In this article, we will understand the concept of inductive EMF in situations where it occurs. We will also look at inductance as a key parameter for the emergence of magnetic flux when an electric field appears in a conductor.
Electromagnetic induction is the generation of electric current by magnetic fields that change over time. Thanks to the discoveries of Faraday and Lenz, regularities were formulated into laws, which introduced symmetry into the understanding of electromagnetic fluxes. Maxwell's theory brought together knowledge of electric current and magnetic fluxes. Through Hertz's discoveries, mankind learned about telecommunications.
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Magnetic flux
An electromagnetic field appears around a conductor with an electric current, but the opposite phenomenon, electromagnetic induction, also occurs in parallel. Let's consider magnetic flux as an example: if a conductor frame is placed in an electric field with induction and moved from top to bottom along the magnetic lines of force or from right to left perpendicular to them, then the magnetic flux passing through the frame will be a constant value.
If the frame rotates around its axis, then after some time the magnetic flux will change by a certain value. As a result, an EMF of induction will occur in the frame and an electric current will appear, which is called induction current.
EMF of induction
Let's understand in detail what the concept of inductive EMF is. When a conductor is placed in a magnetic field and moves with the field lines crossing, an electromotive force called inductive EMF appears in the conductor. It also occurs if the conductor remains stationary and the magnetic field moves and crosses field lines with the conductor.
When a conductor, where EMF occurs, closes to an external circuit, an induction current begins to flow through the circuit due to the presence of this EMF. Electromagnetic induction involves the phenomenon of induction of EMF in a conductor at the moment it is crossed by magnetic field lines.
Electromagnetic induction is the reverse process of transformation of mechanical energy into electric current. This concept and its laws are widely used in electrical engineering, most electric machines are based on this phenomenon.
Faraday's and Lenz's Laws
Faraday's and Lenz's laws depict the patterns of electromagnetic induction.
Faraday revealed that magnetic effects appear as a result of changes in magnetic flux over time. The moment a conductor is crossed by an alternating magnetic current, an electromotive force arises in the conductor, resulting in an electric current. Both a permanent magnet and an electromagnet can generate current.
The scientist determined that the intensity of the current increases with a rapid change in the number of power lines that cross the circuit. That is, the EMF of electromagnetic induction stays in direct dependence on the rate of magnetic flux.
According to Faraday's law, the formulas for EMF induction are defined as follows:
E = - dF/dt.
The "minus" sign indicates the relationship between the polarity of the induced EMF, the flux direction, and the changing velocity.
According to Lenz's law, it is possible to characterize the electromotive force depending on its direction. Any change in the magnetic flux in the coil results in an EMF of induction, and with a rapid change there is an increasing EMF.
If a coil with induction EMF is shorted to an external circuit, then an induction current flows through it, due to which a magnetic field appears around the conductor and the coil acquires the properties of a solenoid. As a result, a magnetic field of its own is formed around the coil.
E. H. Lenz established the law according to which the direction of the induction current in the coil and the induction EMF are determined. The law states that the EMF of induction in the coil forms a current in the coil of the direction in which the given magnetic flux of the coil makes it possible to avoid a change in the extraneous magnetic flux.
Lenz's law applies to all situations of electric current induction in conductors, regardless of their configuration or method of changing the external magnetic field.
Movement of a wire in a magnetic field
The value of the induced EMF is determined according to the length of the conductor crossed by the field lines. If there are more lines of force, the value of induced EMF increases. As the magnetic field and induction increase, a greater value of EMF arises in the conductor. Thus, the value of EMF induction in a conductor moving in a magnetic field is in direct dependence on the magnetic field induction, the length of the conductor and the speed of its movement.
This dependence is reflected in the formula E = Blv, where E is the EMF of induction; B is the value of magnetic induction; I is the length of the conductor; v is the speed of its movement.
Note that in a conductor that moves in a magnetic field, the induction EMF appears only when it crosses the magnetic field lines of force. If the conductor moves along the field lines, then no EMF is induced. For this reason, the formula only applies when the motion of the conductor is directed perpendicular to the lines of force.
The direction of the induced EMF and electric current in the conductor is determined by the direction of the conductor itself. A right hand rule has been developed to reveal the direction. If you hold the palm of your right hand so that the field lines enter in its direction and your thumb indicates the direction of motion of the conductor, then the other four fingers show the direction of the induced EMF and the direction of the electric current in the conductor.
Rotating coil
The function of an electric current generator is based on the rotation of a coil in a magnetic flux, where there are a certain number of turns. EMF is induced in an electric circuit always when it is crossed by magnetic flux, based on the formula magnetic flux F = B x S x cos α (magnetic induction multiplied by the surface area through which magnetic flux passes and the cosine of the angle formed by the direction vector and perpendicular to the line plane).
According to the formula, F is affected by changes in situations:
- the direction vector changes when the magnetic flux changes;
- the area enclosed by the circuit changes;
- the angle changes.
It is allowed to induce EMF when the magnet is stationary or the current is unchanged, but simply when the coil rotates around its axis within the magnetic field. In this case, the magnetic flux changes as the value of the angle changes. The coil crosses the magnetic flux lines of force as it rotates, resulting in an EMF. With uniform rotation, there is a periodic change in magnetic flux. Also the number of lines of force that are crossed every second becomes equal in equal time intervals.
In practice, in alternators, the coil remains stationary and the electromagnet performs rotations around it.
Self-induction EMF
When an alternating electric current passes through a coil, an alternating magnetic field is generated, which is characterized by a changing magnetic flux that induces an EMF. This phenomenon is called self-induction.
Because magnetic flux is proportional to the intensity of the electric current, then the formula for self-induction EMF is as follows:
F = L x I, where L is the inductance, which is measured in Gn. Its value is determined by the number of turns per unit length and the size of their cross section.
Mutual Induction
When two coils are placed next to each other, there is an EMF of mutual induction, which is determined by the configuration of the two circuits and their mutual orientation. As the circuit separation increases, the value of mutual inductance decreases because there is a decrease in the magnetic flux common to the two coils.
Let's consider in detail the process of mutual induction. There are two coils, along the wire of one with N1 turns current I1 flows, which creates magnetic flux and goes through the second coil with N2 number of turns.
The value of the mutual inductance of the second coil with respect to the first:
M21 = (N2 x F21)/I1.
Value of magnetic flux:
F21 = (M21/N2) x I1.
The induced EMF is calculated by the formula:
E2 = - N2 x dF21/dt = - M21x dI1/dt.
In the first coil, the value of the induced EMF is:
E1 = - M12 x dI2/dt.
It is important to note that the electromotive force induced by mutual induction in one of the coils is in any case directly proportional to the change in electric current in the other coil.
The mutual inductance is then considered to be equal:
M12 = M21 = M.
As a consequence , E1 = - M x dI2/dt and E2 = M x dI1/dt. M = K √ (L1 x L2), where K is the coupling factor between the two values of inductance.
Interinduction is widely used in transformers, which give the possibility to change the values of alternating electric current. The device is a pair of coils that are wound on a common core. The current in the first coil forms the changing magnetic flux in the magnetic core and the current in the second coil. With fewer turns in the first coil than in the second coil, the voltage increases, and correspondingly with more turns in the first coil, the voltage decreases.
In addition to generating and transforming electrical energy, the phenomenon of magnetic induction is used in other devices. For example, in magnetic levitation trains, moving without direct contact with the current in the rails, but a couple of centimeters higher because of electromagnetic repulsion.
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