport metal detector

Magnetic levitation train

Showing videos about the application of the phenomenon of electromagnetic induction: metal detector, recording information on magnetic media and reading from them - disk "Physics 7-11 grades. Library visual aids»Educational complexes.

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Annotation to the presentation

The presentation "Electromagnetic induction" describes Faraday's experience, the discovery of electromagnetic induction and the law that regulates it, the method of obtaining induction current, etc. The second half of the presentation contains a number of tasks and tasks that will help students prepare for passing the GIA.

• Faraday's experience;
• Magnetic flux;
• Faraday's law of electromagnetic induction;
• Lenz's rule;
• Receiving induction current.

Format

pptx (powerpoint)

Number of slides

Popova I.A.

The audience

The words

Abstract

Present

Purpose

• To teach a lesson by a teacher

  For test / verification work

Slide 1

Slide 2

goal

Repetition of the basic concepts of kinematics, types of motion, graphs and kinematic formulas in accordance with the GIA codifier and plan demo version examination work.

Slide 3

Discovery of the phenomenon of electromagnetic induction

• The phenomenon of electromagnetic induction was discovered by the outstanding English physicist M. Faraday in 1831. It consists in the generation of an electric current in a closed conducting circuit when the magnetic flux penetrating the circuit changes over time.
• Faraday Michael (22.09.1791–25.08.1867)
• English physicist and chemist.

Slide 4

Faraday's experience

Slide 5

The phenomenon of electromagnetic induction

The phenomenon of electromagnetic induction consists in the appearance of an electric current in a closed conducting circuit when the magnetic flux penetrating the circuit changes over time.

Slide 6

The phenomenon of electromagnetic induction

Slide 7

Magnetic flux

• Magnetic flux Φ through the area S of the loop is called the value
• Φ \u003d B S cos α
• where B is the modulus of the magnetic induction vector,
• α is the angle between the vector and the normal to the contour plane
• The SI unit of magnetic flux is called Weber (Wb)

Slide 8

The phenomenon of electromagnetic induction

Slide 9

Faraday's law of electromagnetic induction

Lenz's rule:

• When the magnetic flux changes in the conducting circuit, an induction EMF Eind arises, equal to the rate of change in the magnetic flux through the surface bounded by the circuit, taken with a minus sign:
• In this example, a ind< 0. Индукционный ток Iинд течет навстречу выбранному положительному направлению обхода контура.

Slide 10

Dependence of induction current on the rate of change of magnetic flux

Slide 11

Lenz's rule

• I case
• II case
• III case
• IV case

Slide 12

Change in magnetic flux

A change in the magnetic flux permeating a closed loop can occur for two reasons:

• The magnetic flux changes due to the movement of the circuit or its parts in a magnetic field constant in time.
• Time variation of the magnetic field with a stationary circuit.

Slide 13

Receiving induction current

Slide 14

Alternator

Slide 15

The phenomenon of electromagnetic induction is observed in cases

• movement of the magnet relative to the coil (or vice versa);
• movement of the coils relative to each other;
• changing the current in the circuit of the first coil (using a rheostat or by closing and opening the switch);
• by rotating the circuit in a magnetic field;
• by rotating the magnet inside the circuit.

Slide 16

Consider the tasks

A selection of tasks in kinematics (from the tasks of the GIA 2008-2010)

Slide 17

Tasks

When the south pole of the magnet is inserted into the coil, the ammeter detects the occurrence of an induction current. What needs to be done to increase the strength of the induction current?

• increase the rate of magnet insertion
• bring a magnet into the coil with the north pole
• change the polarity of the ammeter connection
• take an ammeter with a lower division value

Slide 18

The coil is closed to a galvanometer. In which of the following cases does an electric current occur in it? A) An electromagnet is inserted into the coil. B) There is an electromagnet in the coil.

1. Only A.
2. Only B.
3. In both cases.
4. In none of the above cases.

Slide 19

Two identical coils A and B are each closed to its own galvanometer. A strip magnet is introduced into coil A, and the same strip magnet is removed from coil B. In which coils will the galvanometer measure the induction current?

1. in none of
2. in both coils
3. only in coil A
4. reel only

Slide 20

Once with a canvas, the magnet falls through a fixed metal ring with the south pole down, the second time with the north pole down. Ring current

1. occurs in both cases

Slide 21

The coil current changes according to the graph in the figure. At what time intervals near the end of the coil can you detect not only a magnetic, but also an electric field?

1. 0 to 2 s and 5 to 7 s.
2. Only from 0 to 2 s.
3. Only 2 to 5 seconds.
4. At all specified intervals.

Slide 22

A magnet is inserted into the metal ring for the first two seconds, for the next two seconds the magnet is left motionless inside the ring, for the next two seconds it is removed from the ring. How long does the current flow in the coil?

1. 0-6 s
2. 0-2 s and 4-6 s
3. 2-4 s
4. only 0-2 s

Slide 23

The permanent magnet is inserted into a closed aluminum ring on a thin long hanger (see figure). The first time - the North Pole, the second time - the South Pole. Wherein

1. in both experiments the ring is repelled from the magnet
2. in both experiments, the ring is attracted to the magnet
3. in the first experiment, the ring is repelled from the magnet, in the second, the ring is attracted to the magnet
4. in the first experiment, the ring is attracted to the magnet, in the second - the ring is repelled from the magnet

Slide 24

The magnet is removed from the ring as shown in the figure. Which pole of the magnet is closer to the ring?

1. northern
2. southern
3. negative
4. positive

Slide 25

The figure shows a demonstration of the experience of checking the Lenz rule. The experiment is carried out with a solid ring, not a cut one, because

1. the solid ring is made of steel and the cut ring is made of aluminum
2. a vortex electric field does not appear in a solid ring, and in a cut one, a
3. induction current arises in a solid ring, but not in a cut one
4. eMF of induction appears in a solid ring, but not in a cut one

Slide 26

The figure shows two ways to rotate the frame in a uniform magnetic field. Frame current

1. occurs in both cases
2. does not occur in any of the cases
3. occurs only in the first case
4. occurs only in the second case

Slide 27

The figure shows the moment of a demonstration experiment to test Lenz's rule when all objects are motionless. The south pole of the magnet is inside the solid metal ring, but does not touch it. The rocker arm with metal rings can rotate freely around the vertical support. When the magnet is pulled out of the ring, it will

1. stay still
2. move counterclockwise
3. hesitate
4. follow the magnet

Slide 28

Literature

• http: // site /

View all slides

Abstract

physics teacher

Belovo 2013

Explanatory note

Literature

Peryshkin, A.V., Physics. 7th grade. Textbook for secondary schools / A. V. Peryshkin. - M .: Bustard, 2009 .-- 198 p.

Peryshkin, A.V., Physics. 8th grade. Textbook for secondary schools / A. V. Peryshkin. - M .: Bustard, 2009 .-- 196 p.

Municipal budgetary atypical educational institution

“Gymnasium No. 1 named after Tasirov G.Kh. City of Belovo "

Electromagnetic induction. Faraday's experiments Preparation for GIA.

Methodological guide (presentation)

physics teacher

Belovo 2013

Explanatory note

Methodical manual (presentation) “Electromagnetic induction. Faraday's experiments. Preparation for the GIA ”is compiled in accordance with the requirements for the State Final Attestation (GIA) in Physics 2010 and is intended to prepare graduates of the basic school for the exam.

The brevity and clarity of the presentation allows you to quickly and efficiently repeat the material covered when repeating the physics course in grade 9, as well as using examples of demos of the GIA in physics in 2008-2010 to show the application of the basic laws and formulas in the options for exam tasks of level A and B.

The manual can also be used for grades 10-11 with a repetition of the relevant topics, which will help orient students to the elective exam in graduation years.

Note: the movie file exceeds the maximum upload size on the portal; when compressed, the playback quality suffers. Therefore, to insert video clips on slides (there are recommendations in the presentation), download the film at the addresses indicated on the slides and paste them in the indicated places. When inserting, set "play automatically during slide show", on the "Options" tab, check the box "Full screen"

Literature

Zorin, N.I. GIA 2010. Physics. Training tasks: Grade 9 / N.I. Zorin. - M .: Eksmo, 2010 .-- 112 p. - (State (final) certification (in a new form).

Kabardin, O.F. Physics. Grade 9: a collection of test items to prepare for the final certification for the course of the basic school / O.F. Kabardin. - M .: Bustard, 2008 .-- 219 p;

Peryshkin, A.V., Physics. 7th grade. Textbook for secondary schools / A. V. Peryshkin. - M .: Bustard, 2009 .-- 198 p.

Peryshkin, A.V., Physics. 8th grade. Textbook for secondary schools / A. V. Peryshkin. - M .: Bustard, 2009 .-- 196 p.

Download abstract

Municipal educational institution

"Secondary school number 72"

Electrodynamics Electromagnetic induction

(1st part)

The presentation was prepared by

physics teacher

V.S.Dubovik

saratov

Electromagnetic induction

In this lesson, you should study the following questions:

• the phenomenon of electromagnetic induction;
• difference between alternating electric and magnetic fields from constant ones;
• magnetic flux;
• direction of induction current;
• lenz's rule;
• the law of electromagnetic induction;
• vortex electric field;
• EMF of induction in moving conductors;
• application of the phenomenon of electromagnetic induction.

As a result, you must learn to:

• determine the direction of the induction current of the magnetic induction;
• calculate magnetic flux;
• calculate the EMF of induction.

For this:

• Study the materials of the textbook;
• Answer questions for self-control;
• Consider a technique for solving problems of this type;

Discovery of the phenomenon of electromagnetic induction

MICHAEL FARADEY

(1791-1867)

Engraved: Michael Faraday giving a lecture with visual demonstrations of his experiments at the Royal Institution in London in 1830

Observing the phenomenon of electromagnetic induction

The phenomenon of EMF in the circuit when the magnetic flux permeating the circuit changes is called electromagnetic induction.

Magnetic flux. The law of electromagnetic induction

Magnetic flux Φ through the area S the contour is called the value:

Φ = B · S Cos α

The SI unit of magnetic flux is called pick (Wb). A magnetic flux of 1 Wb is created by a magnetic field with an induction of 1 T, penetrating a flat contour with an area of \u200b\u200b1 m in the normal direction 2 .

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

0, and EMF ind I ind flows towards the selected positive direction of the loop bypass. Lenz's rule reflects the experimental fact that the EMF ind and ΔF / Δt always have opposite signs (the "minus" sign in the Faraday formula). Lenz's rule has a deep physical meaning - it expresses the law of conservation of energy. "Width \u003d" 640 "

Induction current direction. Lenz's rule

Experience shows that the induction current excited in a closed loop when the magnetic flux changes is always directed so that the magnetic field created by it prevents the change in the magnetic flux that causes the induction current. This statement is called Lenz's rule (1833).

Lenz Emiliy Khristianovich

Lenz's rule illustration.

In this example, ΔФ / Δ t 0, and the EMF ind I ind flows towards the selected positive direction of the loop bypass.

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

EMF of induction in moving conductors

The emergence of the EMF of induction is explained by the action of the Lorentz force on free charges in moving conductors. The Lorentz force plays in this case the role of an external force.

Work force F L on the way l is equal to A \u003d F Л l \u003d eυB l .

By definition of EMF

The ratio for EMF ind can be given a familiar look. During the time Δt, the contour area changes by ΔS \u003d l υΔt. The change in the magnetic flux during this time is

ΔΦ \u003d BlυΔt. Hence,

Solving problems

Solving problems

B i

Solving problems

Solving problems

Solving problems

Solving problems

Solving problems

Solving problems

Solving problems

The "-" sign can be ignored because not set,

how the magnetic flux changes.

Solving problems

Solving problems

Solving problems

Solving problems

Homework

§§ 11.13 Ex. 2 (8.9)

Consider all tasks from trial options for the exam for 2006 - 2009 on the subject of electromagnetic induction.

ELECTROMAGNETIC INDUCTION

In 1824, the Frenchman Arago discovered that the oscillations of a freely suspended magnetic needle
decay much faster if there is a magnetic plate under them. Later experiments showed that with the rapid rotation of the copper plate, the magnetic needle located above it begins to oscillate in the same direction.
The explanation for this was given by the Englishman Faraday
(1831). He proceeded from the fact that the electric and magnetic fields are interconnected, and if around a conductor with
electric current arises magnetic, then the reverse is also true:
ELECTRIC CURRENT IN A CLOSED CONDUCTOR,
UNDER THE ACTION OF A MAGNETIC FIELD.

Faraday conducted a series of experiments. Non-magnetic
1
rod wound two pieces of copper wire
water. One (1) connected to battery B to B
swarm (2) to galvanometer G. At constant
current in wire 1 pointer of galvanometer is not
D
deviates, which means there is no current in wire 2. 2
When the key K was closed and opened, the galvanometer needle slightly deflected and quickly
returned to initial positionwhich showed
the occurrence in the circuit 2 of a short-time current called INDUCTION CURRENT. The direction of this
current when opening and closing the key was opposite. It was unclear what was causing
induction current generation: a change in the initial current or magnetic field.

If to the coil K₂ with the galvanometer Г K₁ I
S
1
bring the K₁ coil with battery B
B
creating a current I 1, then in К₂ there will be
N
current I 2. When removing the K₁ coil from
K₂ current I 2 arises, but directed K₂ I
2
the opposite.
D
Induction current occurs, as well
if to the coil with galvanometer
bring the magnet in and move it along the coil.
The direction of the induction current depends on which end of the magnet was facing the coil, and on
whether he approached or receded.
The reason for the appearance of the induction current I 2 is
change in the magnetic field generated by the coil
K₁ or magnet.

FARADAY'S LAW

ELECTROMAGNETIC INDUCTION

The phenomenon discovered by Faraday was named:
ELECTROMAGNETIC INDUCTION - occurrence
electromotive force in a conductor moving in
magnetic field, or in a closed conducting loop when changing its flux linkage. (due to
contour movement in a magnetic field or changes
the field itself).
The occurrence of an induction current in the circuit indicates
the presence in the circuit of an electromotive force (EMF), called the electromotive force of the electromagnetic
induction (induction EMF Ei).
The value of the induction current, and hence the EMF of induction
are determined only by the rate of change of the magnetic flux.

THE LAW OF ELECTROMAGNETIC INDUCTION OF FARADAY

EMF of electromagnetic induction in the circuit is numerically equal and opposite in sign to the rate of change
magnetic flux through a limited surface
this outline.
The law is universal Ei does not depend on the method of change
magnetic flux.
d
Ei
dt
BASIC LAW OF ELECTROMAGNETIC INDUCTION
The unit of measurement for Ei is V (volts).
Wb
T m 2
N m2
J
A B c
d
IN
dt
from
from
A
m
from
A
from
A
from

LENTZ RULE

Sign "-" - indicates that the increase in flow d dt 0
induces EMF of induction less than zero d dt 0 Ei 0
that is, the field of the induction current is directed towards the flow, and vice versa, d dt 0 Ei 0, that is, the direction of the flow and the field of the induced current coincided.
The "-" sign is a mathematical expression LENTZ RULES
– general rule to find the direction of the induction current.
The induction current in the circuit always has such a direction that the magnetic field created by it prevents a change in the magnetic flux that caused this
induction current.

To explain the occurrence of the EMF of induction in fixed conductors, Maxwell suggested that any alternating magnetic field excites an electric field in the surrounding space, which is the cause of the induction current in
conductor.
The circulation of the vector of the intensity of this field E B along any fixed contour L is
EMF of electromagnetic induction.
d
Ei E B dl
dt
L

FRAME ROTATION IN A MAGNETIC FIELD

Let the frame rotate ω
S
with angular velocity w const,
α
in a uniform magnetic field
IN
with induction B const.
Magnetic flux coupled with
the frame at any time t will be equal to:
Bn S BS cos BS cos t
t is the angle of rotation of the frame at time t.
When the frame rotates, the EMF of induction Ei d dt BS sin t will appear in it, changing according to the harmonic law.
Ei max BS Ei Ei max sin t

If the frame rotates in a uniform magnetic field, then
a variable EMF arises in it, changing along
harmonious law.
The phenomenon of electromagnetic induction was the basis,
on the basis of which electric motors, generators and transformers were created.
GENERATORS - used to convert one
kind of energy to another.
The simplest generator that converts mechanical
energy into the energy of an electric field - the frame considered above rotating in a uniform magnetic field. Mechanical conversion process
energy into electrical reversible. On this principle
based on the operation of electric motors that convert electrical energy into mechanical energy.

EDDY CURRENTS (FUKO CURRENTS)

Induction current occurs not only in
thin wires, but also in massive solid conductors placed in an alternating magnetic field. These currents turn out to be closed in the thickness of the conductor and
are called eddy currents or Foucault currents.
Foucault currents obey Lenz's rule: their
the magnetic field is directed so that
counteract the change in magnetic flux inducing vortex
currents.
Eddy currents occur in wires through which alternating current flows.
The direction of Foucault currents can be determined
dI
0
dt
I
dI
0
dt
I

pour according to Lenz's rule: if the primary current I increases (dI dt 0) then the Foucault currents are directed against the direction I, and if it decreases (dI dt 0) then in the direction.
The direction of the eddy currents is such that they prevent a change in the primary current inside the conductor
and contribute to its change near the surface.
These are manifestations of the skin effect or surface effect.
Since high-frequency currents practically flow in a thin
surface layer, then the wires for them make
hollow.

CIRCUIT INDUCTION SELF-INDUCTION MUTUAL INDUCTION TRANSFORMERS

INDUCTANCE. SELF-INDUCTION

The electric current flowing in the circuit creates an electromagnetic field around itself, the induction of which is proportional to the current. Therefore, linked to the contour
the magnetic flux is proportional to the current in the circuit.
LI
L - loop inductance (induction coefficient)
When the current in the circuit changes, the
so is the magnetic flux attached to it, which means that an EMF will be induced in the circuit.
The emergence of an EMF induction in a conducting circuit,
when the current strength changes in it, it is called -
SELF-INDUCTION.

The unit of measure for inductance is Henry (H).
1 H - inductance of such a circuit, magnetic flux
self-induction of which at a current of 1 A is equal to 1 Wb.
For an infinitely long solenoid, the total magnetic flux (flux linkage) will be:
N 2I
N 0
S
l
Hence, the inductance of an infinitely long loop is:
N 2S
L 0
l
The solenoid inductance depends on the number of turns N,
length l, solenoid area S and magnetic permeability of the substance from which the solenoid is made.

EMF OF SELF-INDUCTION

In general, the inductance of the circuit depends only on
from the geometric shape, size and magnetic pro
worthlessness environment contour, and, you can
say that the inductance of the circuit is analogous to the electrical capacitance of a solitary conductor.
Applying Faraday's law to self-induction (Ei d dt)
we get:
d
d
dL
dI
Es
LI L I
dt
dt
dt
dt
If the contour is not deformed (L const), and the magnetic
the permeability of the environment does not change
hence:
dI
Es L
dt

The “-” sign indicates that the presence of inductance in the circuit leads to a slowdown in the change in current in it.
If the current increases with time, then ES 0 and dI dt 0 then
there is a self-induction current directed towards the current caused by external source, and slows it down
increase.
If over time the current decreases ES 0 and dI dt 0, then the induction current has the same direction as
decreasing current in the circuit and slows down its decrease.
The circuit with a certain inductance acquires electrical inertness: any change
current is inhibited the more, the greater the inductance of the circuit.

CURRENTS FOR OPENING AND CLOSING CIRCUITS

With any change in the current strength in the conducting circuit
EMF of self-induction occurs, as a result of which additional currents appear in the circuit called
SELF-INDUCTION EXTRATORS. According to the rule
Lenz, they are always directed so as to prevent a change in the current in the circuit (opposite to the current from
R
E
TO
power source).
Consider a circuit having a source toL
ka with EMF E, resistance resistor R, inductance coil L. Under the action of an external EMF in the circuit
a direct current flows I 0 E R.
At time t \u003d 0, the current source was turned off. The current through coil L will begin to decrease. What will cause the appearance of EMF of self-induction Es L dI dt

according to Lenz's rule to decrease
current. At every moment in time
current is determined by Ohm's law:
ES
dI
dI
R
I
IR L
dt
R
dt
I
L
I
I0
closure
opening
t
Integrating this expression over I (changing from I 0 to I) and
by t (changing from 0 to t) we get:
I
Rt
ln
I0
L
I I 0e
t
Current at time t after switching off the source.
L
Is the constant relaxation time (the time during which R
the current strength decreases by a factor of e).
The greater the inductance of the circuit and the lower the resistance, the less, and therefore the slower the decrease

there is a current in the circuit when opening.
When the circuit is closed, in addition to the external EMF E,
EMF of self-induction Es L dI dt preventing the increase in current. According to Ohm's Law:
dI
IR E Es E - L
dt
du
dt
Let u IR E
u
At the moment of circuit closure, the current strength I 0 and u E, which means integrating over u (from E to IR E) and over t (from 0 to t)
IR E t
get
ln
E
t
I I 0 (1 e)
E
Current at time t after switching on. (I 0).
R

MUTUAL INDUCTION

Consider two fixed ends I1 1 I 2 2
tours 1 and 2 located close
apart. In circuit 1 flows
the current I1 and the flux generated by this circuit are proportional to I1.
Let us denote by 21 that part of the magnetic flux that penetrates the contour 2. 21 L21 I1 (L21 is the proportionality coefficient).
If the current I1 changes, then in circuit 2, Ei 2
EMF, which, according to Faraday's law, is equal and opposite in sign to the rate of change of the magnetic
flow 21 created by the current in the first circuit and the penetrating circuit 2.

d 21
dI1
Ei 2
L21
dt
dt
Similarly, when the current flows in the circuit 2, we get:
12 L12 I 2
d 12
dI 2
Ei1
L12
dt
dt
The phenomenon of the emergence of an EMF in one of the circuits, when
change in current strength in another is called
MUTUAL INDUCTION.
L12 and L21 - mutual inductance of the circuits, depend
on the geometric shape of the dimensions, the relative position of the contours and the magnetic permeability
environment. The unit of measurement is Henry (H).
L12 L21
Experiments have shown that:

Let's calculate the mutual inductance
l
two coils wound on a loop- I
1
N2
toroidal core.
N1
S
The magnetic induction of the field created by the first coil, with the number of turns N1, current I 1 and
magnetic permeability of the core length l
N1 I 1
is equal to:
B 0
l
Magnetic flux through one turn of the second coil:
N1 I 1
2 BS 0
S
l
Full magnetic flux (flux linkage) through
secondary winding containing N 2 turns:
N1 N 2
N 2 2 0
I1 S
l

Since flux linkage is created by current I 1, then:
N1 N 2
L21 0
S
I1
l
If we calculate the magnetic flux created by the coil 2 through the coil 1, then for the inductance L12 we will similarly get the same value. Means
mutual inductance of two coils wound on
common toroidal core:
N1 N 2
L12 L21 0
S
I1
l

TRANSFORMERS

For the first time, transformers were
R1
designed by russian elements E1 N1
N 2E2
technician P.N. Yablochkov
(1847-1894) and physicist I.F. Usagin (1855-1919).
The principle of operation of transformers used for
increase or decrease in AC voltage
current, based on the phenomenon of mutual induction.
Let the primary and secondary coils (windings) having N1 and N 2 turns, respectively, are fixed on a closed iron core. The ends of the first winding
attached to the EMF source E1, an alternating current I 1 arises in it, creating an alternating magnetic flux in the transformer core, practically

completely localized in the iron core,
which means that completely penetrating the turns of the secondary
windings. A change in this flux causes the appearance of an EMF of mutual induction in the secondary winding,
and in the primary EMF of self-induction.
The current I 1 of the primary winding is determined using Ohm's law where R1 is the resistance of the primary winding.
d N1
E1
I1 R1
dt
The voltage drop I1 R1 across the resistance R1 at rapidly alternating fields is small compared to each
from the EMF, and we can assume that:
d
E1 N1
dt

EMF of mutual induction arising in the secondary winding:
d (N)
d
E2
N 2
dt
dt
Comparing the values \u200b\u200bof the EMF of mutual E2 and self-inductions E1
2
we get:
N2
E2
E1
N1
E2 - EMF arising in the second winding, sign "-"
shows that the EMF in the first and second windings are opposite in phase.
N2
- transformation ratio, shows in skoN1
only times the EMF in the secondary winding is more (less)
than in the primary.

Neglecting energy losses (about 2%), and applying the energy conservation law, we can assume that
E2 I 2 E1 I1
Hence:
N2
1
N1
E2
I1 N 2
E1 I 2 N1
- step-up transformer increasing
alternating EMF and step-down current (applied
for transmission of electricity over long distances)
N2
1 - step-down transformer reducing
N1EMF and rising current (used in electric welding, where a large current is required at low voltage).