A MAGNETIC FIELD
The magnetic interaction of moving electric charges, according to the concepts of field theory, is explained as follows: every moving electric charge creates a magnetic field in the surrounding space that can act on other moving electric charges.
B is a physical quantity that is a force characteristic of a magnetic field. It is called magnetic induction (or magnetic field induction).
Magnetic induction- vector quantity. The magnitude of the magnetic induction vector is equal to the ratio of the maximum value of the Ampere force acting on a straight conductor with current to the current strength in the conductor and its length:
Unit of magnetic induction. In the International System of Units, the unit of magnetic induction is taken to be the induction of a magnetic field in which a maximum Ampere force of 1 N acts on each meter of conductor length with a current of 1 A. This unit is called tesla (abbreviated: T), in honor of the outstanding Yugoslav physicist N. Tesla:
LORENTZ FORCE
The movement of a current-carrying conductor in a magnetic field shows that the magnetic field acts on moving electric charges. Ampere force acts on the conductor F A = IBlsin a, and the Lorentz force acts on a moving charge:
Where a- angle between vectors B and v.
Movement of charged particles in a magnetic field. In a uniform magnetic field, a charged particle moving at a speed perpendicular to the magnetic field induction lines is acted upon by a force m, constant in magnitude and directed perpendicular to the velocity vector. Under the influence of a magnetic force, the particle acquires acceleration, the modulus of which is equal to:
In a uniform magnetic field, this particle moves in a circle. The radius of curvature of the trajectory along which the particle moves is determined from the condition from which it follows,
The radius of curvature of the trajectory is a constant value, since a force perpendicular to the velocity vector changes only its direction, but not its magnitude. And this means that this trajectory is a circle.
The period of revolution of a particle in a uniform magnetic field is equal to:
The last expression shows that the period of revolution of a particle in a uniform magnetic field does not depend on the speed and radius of its trajectory.
If the electric field strength is zero, then the Lorentz force l is equal to the magnetic force m:
ELECTROMAGNETIC INDUCTION
The phenomenon of electromagnetic induction was discovered by Faraday, who established that an electric current arises in a closed conducting circuit with any change in the magnetic field penetrating the circuit.
MAGNETIC FLUX
Magnetic flux F(flux of magnetic induction) through a surface of area S- a value equal to the product of the magnitude of the magnetic induction vector and the area S and cosine of the angle A between the vector and the normal to the surface:
Ф=BScos
In SI, the unit of magnetic flux is 1 Weber (Wb) - magnetic flux through a surface of 1 m2 located perpendicular to the direction of a uniform magnetic field, the induction of which is 1 T:
Electromagnetic induction- the phenomenon of the occurrence of electric current in a closed conducting circuit with any change in the magnetic flux penetrating the circuit.
Arising in a closed circuit, the induced current has such a direction that its magnetic field counteracts the change in the magnetic flux that causes it (Lenz's rule).
LAW OF ELECTROMAGNETIC INDUCTION
Faraday's experiments showed that the strength of the induced current I i in a conducting circuit is directly proportional to the rate of change in the number of magnetic induction lines penetrating the surface bounded by this circuit.
Therefore, the strength of the induction current is proportional to the rate of change of the magnetic flux through the surface bounded by the contour:
It is known that if a current appears in the circuit, this means that external forces act on the free charges of the conductor. The work done by these forces to move a unit charge along a closed loop is called electromotive force (EMF). Let's find the induced emf ε i.
According to Ohm's law for a closed circuit
Since R does not depend on , then
The induced emf coincides in direction with the induced current, and this current, in accordance with Lenz’s rule, is directed so that the magnetic flux it creates counteracts the change in the external magnetic flux.
Law of Electromagnetic Induction
The induced emf in a closed loop is equal to the rate of change of the magnetic flux passing through the loop taken with the opposite sign:
SELF-INDUCTION. INDUCTANCE
Experience shows that magnetic flux F associated with a circuit is directly proportional to the current in that circuit:
Ф = L*I .
Loop inductance L- proportionality coefficient between the current passing through the circuit and the magnetic flux created by it.
The inductance of a conductor depends on its shape, size and properties of the environment.
Self-induction- the phenomenon of the occurrence of induced emf in a circuit when the magnetic flux changes caused by a change in the current passing through the circuit itself.
Self-induction is a special case of electromagnetic induction.
Inductance is a quantity numerically equal to the self-inductive emf that occurs in a circuit when the current in it changes by one per unit of time. In SI, the unit of inductance is taken to be the inductance of a conductor in which, when the current strength changes by 1 A in 1 s, a self-inductive emf of 1 V occurs. This unit is called henry (H):
MAGNETIC FIELD ENERGY
The phenomenon of self-induction is similar to the phenomenon of inertia. Inductance plays the same role when changing current as mass does when changing the speed of a body. The analogue of speed is current.
This means that the energy of the magnetic field of the current can be considered a value similar to the kinetic energy of the body:
Let us assume that after disconnecting the coil from the source, the current in the circuit decreases with time according to a linear law.
The self-induction emf in this case has a constant value:
where I is the initial value of the current, t is the time period during which the current strength decreases from I to 0.
During time t, an electric charge passes through the circuit q = I cp t. Because I cp = (I + 0)/2 = I/2, then q=It/2. Therefore, the work of electric current is:
This work is done due to the energy of the magnetic field of the coil. Thus we again get:
Example. Determine the energy of the magnetic field of the coil in which, at a current of 7.5 A, the magnetic flux is 2.3 * 10 -3 Wb. How will the field energy change if the current strength is halved?
The energy of the magnetic field of the coil is W 1 = LI 1 2 /2. By definition, the inductance of the coil is L = Ф/I 1. Hence,
Among the many definitions and concepts associated with the magnetic field, special mention should be made of magnetic flux, which has a certain directionality. This property is widely used in electronics and electrical engineering, in the design of instruments and devices, as well as in the calculation of various circuits.
Concept of magnetic flux
First of all, it is necessary to establish exactly what is called magnetic flux. This value should be considered in combination with a uniform magnetic field. It is homogeneous at every point in the designated space. A certain surface having a certain area, designated by the symbol S, is affected by the magnetic field. The field lines act on this surface and intersect it.
Thus, the magnetic flux Ф crossing a surface with area S consists of a certain number of lines coinciding with the vector B and passing through this surface.
This parameter can be found and displayed in the form of the formula Ф = BS cos α, in which α is the angle between the normal direction to the surface S and the magnetic induction vector B. Based on this formula, it is possible to determine the magnetic flux with a maximum value at which cos α = 1 , and the position of vector B will become parallel to the normal perpendicular to the surface S. And, conversely, the magnetic flux will be minimal if vector B is located perpendicular to the normal.
In this version, vector lines simply slide along the plane and do not intersect it. That is, the flux is taken into account only along the lines of the magnetic induction vector intersecting a specific surface.
To find this value, weber or volt-seconds are used (1 Wb = 1 V x 1 s). This parameter can be measured in other units. The smaller value is the maxwell, which is 1 Wb = 10 8 μs or 1 μs = 10 -8 Wb.
Magnetic field energy and magnetic flux
If an electric current is passed through a conductor, a magnetic field with energy is formed around it. Its origin is associated with the electrical energy of the current source, which is partially consumed to overcome the self-inductive emf that occurs in the circuit. This is the so-called self-energy of the current, due to which it is formed. That is, the field and current energies will be equal to each other.
The value of the current's own energy is expressed by the formula W = (L x I 2)/2. This definition is considered equal to the work done by a current source that overcomes inductance, that is, the self-inductive emf and creates a current in an electrical circuit. When the current stops operating, the energy of the magnetic field does not disappear without a trace, but is released, for example, in the form of an arc or spark.
The magnetic flux arising in the field is also known as magnetic induction flux with a positive or negative value, the direction of which is conventionally designated by a vector. As a rule, this flow passes through a circuit through which electric current flows. With a positive direction of the normal relative to the contour, the direction of current movement is a value determined in accordance with. In this case, the magnetic flux created by a circuit with an electric current and passing through this circuit will always have a value greater than zero. Practical measurements also indicate this.
Magnetic flux is usually measured in units established by the international SI system. This is the already well-known Weber, which represents the amount of flow passing through a plane with an area of 1 m2. This surface is placed perpendicular to the magnetic field lines with a uniform structure.
This concept is well described by Gauss's theorem. It reflects the absence of magnetic charges, so induction lines always appear closed or going to infinity without beginning or end. That is, the magnetic flux passing through any type of closed surface is always zero.
The flow of the magnetic induction vector B through any surface. The magnetic flux through a small area dS, within which the vector B is unchanged, is equal to dФ = ВndS, where Bn is the projection of the vector onto the normal to the area dS. Magnetic flux F through the final... ... Big Encyclopedic Dictionary
MAGNETIC FLUX- (magnetic induction flux), flux F of the magnetic vector. induction B through k.l. surface. M. p. dФ through a small area dS, within the limits of which the vector B can be considered unchanged, is expressed by the product of the area size and the projection Bn of the vector onto ... ... Physical encyclopedia
magnetic flux- A scalar quantity equal to the flux of magnetic induction. [GOST R 52002 2003] magnetic flux The flux of magnetic induction through a surface perpendicular to the magnetic field, defined as the product of the magnetic induction at a given point by the area... ... Technical Translator's Guide
MAGNETIC FLUX- (symbol F), a measure of the strength and extent of the MAGNETIC FIELD. The flux through area A at right angles to the same magnetic field is Ф = mHA, where m is the magnetic PERMEABILITY of the medium, and H is the intensity of the magnetic field. Magnetic flux density is the flux... ... Scientific and technical encyclopedic dictionary
MAGNETIC FLUX- flux Ф of the magnetic induction vector (see (5)) B through the surface S normal to the vector B in a uniform magnetic field. SI unit of magnetic flux (cm) ... Big Polytechnic Encyclopedia
MAGNETIC FLUX- a value characterizing the magnetic effect on a given surface. The magnetic field is measured by the number of magnetic lines of force passing through a given surface. Technical railway dictionary. M.: State transport... ... Technical railway dictionary
Magnetic flux- a scalar quantity equal to the flux of magnetic induction... Source: ELECTRICAL ENGINEERING. TERMS AND DEFINITIONS OF BASIC CONCEPTS. GOST R 52002 2003 (approved by Resolution of the State Standard of the Russian Federation dated 01/09/2003 N 3 art.) ... Official terminology
magnetic flux- flux of magnetic induction vector B through any surface. The magnetic flux through a small area dS, within which the vector B is unchanged, is equal to dФ = BndS, where Bn is the projection of the vector onto the normal to the area dS. Magnetic flux F through the final... ... encyclopedic Dictionary
magnetic flux- , the flux of magnetic induction is the flux of the magnetic induction vector through any surface. For a closed surface, the total magnetic flux is zero, which reflects the solenoidal nature of the magnetic field, i.e. the absence in nature... Encyclopedic Dictionary of Metallurgy
Magnetic flux- 12. Magnetic flux Magnetic induction flux Source: GOST 19880 74: Electrical engineering. Basic concepts. Terms and definitions original document 12 magnetic on ... Dictionary-reference book of terms of normative and technical documentation
Books
- , Mitkevich V. F.. This book contains a lot that is not always paid due attention when it comes to magnetic flux, and that has not yet been stated clearly enough or has not been... Buy for 2252 UAH (Ukraine only)
- Magnetic flux and its transformation, Mitkevich V.F.. This book will be produced in accordance with your order using Print-on-Demand technology. This book contains a lot that is not always given due attention when it comes to...
Let there be a magnetic field in some small region of space that can be considered uniform, that is, in this region the magnetic induction vector is constant, both in magnitude and direction.
Let us select a small area with an area ΔS, the orientation of which is specified by the unit normal vector n(Fig. 445).
rice. 445
Magnetic flux through this area ΔФ m is defined as the product of the area of the site and the normal component of the magnetic field induction vector
Where 
dot product of vectors B And n;
Bn− component of the magnetic induction vector normal to the site.
In an arbitrary magnetic field, the magnetic flux through an arbitrary surface is determined as follows (Fig. 446): 
rice. 446
− the surface is divided into small areas ΔS i(which can be considered flat);
− the induction vector is determined B i on this site (which within the site can be considered permanent);
− the sum of flows through all areas into which the surface is divided is calculated
This amount is called flux of the magnetic field induction vector through a given surface (or magnetic flux).
Note that when calculating the flux, the summation is carried out over the field observation points, and not over the sources, as when using the superposition principle. Therefore, magnetic flux is an integral characteristic of the field, describing its averaged properties over the entire surface under consideration.
It is difficult to find the physical meaning of magnetic flux, as for other fields it is a useful auxiliary physical quantity. But unlike other fluxes, magnetic flux is so common in applications that in the SI system it was awarded a “personal” unit of measurement - Weber 2: 1 Weber− magnetic flux of a uniform magnetic field of induction 1 T across the area 1 m2 oriented perpendicular to the magnetic induction vector.
Now we will prove a simple but extremely important theorem about magnetic flux through a closed surface.
Previously, we established that the forces of any magnetic field are closed; it already follows from this that the magnetic flux through any closed surface is equal to zero.
Nevertheless, we present a more formal proof of this theorem.
First of all, we note that the principle of superposition is valid for magnetic flux: if a magnetic field is created by several sources, then for any surface the field flux created by a system of current elements is equal to the sum of the field fluxes created by each current element separately. This statement follows directly from the superposition principle for the induction vector and the directly proportional relationship between the magnetic flux and the magnetic induction vector. Therefore, it is sufficient to prove the theorem for the field created by a current element, the induction of which is determined by the Biot-Savarre-Laplace law. Here the structure of the field, which has axial circular symmetry, is important for us; the value of the modulus of the induction vector is unimportant.
Let us choose as a closed surface the surface of a block cut out as shown in Fig. 447. 
rice. 447
The magnetic flux is nonzero only through its two lateral faces, but these fluxes have opposite signs. Recall that for a closed surface, an outer normal is chosen, so on one of the indicated faces (the front) the flux is positive, and on the back it is negative. Moreover, the modules of these flows are equal, since the distribution of the field induction vector on these faces is the same. This result does not depend on the position of the considered block. An arbitrary body can be divided into infinitesimal parts, each of which is similar to the considered bar.
Finally, let us formulate another important property of the flow of any vector field. Let an arbitrary closed surface bound a certain body (Fig. 448). 
rice. 448
Let us divide this body into two parts, limited by parts of the original surface Ω 1 And Ω 2, and close them with a common interface between the body. The sum of the fluxes through these two closed surfaces is equal to the flux through the original surface! Indeed, the sum of the flows across the boundary (once for one body, another time for another) is equal to zero, since in each case it is necessary to take different, opposite normals (each time external). Similarly, one can prove the statement for an arbitrary partition of a body: if a body is divided into an arbitrary number of parts, then the flux through the surface of the body is equal to the sum of the fluxes through the surfaces of all parts of the partition of the body. This statement is obvious for fluid flow.
In fact, we have proven that if the flux of a vector field is zero through some surface bounding a small volume, then this flux is zero through any closed surface.
So, for any magnetic field the magnetic flux theorem is valid: the magnetic flux through any closed surface is zero Ф m = 0.
Previously, we looked at flow theorems for the fluid velocity field and the electrostatic field. In these cases, the flow through a closed surface was completely determined by point sources of the field (sources and sinks of liquid, point charges). In the general case, the presence of a non-zero flux through a closed surface indicates the presence of point field sources. Hence, The physical content of the magnetic flux theorem is the statement about the absence of magnetic charges.
If you have a good understanding of this issue and are able to explain and defend your point of view, then you can formulate the magnetic flux theorem like this: “No one has yet found the Dirac monopole.”
It should be especially emphasized that when we talk about the absence of field sources, we mean precisely point sources, similar to electric charges. If we draw an analogy with the field of a moving fluid, electric charges are like points from which fluid flows out (or flows in), increasing or decreasing its amount. The emergence of a magnetic field, due to the movement of electric charges, is similar to the movement of a body in a liquid, which leads to the appearance of vortices that do not change the total amount of liquid.
Vector fields for which the flux through any closed surface is zero received a beautiful, exotic name - solenoidal. A solenoid is a coil of wire through which electric current can be passed. Such a coil can create strong magnetic fields, so the term solenoidal means “similar to the field of a solenoid,” although such fields could be called more simply “magnetic-like.” Finally, such fields are also called vortex, similar to the velocity field of a fluid that forms all kinds of turbulent vortices in its movement.
The magnetic flux theorem is of great importance; it is often used to prove various properties of magnetic interactions, and we will encounter it several times. For example, the magnetic flux theorem proves that the induction vector of the magnetic field created by an element cannot have a radial component, otherwise the flux through a cylindrical surface coaxial with the current element would be non-zero.
We now illustrate the application of the magnetic flux theorem to calculate the magnetic field induction. Let the magnetic field be created by a ring with current, which is characterized by a magnetic moment p m. Let us consider the field near the axis of the ring at a distance z from the center, significantly larger than the radius of the ring (Fig. 449). 
rice. 449
Previously, we obtained a formula for the magnetic field induction on the axis for large distances from the center of the ring 
We will not make a big mistake if we assume that the vertical (let the axis of the ring is vertical) component of the field within a small ring of radius has the same value r, the plane of which is perpendicular to the axis of the ring. Since the vertical field component changes with distance, radial field components must inevitably be present, otherwise the magnetic flux theorem will not hold! It turns out that this theorem and formula (3) are enough to find this radial component. Select a thin cylinder with a thickness Δz and radius r, the lower base of which is at a distance z from the center of the ring, coaxial with the ring and apply the magnetic flux theorem to the surface of this cylinder. The magnetic flux through the lower base is equal to (note that the induction and normal vectors are opposite here) 
Where Bz(z) z;
the flow through the upper base is
Where B z (z + Δz)− value of the vertical component of the induction vector at height z + Δz;
flow through the side surface (from axial symmetry it follows that the modulus of the radial component of the induction vector B r is constant on this surface): 
According to the proven theorem, the sum of these flows is equal to zero, so the equation is valid
from which we determine the required value
It remains to use formula (3) for the vertical component of the field and carry out the necessary calculations 3 
Indeed, a decrease in the vertical component of the field leads to the appearance of horizontal components: a decrease in outflow through the bases leads to “leakage” through the side surface.
Thus, we have proven the “criminal theorem”: if less flows out of one end of a pipe than is poured into it from the other end, then somewhere they are stealing through the side surface.
1 It is enough to take the text with the definition of the flow of the electric field strength vector and change the notation (which is what is done here).
2 Named in honor of the German physicist (member of the St. Petersburg Academy of Sciences) Wilhelm Eduard Weber (1804 – 1891)
3 The most literate can see the derivative of function (3) in the last fraction and simply calculate it, but we will have to once again use the approximate formula (1 + x) β ≈ 1 + βx.
In order to understand the meaning of the new concept of “magnetic flux”, we will analyze in detail several experiments with inducing an EMF, paying attention to the quantitative side of the observations made.
In our experiments we will use the setup shown in Fig. 2.24.
It consists of a large multi-turn coil wound, say, on a tube of thick glued cardboard. The coil is powered from the battery through a switch and an adjusting rheostat. The amount of current installed in the coil can be judged by an ammeter (not shown in Fig. 2.24).
Inside the large coil, another small coil can be installed, the ends of which are connected to a magnetoelectric device - a galvanometer.
For clarity of the picture, part of the coil is shown cut out - this allows you to see the location of the small coil.
When the switch is closed or opened, an EMF is induced in the small coil and the galvanometer needle is thrown from the zero position for a short time.
Based on the deviation, one can judge in which case the applied EMF is greater and in which it is less.
Rice. 2.24. A device on which you can study the induction of EMF by a changing magnetic field
By noticing the number of divisions by which the arrow is thrown, one can quantitatively compare the effect produced by the induced emf.
First observation. Having inserted a small one inside the large coil, we will secure it and for now we will not change anything in their location.
Let's turn on the switch and, by changing the resistance of the rheostat connected after the battery, set a certain current value, for example
Let us now turn off the switch while observing the galvanometer. Let its discard n be equal to 5 divisions to the right:
When the 1A current is turned off.
Let's turn on the switch again and, changing the resistance, increase the current of the large coil to 4 A.
Let's let the galvanometer calm down and turn off the switch again, observing the galvanometer.
If its discard was 5 divisions when turning off the current 1 A, now when turning off 4 A, we note that the discard has increased 4 times:
When the 4A current is turned off.
Continuing such observations, it is easy to conclude that the rejection of the galvanometer, and therefore the induced EMF, increases in proportion to the increase in the switched current.
But we know that a change in current causes a change in the magnetic field (its induction), so the correct conclusion from our observation is this:
the induced emf is proportional to the rate of change of magnetic induction.
More detailed observations confirm the correctness of this conclusion.
Second observation. Let's continue observing the galvanometer's rejection, turning off the same current, say, 1-4 A. But we will change the number of turns N of the small coil, leaving its location and dimensions unchanged.
Let us assume that the galvanometer rejection
observed at (100 turns on a small coil).
How will the rejection of the galvanometer change if the number of turns is doubled?
Experience shows that
This is exactly what was to be expected.
In fact, all turns of a small coil are under the same influence of a magnetic field, and the same EMF must be induced in each turn.
Let us denote the EMF of one turn by the letter E, then the EMF of 100 turns connected in series one after the other should be 100 times greater:
At 200 turns
For any other number of turns
If the emf increases in proportion to the number of turns, then it goes without saying that the rejection of the galvanometer should also be proportional to the number of turns.
This is what experience shows. So,
the induced emf is proportional to the number of turns.
We emphasize once again that the dimensions of the small coil and its location remained unchanged during our experiment. It goes without saying that the experiment was carried out in the same large coil with the same current turned off.
Third observation. Having carried out several experiments with the same small coil while the switched current remains constant, it is easy to verify that the magnitude of the induced emf depends on how the small coil is positioned.
To observe the dependence of the induced EMF on the position of the small coil, we will improve our setup somewhat (Fig. 2.25).
To the outward end of the axis of the small coil we attach an index arrow and a circle with division (like
Rice. 2.25. A device for turning a small coil mounted on a rod passed through the walls of a large coil. The rod is connected to the index arrow. The position of the arrow on the semi-circle with divisions shows how the small coil of those that can be found on radios is located).
By turning the rod, we can now judge by the position of the index arrow the position occupied by the small coil inside the large one.
Observations show that
the greatest emf is induced when the axis of the small coil coincides with the direction of the magnetic field,
in other words, when the axes of the large and small coils are parallel.
Rice. 2.26. To the conclusion of the concept of “magnetic flux”. The magnetic field is depicted by lines drawn at the rate of two lines per 1 cm2: a - a coil with an area of 2 cm2 is located perpendicular to the direction of the field. A magnetic flux is coupled to each turn of the coil. This flux is depicted by four lines crossing the coil; b - a coil with an area of 4 cm2 is located perpendicular to the direction of the field. A magnetic flux is coupled to each turn of the coil. This flux is depicted by eight lines crossing the coil; c - a coil with an area of 4 cm2 is located obliquely. The magnetic flux associated with each of its turns is depicted by four lines. It is equal as each line depicts, as can be seen from Fig. 2.26, a and b, flow c. The flux coupled to the coil is reduced due to its tilt
This arrangement of a small coil is shown in Fig. 2.26, a and b. As the coil rotates, the emf induced in it will become less and less.
Finally, if the plane of the small coil becomes parallel to the field lines, no emf will be induced in it. The question may arise, what will happen with further rotation of the small coil?
If we rotate the coil more than 90° (relative to the initial position), then the sign of the induced EMF will change. The field lines will enter the coil from the other side.
Fourth observation. It is important to make one final observation.
Let's choose a certain position in which we will place the small coil.
Let us agree, for example, to always place it in such a position that the induced EMF is as large as possible (of course, for a given number of turns and a given value of the switched-off current). Let's make several small coils of different diameters, but with the same number of turns.
We will place these coils in the same position and, turning off the current, we will observe the rejection of the galvanometer.
Experience will show us that
the induced emf is proportional to the cross-sectional area of the coils.
Magnetic flux. All observations allow us to conclude that
the induced emf is always proportional to the change in magnetic flux.
But what is magnetic flux?
First, we will talk about the magnetic flux through a flat area S forming a right angle with the direction of the magnetic field. In this case, the magnetic flux is equal to the product of the area and the induction or
here S is the area of our site, m2;; B - induction, T; F - magnetic flux, Wb.
The unit of flow is the weber.
Representing the magnetic field through lines, we can say that the magnetic flux is proportional to the number of lines piercing the area.
If the field lines are drawn so that their number on a perpendicular plane is equal to the field induction B, then the flux is equal to the number of such lines.
In Fig. 2.26 magnetic lule in is depicted by lines drawn at the rate of two lines per each line, thus corresponding to a magnetic flux of magnitude
Now, in order to determine the magnitude of the magnetic flux, it is enough to simply count the number of lines piercing the site and multiply this number by
In the case of Fig. 2.26, and the magnetic flux through an area of 2 cm2, perpendicular to the direction of the field,
In Fig. 2.26, and this area is pierced by four magnetic lines. In the case of Fig. 2.26, b magnetic flux through a transverse area of 4 cm2 at an induction of 0.2 T
and we see that the site is pierced by eight magnetic lines.
Magnetic flux coupled to a coil. When talking about induced EMF, we need to keep in mind the flux coupled to the coil.
A flow coupled with a coil is a flow that penetrates the surface bounded by the coil.
In Fig. 2.26 flux coupled to each turn of the coil, in the case of Fig. 2.26, a is equal to a in the case of Fig. 2.26, b the flow is
If the area is not perpendicular, but inclined to the magnetic lines, then it is no longer possible to determine the flux simply by multiplying the area by the induction. The flux in this case is defined as the product of induction and the projection area of our site. We are talking about a projection onto a plane perpendicular to the lines of the field, or, as it were, about a shadow cast by the platform (Fig. 2.27).
However, for any shape of the site, the flow is still proportional to the number of lines passing through it, or equal to the number of single lines piercing the site.
Rice. 2.27. To the output of the site projection. Carrying out the experiments in more detail and combining our third and fourth observations, one could draw the following conclusion; the induced emf is proportional to the area of the shadow that our small coil would cast on a plane perpendicular to the field lines if it were illuminated by rays of light parallel to the field lines. This shadow is called a projection
So, in Fig. 2.26, the flux through an area of 4 cm2 at an induction of 0.2 T is equal to only (lines priced at ). Representing the magnetic field with lines is very helpful in determining the flux.
If flux Ф is linked to each of the N turns of the coil, the product NФ can be called the complete flux linkage of the coil. The concept of flux linkage can be used especially conveniently when different flows are linked to different turns. In this case, the total flux linkage is the sum of the fluxes linked to each of the turns.
A few notes about the word "flow". Why are we talking about flow? Is this word associated with the idea of some kind of flow of something magnetic? In fact, when we say “electric current,” we imagine the movement (flow) of electric charges. Is the situation the same in the case of magnetic flux?
No, when we say “magnetic flux,” we only mean a specific measure of the magnetic field (field strength times area), similar to the measure used by engineers and scientists who study the movement of fluids. When water moves, they call it the flow of the product of the speed of water and the area of the transversely located platform (the flow of water in a pipe is equal to its speed by the cross-sectional area of the pipe).
Of course, the magnetic field itself, which is one of the types of matter, is also associated with a special form of motion. We do not yet have sufficiently clear ideas and knowledge about the nature of this movement, although modern scientists know a lot about the properties of the magnetic field: the magnetic field is associated with the existence of a special form of energy, its main measure is induction, another very important measure is magnetic flux.
