Determine the rate of change of current in the electromagnet winding. Open Library - an open library of educational information Rate of change of current strength formula
The change in the current strength in the circuit is prevented by the self-induction EMF, which is equal to the product of the circuit inductance and the rate of change in the current strength.
An electric current creates a magnetic field around itself, and part of the lines of magnetic induction of this field always passes through the circuit through which the current flows (Fig. 6a). If the current through the circuit changes in time (alternating current), then the magnetic flux through this circuit also changes, which means that an induction emf arises that prevents the change in the magnetic flux (Lenz's rule). Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, when the current changes in any circuit, an induction emf arises, preventing these changes. This phenomenon is called self-induction, and the corresponding EMF is self-induction EMF, Eis.
The phenomenon of self-induction is demonstrated in fig. 6b, which shows how the current strength through the coil changes when the current source is connected and disconnected. It can be seen that when the circuit is closed, the current through the coil reaches a value corresponding to the resistance of the coil, not instantly, but gradually. The reason for this slowdown in the growth of the current strength is the self-induction EMF directed against the EMF of the current source. When the circuit is opened, an EMF of self-induction arises in the coil, seeking to maintain the current strength that was before the key was opened, as a result of which the current strength through the coil does not drop instantly, but gradually. The energy required for the current to flow through the coil after the current source has been disconnected (Fig. 6b) is the energy of the coil's magnetic field.
To quantitatively describe the phenomenon of self-induction, we find the dependence of the magnetic flux Ф through the circuit on the current strength I in this circuit. Obviously, the magnetic flux through the circuit is proportional to the magnetic induction inside the circuit, and the magnetic induction is proportional to the current strength in the conductor. For this reason, the magnetic flux must be proportional to the current strength:
Ф = L.I , (6.1)
where L is a proportionality factor, called the loop inductance. A circuit with inductance is indicated in the diagram by the corresponding icon (see Fig. 6b) Using (6.1), the law of electromagnetic induction (5.2), and also assuming that the inductance of the circuit does not change when the current in it changes, you can find the EMF of self-induction Eis :
The SI unit of inductance is the henry (H). From (6.2) it follows that the inductance of the circuit depends on the shape and dimensions of this circuit. So, the inductance of a flat circuit is the greater, the larger its surface area, and the inductance of the coil is proportional to its diameter and the number of turns in it. However, the inductance
The coil increases when there is a core of iron or an alloy capable of being magnetized inside it.
The phenomenon of self-induction resembles the phenomenon of inertia in mechanics. The inertia of a body, measured by its mass m, slows down the reaction of the body to the force applied to it. The same thing happens in the circuit when they want to change the strength of the current in it. In this case, as follows from (6.2), the measure of the "inertia" of the circuit is its inductance. The analogy between electromagnetic and mechanical phenomena allows us to assume that the current in the circuit plays the same role as the speed of the body v, and the EMF is similar to the force acting on the body. Continuing this analogy, we can derive a formula for the energy of the magnetic field of the coil, based on the fact that the kinetic energy of the body is equal to. Replacing m with L and v with I, we obtain the following expression for the energy WM of the magnetic field of the circuit with inductance L and current I:
Calculations show that expression (6.3) is indeed true, proving the correctness of analogies between mechanical and electromagnetic phenomena.
Review questions:
What is the phenomenon of self-induction?
What is called inductance, and in what units is it measured?
What is the EMF of self-induction?
· What is the energy of the magnetic field of the circuit with current?
Rice. 6. (a) - lines of magnetic induction of the coil with current; (b) is a graph of the change in current through the coil when the current source is turned on and off.
Repeat the theory:
1. Self-induction is ____________________________________________________________
____________________________________________________________________________________________________________________________________________________________________________.
2. Inductance - ____________________________________________________________________________
__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
[L] = ______.
3.EMF self-induction : ______________, where L- ______________________________, -_______________________Δ I - _______________________________.
4. Lenz's rule: ______________________________________________________________________________
5. Lenz's rule: ______________________________________________________________________________
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
6. The inductive current arising in a closed circuit has such a direction in which its own magnetic flux created by it through the area bounded by the circuit tends to __________________ change in the external magnetic flux that caused this current.
7. Magnetic flux penetrating the solenoid Ф = ________________.
8. Induction current is _____________________________________________________________________________
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
9. Magnetic field energy W m =______________
10. Volumetric energy density of the magnetic field ω=_________________________.
Solve problems:
1. What is the inductance of the circuit if, at a current strength of 5A, a magnetic flux of 0.5mWb occurs in it?
Given: SI: Solution:
2. With a uniform decrease within 0.1 s of the current in the coil from 10 A to zero, an EMF of self-induction of 60 V appeared in it. Determine the inductance of the coil.
Given: Solution:
3. With the help of a rheostat, the current in the coil is uniformly increased at a speed of 2 A / s. Coil inductance 200 mH. What is the EMF of self-induction in the coil?
Given: SI: Solution:
4. In a coil with an inductance of 0.6H, the current strength is 20A. What is the energy of the coil's magnetic field? How will the field energy change if the current is halved?
Given: Solution:
Answer: the energy of the magnetic field _____________ by __________ times when the current strength is halved.
5. What should be the current strength in the inductor winding with an inductance of 0.5H in order for the field energy to be equal to 1J?
Given: Solution:
6. What is the energy of the magnetic field of the solenoid, in which, at a current of 1A, a magnetic flux of 0.3Wb occurs?
Given: Solution:
check yourself:
1. What magnetic flux occurs in a circuit with an inductance of 0.2mH at a current of 10A?
Given: SI: Solution:
2. Find the inductance of the conductor, in which a uniform change in current strength by 2A for 0.25 s excites an EMF of self-induction of 20mV.
Given: SI: Solution:
3. Find the energy of the magnetic field of the solenoid, in which, at a current strength of 10A, a magnetic flux of 0.5 Wb arises.
Given: Solution:
4. Coil inductance 0.1mH. At what current strength will the magnetic field energy be equal to 0.2 mJ?
Given: SI: Solution:
Date "___" _________20____
Task 35
Independent work on the topic
"A magnetic field. Electromagnetic induction"
OPTION 1
1. A magnetic field is created
1) electric charges 2) magnetic charges
3) moving electric charges 4) any body
2. Lines of magnetic induction around a conductor with current are correctly shown in the case.
1) A 2) B 3) C 4) D
3. A straight conductor with current / is located between the poles of the magnet (the conductor is located perpendicular to the plane of the sheet, the current flows to the reader). The ampere force acting on the conductor is directed
1) right → 2) left ← 3) up 4) down ↓
4. Trajectory of an electron flying into a uniform magnetic field at an angle of 60°
5. Which of the following processes is explained by the phenomenon of electromagnetic induction?
1) the interaction of conductors with current.
2) deviation of the magnetic needle when passing through the wire of electric current.
3) 
the occurrence of an electric current in a closed coil with an increase in the current strength in the coil located next to it.
4) the emergence of a force acting on a straight conductor with current.
6. A light wire ring is suspended from a thread. When a magnet is pushed into the ring, the north pole will be:
1) repel from the magnet 2) be attracted to the magnet 3) motionless 4) first repel, then attract
7. 
The figure shows a graph of the dependence of the current in the inductor on time. The self-induction EMF module takes on the largest value in the time interval
1) 0 s to 1 s 2) 1 s to 5 s 3) 5 s to 6 s 4) 6 s to 8 s
8. Match the technical devices from the left column of the table with the physical phenomena used in them in the right column.
Devices Phenomena
A. electric motor 1) the effect of a magnetic field on a permanent magnet
B. compass 2) the effect of a magnetic field on a moving electric charge
B. Galvanometer 3) the effect of a magnetic field on a current-carrying conductor
D. MHD - Generator PART C
Solve the problem.
11. A conductor 1 m long slides along horizontal rails located in a vertical magnetic field with an induction of 0.01 T at a constant speed of 10 m/s. The rail ends are connected to a 2 ohm resistor. Find the amount of heat released in the resistor in 4 seconds. Ignore the resistance of the rails and the conductor.
Given: SI: Solution
Grade _____ teacher's signature ________________ / L.S. Tishkina/
OPTION 2
PART A Choose one correct answer
1. A moving electric charge creates
1) electric field only 2) magnetic field only
3) both electric and magnetic fields 4) only gravitational field
2. The figure shows a cylindrical conductor through which an electric current flows. The direction of the current is indicated by an arrow. How is the magnetic induction vector directed at point C?
1) in the drawing plane up
2) in the drawing plane down
3) from us perpendicular to the plane of the drawing
4) to us perpendicular to the plane of the drawing
3. A current-carrying conductor introduced into a magnetic field is subjected to a force directed
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EMF self-induction With any change in the current in the coil (or in general in the conductor), an EMF of self-induction is induced in it itself.
The greater the rate of current change, the greater the EMF of self-induction.
Any decrease in electric current is accompanied by the appearance of e. d.s. self-induction, tending, according to Lenz's rule, to maintain a decreasing current. As a result, the voltage on the inductors can increase significantly when the current circuit is broken. Sometimes these voltages are so high that the windings can burn out; to protect the windings, so-called discharge resistances are connected in parallel with them.
Proportionality factorLis called inductance.Inductance is measured in Henry. Such a circuit has an inductance of one henry, in which, with a uniform change in current at a rate of one ampere per second, e. d.s., equal to one volt.
The inductance of a coil is a value that characterizes the property of the coil to induce an EMF of self-induction in itself.
The inductance of a given coil is a constant value, independent of both the strength of the current passing through it and the rate of its change.
It should not be forgotten that if the current in the coil does not change, then no self-induction EMF occurs. The phenomenon of self-induction is especially pronounced in a circuit containing a coil with an iron core, since iron significantly increases the magnetic flux of the coil, and, consequently, the magnitude of the self-induction EMF when it changes.In practice, sometimes you need a coil (or winding) that does not have inductance. In this case, the wire is wound on a coil, having previously folded it in half. This method of winding is called bifilar.
Mutual induction emf
To cause an induction EMF in one coil by changing the current in another, it is not at all necessary to insert one of them inside the other, but you can place them side by side
And in this case, when the current in one coil changes, the resulting alternating magnetic flux will penetrate (cross) the turns of the other coil and cause an EMF in it.
Mutual induction makes it possible to interconnect various electrical circuits by means of a magnetic field. Such a connection is called an inductive connection.
The magnitude of the EMF of mutual induction depends primarily on the rate at which the current in the first coil changes. The faster the current changes in it, the greater the EMF of mutual induction is created.
In addition, the magnitude of the EMF of mutual induction depends on the magnitude of the inductance of both coils and on their relative position, as well as on the magnetic permeability of the environment.In order to be able to distinguish between different pairs of coils by their ability to mutually induce EMF, the concept of mutual inductance or mutual inductance coefficient has been introduced.
The mutual inductance is denoted by the letter M. The unit of its measurement, as well as the inductance, is the henry.
Henry is such a mutual inductance of two coils, in which a change in current in one coil by 1 ampere per 1 second causes a mutual induction EMF in the other coil equal to 1 volt.
The magnitude of the EMF of mutual induction is affected by the magnetic permeability of the environment. The greater the magnetic permeability of the medium through which the alternating magnetic flux connecting the coils closes, the stronger the inductive coupling of the coils and the greater the magnitude of the mutual induction EMF.
The operation of such an important electrical device as a transformer is based on the phenomenon of mutual induction.