Magnetic lines of force are. What are magnetic field lines
What do we know about power lines? magnetic field, besides the fact that in the local space near permanent magnets or current-carrying conductors, there is a magnetic field that manifests itself in the form of lines of force, or in a more familiar combination - in the form of magnetic force lines?
There is very convenient way get a clear picture of the magnetic field lines using iron filings. To do this, you need to sprinkle some iron filings on a sheet of paper or cardboard and bring one of the magnet poles from below. The sawdust is magnetized and arranged along the magnetic field lines in the form of chains of micro magnets. In classical physics, magnetic field lines are defined as magnetic field lines, the tangents to which at each point indicate the direction of the field at that point.
Using the example of several figures with different locations of magnetic field lines, let us consider the nature of the magnetic field around current-carrying conductors and permanent magnets.
Figure 1 shows the view of the magnetic force lines of a circular coil with current, and Figure 2 shows the picture of the magnetic force lines around a straight wire with current. In Fig. 2, small magnetic arrows are used instead of sawdust. This figure shows how when the direction of the current changes, the direction of the magnetic field lines also changes. The relationship between the direction of the current and the direction of the magnetic force lines is usually determined using the “gimlet rule”, the rotation of the handle of which will show the direction of the magnetic force lines if the gimlet is screwed in in the direction of the current.
Figure 3 shows a picture of the magnetic force lines of a strip magnet, and Fig. 4 shows a picture of the magnetic force lines of a long solenoid with current. Noteworthy is the similarity in the external location of the magnetic field lines in both figures (Fig. 3 and Fig. 4). Lines of force from one end of the solenoid with current stretch to the other in the same way as with a strip magnet. The very shape of the magnetic force lines outside the current-carrying solenoid is identical to the shape of the lines of a strip magnet. A current-carrying solenoid also has north and south poles and a neutral zone. Two current-carrying solenoids, or a solenoid and a magnet, interact like two magnets.
What can you see by looking at pictures of the magnetic fields of permanent magnets, straight current-carrying conductors, or current-carrying coils using iron filings? main feature Magnetic force lines, as shown by pictures of the arrangement of sawdust, is their closedness. Another feature of magnetic force lines is their direction. A small magnetic needle placed at any point in the magnetic field will indicate the direction of the magnetic field lines with its north pole. For definiteness, we agreed to assume that the magnetic field lines emanate from the north magnetic pole of the strip magnet and enter its south pole. The local magnetic space near magnets or current-carrying conductors is a continuous elastic medium. The elasticity of this medium is confirmed by numerous experiments, for example, with the repulsion of like poles of permanent magnets.
Even earlier, I hypothesized that the magnetic field around magnets or current-carrying conductors is a continuous elastic medium with magnetic properties, in which interference waves are formed. Some of these waves are closed. It is in this continuous elastic medium that an interference pattern of magnetic field lines is formed, which manifests itself using iron filings. A continuous medium is created by radiation from sources in the microstructure of matter.
Let us recall the experiments on wave interference from a physics textbook, in which an oscillating plate with two points strikes water. This experiment shows that the mutual intersection of two waves at different angles does not have any effect on their further movement. In other words, the waves pass through each other without further affecting the propagation of each of them. For light (electromagnetic) waves the same pattern is true.
What happens in those areas of space in which two waves intersect (Fig. 5) - superimpose one on top of the other? Each particle of the medium located in the path of two waves simultaneously participates in the oscillations of these waves, i.e. its motion is the sum of the oscillations of two waves. These oscillations represent a picture of interference waves with their maxima and minima as a result of the superposition of two or more waves, i.e. the addition of their oscillations at each point in the medium through which these waves pass. Experiments have established that the phenomenon of interference is observed both in waves propagating in media and in electromagnetic waves, that is, interference is exclusively a property of waves and does not depend either on the properties of the medium or on its presence. It should be remembered that wave interference occurs provided that the oscillations are coherent (harmonized), i.e. the oscillations must have a constant phase difference over time and the same frequency.
In our case with iron filings magnetic force lines are the lines with the largest number sawdust located at the maxima of the interference waves, and lines with fewer sawdust located between the maxima (at the minima) of the interference waves.
Based on the above hypothesis, the following conclusions can be drawn.
1. A magnetic field is a medium that forms near permanent magnet or a conductor with current as a result of radiation from sources in the microstructure of a magnet or conductor of individual micromagnetic waves.
2. These micromagnetic waves interact at every point of the magnetic field, forming an interference pattern in the form of magnetic field lines.
3. Micromagnetic waves are closed micro energy vortices with micro poles that can attract each other, forming elastic closed lines.
4. Micro sources in the microstructure of matter, emitting micromagnetic waves that form an interference pattern of the magnetic field, have the same oscillation frequency, and their radiation has a constant phase difference over time.
How does the process of magnetization of bodies occur, which leads to the formation of a magnetic field around them, i.e. what processes occur in the microstructure of magnets and current-carrying conductors? To answer this and other questions, it is necessary to recall some features of the structure of the atom.
A MAGNETIC FIELD. BASICS OF FLUGE CONTROL
We live in the earth's magnetic field. A manifestation of the magnetic field is that the needle of the magnetic compass constantly points north. the same result can be obtained by placing the needle of a magnetic compass between the poles of a permanent magnet (Figure 34).
Figure 34 - Orientation of the magnetic needle near the magnet poles
Usually one of the poles of a magnet (south) is designated by the letter S, other - (northern) - letter N. Figure 34 shows two positions of the magnetic needle. In each position, the opposite poles of the arrow and the magnet attract each other. Therefore, the direction of the compass needle changed as soon as we moved it from its position 1 to position 2 . The reason for the attraction to the magnet and the turn of the arrow is the magnetic field. Turning the arrow as it moves up and to the right shows that the direction of the magnetic field in different points space does not remain unchanged.
Figure 35 shows the result of an experiment with magnetic powder poured onto a sheet of thick paper, which is located above the poles of the magnet. It can be seen that the powder particles form lines.
Powder particles entering a magnetic field become magnetized. Each particle has a north and south pole. Powder particles located nearby not only rotate in the magnetic field, but also stick to each other, lining up in lines. These lines are usually called magnetic field lines.
Figure 35 Arrangement of magnetic powder particles on a sheet of paper located above the magnet poles
By placing a magnetic needle near such a line, you will notice that the needle is located tangentially. In numbers 1 , 2 , 3 Figure 35 shows the orientation of the magnetic needle at the corresponding points. Near the poles, the density of the magnetic powder is greater than at other points on the sheet. This means that the magnitude of the magnetic field there has a maximum value. Thus, the magnetic field at each point is determined by the value of the quantity characterizing the magnetic field and its direction. Such quantities are usually called vectors.
Let's place the steel part between the poles of the magnet (Figure 36). The direction of the power lines in the part is shown by arrows. Magnetic field lines will also appear in the part, only there will be much more of them than in air.
Figure 36 Magnetizing a simple-shaped part
The fact is that the steel part contains iron, consisting of micromagnets called domains. The application of a magnetizing field to a part leads to the fact that they begin to orient themselves in the direction of this field and strengthen it many times. It can be seen that the field lines in the part are parallel to each other, while the magnetic field is constant. A magnetic field, which is characterized by straight parallel lines of force drawn with the same density, is called uniform.
10.2 Magnetic quantities
The most important physical quantity characterizing the magnetic field is the magnetic induction vector, which is usually denoted IN. For each physical quantity it is customary to indicate its dimension. So, the unit of current is Ampere (A), the unit of magnetic induction is Tesla (T). Magnetic induction in magnetized parts usually lies in the range from 0.1 to 2.0 Tesla.
A magnetic needle placed in a uniform magnetic field will rotate. The moment of force turning it around its axis is proportional to the magnetic induction. Magnetic induction also characterizes the degree of magnetization of a material. The lines of force shown in Figures 34, 35 characterize the change in magnetic induction in the air and material (parts).
Magnetic induction determines the magnetic field at every point in space. In order to characterize the magnetic field on some surface (for example, in the cross-sectional plane of a part), another physical quantity, which is called magnetic flux and is denoted Φ.
Let a uniformly magnetized part (Figure 36) be characterized by the value of magnetic induction IN, the cross-sectional area of the part is equal to S, then the magnetic flux is determined by the formula:
Unit magnetic flux- Weber (Wb).
Let's look at an example. The magnetic induction in the part is 0.2 T, the cross-sectional area is 0.01 m 2. Then the magnetic flux is 0.002 Wb.
Let us place a long cylindrical iron rod in a uniform magnetic field. Let the axis of symmetry of the rod coincide with the direction of the lines of force. Then the rod will be uniformly magnetized almost everywhere. The magnetic induction in the rod will be much greater than in the air. Magnetic induction ratio in a material B m to magnetic induction in air In in called magnetic permeability:
μ=B m / B in. (10.2)
Magnetic permeability is a dimensionless quantity. For different grades of steel, the magnetic permeability ranges from 200 to 5,000.
Magnetic induction depends on the properties of the material, which complicates technical calculations of magnetic processes. Therefore, an auxiliary quantity was introduced that does not depend on the magnetic properties of the material. It is called the magnetic field strength vector and is denoted H. The unit of magnetic field strength is Ampere/meter (A/m). During non-destructive magnetic testing of parts, the magnetic field strength varies from 100 to 100,000 A/m.
Between magnetic induction In in and magnetic field strength N there is a simple relationship in the air:
V in =μ 0 H, (10.3)
Where μ 0 = 4π 10 –7 Henry/meter - magnetic constant.
The magnetic field strength and magnetic induction in the material are related to each other by the relationship:
B=μμ 0 H (10.4)
Magnetic field strength N - vector. When fluxgate testing requires determining the components of this vector on the surface of the part. These components can be determined using Figure 37. Here the surface of the part is taken as a plane xy, axis z perpendicular to this plane.
In Figure 1.4 from the vertex of the vector H a perpendicular is dropped onto a plane x,y. A vector is drawn to the point of intersection of the perpendicular and the plane from the origin of coordinates H which is called the tangential component of the magnetic field strength of the vector H . Dropping perpendiculars from the vertex of the vector H on the axis x And y, we define the projections Hx And H y vector H. Projection H per axis z called the normal component of the magnetic field strength Hn . During magnetic testing, the tangential and normal components of the magnetic field strength are most often measured.
Figure 37 Vector of magnetic field strength and its projection on the surface of the part
10.3 Magnetization curve and hysteresis loop
Let us consider the change in magnetic induction of an initially demagnetized ferromagnetic material with a gradual increase in the strength of the external magnetic field. A graph reflecting this dependence is shown in Figure 38 and is called the initial magnetization curve. In the region of weak magnetic fields, the slope of this curve is relatively small, and then it begins to increase, reaching a maximum value. At even higher values of the magnetic field strength, the slope decreases so that the change in magnetic induction with increasing field becomes insignificant - magnetic saturation occurs, which is characterized by the magnitude B S. Figure 39 shows the dependence of magnetic permeability on magnetic field strength. This dependence is characterized by two values: the initial μ n and the maximum μ m magnetic permeability. In the region of strong magnetic fields, the permeability decreases with increasing field. With a further increase in the external magnetic field, the magnetization of the sample remains practically unchanged, and the magnetic induction increases only due to the external field .
Figure 38 Initial magnetization curve
Figure 39 Dependence of permeability on magnetic field strength
Magnetic induction saturation B S depends mainly on chemical composition material for both structural and electrical steels is 1.6-2.1 T. Magnetic permeability depends not only on the chemical composition, but also on thermal and mechanical treatment.
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Figure 40 Limit (1) and partial (2) hysteresis loops
Based on the magnitude of the coercive force, magnetic materials are divided into soft magnetic materials (H c< 5 000 А/м) и магнитотвердые (H c >5,000 A/m).
Soft magnetic materials require relatively low fields to achieve saturation. Hard magnetic materials are difficult to magnetize and remagnetize.
Most structural steels are soft magnetic materials. For electrical steel and special alloys, the coercive force is 1-100 A/m, for structural steels - no more than 5,000 A/m. Permanent magnet attachments use hard magnetic materials.
During magnetization reversal, the material is saturated again, but the induction value has a different sign (– B S), corresponding to negative magnetic field strength. With a subsequent increase in the magnetic field strength towards positive values, the induction will change along another curve, called the ascending branch of the loop. Both branches: descending and ascending, form a closed curve called the limit loop of magnetic hysteresis. The limit loop has a symmetrical shape and corresponds to a maximum value of magnetic induction equal to B S. With a symmetrical change in the magnetic field strength within smaller limits, the induction will change along a new loop. This loop is completely located inside the limit loop and is called a symmetric partial loop (Figure 40).
The parameters of the limiting magnetic hysteresis loop play important role with fluxgate control. At high values residual induction and coercive force can be monitored by pre-magnetizing the material of the part until saturation and then turning off the field source. The magnetization of the part will be sufficient to detect defects.
At the same time, the phenomenon of hysteresis leads to the need to control the magnetic state. In the absence of demagnetization, the material of the part may be in a state corresponding to induction - B r . Then, turning on a magnetic field of positive polarity, for example, equal to Hc, we can even demagnetize the part, although we are supposed to magnetize it.
Magnetic permeability is also important. The more μ , the lower the required value of the magnetic field strength to magnetize the part. That's why technical specifications magnetizing device must be consistent with the magnetic parameters of the test object.
10.4 Magnetic field of defect scattering
The magnetic field of a defective part has its own characteristics. Let's take a magnetized steel ring (part) with a narrow slot. This gap can be considered as a defect in the part. If you cover the ring with a sheet of paper sprinkled with magnetic powder, you can see a picture similar to that shown in Figure 35. The sheet of paper is located outside the ring, and meanwhile the powder particles line up along certain lines. Thus, the magnetic field lines partially pass outside the part, flowing around the defect. This part of the magnetic field is called the leakage field of the defect.
Figure 41 shows a long crack in the part, located perpendicular to the magnetic field lines, and a pattern of field lines near the defect.
Figure 41 Flow of force lines around a surface crack
It can be seen that the magnetic field lines flow around the crack inside and outside the part. The formation of a magnetic stray field by a subsurface defect can be explained using Figure 42, which shows a section of a magnetized part. Magnetic induction lines of force belong to one of three sections of the cross section: above the defect, in the defect zone and below the defect. The product of magnetic induction and cross-sectional area determines the magnetic flux. The components of the total magnetic flux in these sections are designated as Φ 1 ,.., Part of magnetic flux F 2, will flow above and below the section S 2. Therefore, magnetic fluxes in sections S 1 And S 3 will be greater than that of a defect-free part. The same can be said about magnetic induction. Another important feature magnetic induction lines of force is their curvature above and below the defect. As a result, part of the field lines leaves the part, creating a magnetic scattering field of the defect.
3 .
Figure 42 Scattering field of a subsurface defect
The leakage magnetic field can be quantified by the magnetic flux leaving the part, which is called leakage flux. The greater the magnetic flux, the greater the leakage magnetic flux Φ 2 in cross section S 2. Cross-sectional area S 2 proportional to the cosine of the angle , shown in Figure 42. At = 90° this area is zero, at =0° it matters the most.
Thus, to identify defects, it is necessary that the magnetic induction lines in the inspection zone of the part be perpendicular to the plane of the suspected defect.
The distribution of magnetic flux over the cross section of a defective part is similar to the distribution of water flow in a channel with an obstacle. The height of the wave in the zone of a completely submerged obstacle will be greater, the closer the obstacle crest is to the water surface. Similarly, a subsurface defect in a part is easier to detect, the smaller the depth of its occurrence.
10.5 Defect detection
To detect defects, a device is required that allows one to determine the characteristics of the defect's scattering field. This magnetic field can be determined by its components N x, N y, N z.
However, stray fields can be caused not only by a defect, but also by other factors: structural inhomogeneity of the metal, a sharp change in the cross section (in detail complex shape), machining, impacts, surface roughness, etc. Therefore, analysis of the dependence of even one projection (for example, Hz) from spatial coordinate ( x or y) can be a challenging task.
Let's consider the magnetic stray field near the defect (Figure 43). Shown here is an idealized infinitely long crack with smooth edges. It is elongated along the axis y, which is directed towards us in the figure. Numbers 1, 2, 3, 4 show how the magnitude and direction of the magnetic field strength vector changes when approaching the crack from the left.
Figure 43 Magnetic stray field near a defect
The magnetic field is measured at a certain distance from the surface of the part. The trajectory along which the measurements are taken is shown with a dotted line. The magnitudes and directions of the vectors to the right of the crack can be constructed in a similar way (or use the symmetry of the figure). To the right of the scattering field picture is an example of the spatial position of the vector H and its two components Hx And Hz . Projection dependency graphs Hx And Hz scattering fields from the coordinate x are shown below.
It would seem that by looking for the extremum of H x or the zero of H z , one can find a defect. But as noted above, stray fields are formed not only from defects, but also from structural inhomogeneities of the metal, from traces of mechanical influences, etc.
Let's consider a simplified picture of the formation of stray fields on a simple part (Figure 44) similar to the one shown in Figure 41, and graphs of projection dependencies H z , H x from coordinate x(the defect is extended along the axis y).
According to dependency graphs Hx And Hz from x detecting a defect is very difficult, since the values of the extrema Hx And Hz over a defect and over inhomogeneities are commensurate.
A solution was found when it was discovered that in the defect area the maximum rate of change (slope) of the magnetic field strength of a certain coordinate is greater than other maxima.
Figure 44 shows that the maximum slope of the graph Hz(x) between points x 1 And x 2(i.e. in the area where the defect is located) is much greater than in other places.
Thus, the device should measure not the projection of the field strength, but the “rate” of its change, i.e. the ratio of the difference in projections at two adjacent points above the surface of the part to the distance between these points:
(10.5)
Where H z (x 1), H z (x 2)- vector projection values H per axis z at points x 1 , x 2(to the left and right of the defect), Gz(x) is commonly called the magnetic field strength gradient.
Addiction Gz(x) shown in Figure 44. Distance Dx = x 2 – x 1 between the points at which the projections of the vector are measured H per axis z, is selected taking into account the size of the scattering field of the defect.
As follows from Figure 44, and this is in good agreement with practice, the value of the gradient above the defect is significantly greater than its value above the inhomogeneities of the metal of the part. This is what makes it possible to reliably register a defect when the gradient exceeds a threshold value (Figure 44).
By choosing the required threshold value, you can reduce control errors to minimum values.
Figure 44 Magnetic field lines of a defect and inhomogeneities in the metal of a part.
10.6 Fluxgate method
The fluxgate method is based on measuring with a fluxgate device the gradient of the stray magnetic field strength created by a defect in a magnetized product, and comparing the measurement result with a threshold.
Outside the controlled part, there is a certain magnetic field that is created to magnetize it. The use of a flaw detector - gradiometer ensures that the signal caused by the defect is isolated against the background of a rather large component of the magnetic field strength that slowly changes in space.
A fluxgate flaw detector uses a transducer that responds to the gradient component of the normal component of the magnetic field strength on the surface of the part. The flaw detector transducer contains two parallel rods made of a special soft magnetic alloy. When testing, the rods are perpendicular to the surface of the part, i.e. parallel to the normal component of the magnetic field strength. The rods have identical windings through which alternating current flows. These windings are connected in series. Alternating current creates alternating components of magnetic field strength in the rods. These components coincide in magnitude and direction. In addition, there is a constant component of the magnetic field strength of the part at the location of each rod. Magnitude Δx, which is included in formula (10.5), is equal to the distance between the axes of the rods and is called the base of the transducer. The output voltage of the converter is determined by the difference alternating voltages on the windings.
Let's place the flaw detector transducer on the area of the part without a defect, where the values of the magnetic field strength at points x 1; x 2(see formula (10.5)) are the same. This means that the magnetic field strength gradient equal to zero. Then the same constant and alternating components of the magnetic field strength will act on each converter rod. These components will equally remagnetize the rods, so the voltages on the windings are equal to each other. The voltage difference that determines the output signal is zero. Thus, the flaw detector transducer does not respond to the magnetic field if there is no gradient.
If the magnetic field strength gradient is not zero, then the rods will be in the same alternating magnetic field, but the constant components will be different. Each rod is remagnetized by the alternating current of the winding from the state with magnetic induction - In S to + In S According to the law electromagnetic induction voltage on the winding can only appear when the magnetic induction changes. Therefore, the oscillation period alternating current can be divided into intervals when the rod is in saturation and, therefore, the voltage on the winding is zero, and into periods of time when there is no saturation, and, therefore, the voltage differs from zero. During those periods of time when both rods are not magnetized to saturation, equal voltages appear on the windings. At this time, the output signal is zero. The same will happen if both rods are simultaneously saturated, when there is no voltage on the windings. The output voltage appears when one core is in a saturated state and the other is in an unsaturated state.
The simultaneous influence of the constant and variable components of the magnetic field strength leads to the fact that each core is in one saturated state for more than long time than in another. Longer saturation corresponds to the addition of the constant and variable components of the magnetic field strength, and shorter saturation corresponds to subtraction. The difference between time intervals that correspond to the values of magnetic induction + In S And - In S, depends on the strength of the constant magnetic field. Consider a state with magnetic induction + In S at two transducer rods. Uneven values of magnetic field strength at points x 1 And x 2 will correspond to different durations of intervals of magnetic saturation of the rods. The greater the difference between these magnetic field strengths, the more different the time intervals are. During those periods of time when one rod is saturated and the other is unsaturated, the output voltage of the converter occurs. This voltage depends on the gradient of the magnetic field strength.
About two and a half thousand years ago, people discovered that some natural stones have the ability to attract iron. This property was explained by the presence of a living soul in these stones, and a certain “love” for iron.
Today we already know that these stones are natural magnets, and the magnetic field, and not a special location towards the iron, creates these effects. The magnetic field is special kind matter, which is different from matter and exists around magnetized bodies.
Permanent magnets
Natural magnets, or magnetites, do not have very strong magnetic properties. But man has learned to create artificial magnets that have significantly greater strength magnetic field. They are made from special alloys and are magnetized by an external magnetic field. And after that they can be used independently.
Magnetic field lines
Any magnet has two poles, they are called the north and south poles. At the poles the concentration of the magnetic field is maximum. But between the poles the magnetic field is also not located arbitrarily, but in the form of stripes or lines. They are called magnetic field lines. Detecting them is quite simple - just place scattered iron filings in a magnetic field and shake them slightly. They will not be located in any way, but form a kind of pattern of lines starting at one pole and ending at the other. These lines seem to come out of one pole and enter the other.
Iron filings in the field of a magnet become magnetized themselves and are placed along the magnetic lines of force. This is exactly how a compass functions. Our planet is a big magnet. The compass needle picks up the Earth's magnetic field and, turning, is located along the lines of force, with one end pointing to the north magnetic pole, the other to the south. The Earth's magnetic poles are slightly misaligned with the geographic ones, but when traveling away from the poles, this does not matter of great importance, and they can be considered identical.
Variable magnets
The scope of application of magnets in our time is extremely wide. They can be found inside electric motors, telephones, speakers, and radio devices. Even in medicine, for example, when a person swallows a needle or other iron object, it can be removed without surgery using a magnetic probe.
Thus, the magnetic field induction on the axis of a circular coil with current decreases in inverse proportion to the third power of the distance from the center of the coil to a point on the axis. The magnetic induction vector on the coil axis is parallel to the axis. Its direction can be determined using the right screw: if you direct the right screw parallel to the axis of the coil and rotate it in the direction of the current in the coil, then the direction of the translational movement of the screw will show the direction of the magnetic induction vector.
3.5 Magnetic field lines
A magnetic field, like an electrostatic one, can be conveniently represented in graphical form - using magnetic field lines.
A magnetic field line is a line whose tangent at each point coincides with the direction of the magnetic induction vector.
The magnetic field lines are drawn in such a way that their density is proportional to the magnitude of the magnetic induction: the greater the magnetic induction at a certain point, the greater the density of the field lines.
Thus, magnetic field lines are similar to electrostatic field lines.
However, they also have some peculiarities.
Consider the magnetic field created by a straight conductor with current I.
Let this conductor be perpendicular to the plane of the drawing.
At different points located at equal distances from the conductor, the induction is the same in magnitude.
Vector direction IN at different points shown in the figure.
A line whose tangent at all points coincides with the direction of the magnetic induction vector is a circle.
Consequently, the magnetic field lines in this case are circles surrounding the conductor. The centers of all power lines are located on the conductor.
Thus, the magnetic field lines are closed (electrostatic field lines cannot be closed, they begin and end at the charges).
Therefore the magnetic field is vortex(this is the name for fields whose field lines are closed).
The closedness of the field lines means another, very important feature of the magnetic field - in nature there are no (at least not yet discovered) magnetic charges that would be a source of a magnetic field of a certain polarity.
Therefore, there is no separately existing north or south magnetic pole of a magnet.
Even if you cut a permanent magnet in half, you get two magnets, each with both poles.
3.6. Lorentz force
It has been experimentally established that a force acts on a charge moving in a magnetic field. This force is usually called the Lorentz force:
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Lorentz force modulus
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where a is the angle between the vectors v And B .
The direction of the Lorentz force depends on the direction of the vector. It can be defined using the right hand rule or the left hand rule. But the direction of the Lorentz force does not necessarily coincide with the direction of the vector!
The fact is that the Lorentz force is equal to the result of the product of the vector [ v , IN ] to a scalar q. If the charge is positive, then F l parallel to the vector [ v , IN ]. If q< 0, то сила Лоренца противоположна направлению вектора [v , IN ] (see picture).
If a charged particle moves parallel to the magnetic field lines, then the angle a between the velocity and magnetic induction vectors is zero. Consequently, the Lorentz force does not act on such a charge (sin 0 = 0, F l = 0).
If the charge moves perpendicular to the magnetic field lines, then the angle a between the velocity and magnetic induction vectors is equal to 90 0. In this case, the Lorentz force has the maximum possible value: F l = q v B.
The Lorentz force is always perpendicular to the speed of the charge. This means that the Lorentz force cannot change the magnitude of the speed of movement, but changes its direction.
Therefore, in a uniform magnetic field, a charge flying into a magnetic field perpendicular to its lines of force will move in a circle.
If only the Lorentz force acts on the charge, then the motion of the charge obeys the following equation, based on Newton’s second law: ma = F l.
Since the Lorentz force is perpendicular to the speed, the acceleration of the charged particle is centripetal (normal): (here R– radius of curvature of the trajectory of a charged particle).
Without a doubt, magnetic field lines are now known to everyone. At least at school, their manifestation is demonstrated in physics lessons. Remember how the teacher placed a permanent magnet (or even two, combining the orientation of their poles) under a sheet of paper, and on top of it he poured metal filings taken from the labor training classroom? It is quite clear that the metal had to be held on the sheet, but something strange was observed - the lines along which the sawdust lined up were clearly visible. Please note - not evenly, but in stripes. These are the magnetic field lines. Or rather, their manifestation. What happened then and how can it be explained?
Let's start from afar. A special type of matter coexists with us in the visible physical world - a magnetic field. It ensures the interaction of moving elementary particles or larger bodies with electric charge or natural Electrical and are not only interconnected with each other, but also often generate themselves. For example, a wire through which flows electricity, creates magnetic field lines around itself. The opposite is also true: the effect of alternating magnetic fields on a closed conducting circuit creates movement of charge carriers in it. The latter property is used in generators that supply electrical energy to all consumers. A striking example of electromagnetic fields is light.
The magnetic field lines around the conductor rotate or, which is also true, are characterized by a directed vector of magnetic induction. The direction of rotation is determined by the gimlet rule. The indicated lines are a convention, since the field extends evenly in all directions. The thing is that it can be represented in the form of an infinite number of lines, some of which have more pronounced tension. That is why certain “lines” are clearly visible in the sawdust. Interestingly, the magnetic field lines are never interrupted, so it is impossible to say unambiguously where the beginning is and where the end is.
In the case of a permanent magnet (or a similar electromagnet), there are always two poles, conventionally called North and South. The lines mentioned in this case are rings and ovals connecting both poles. Sometimes this is described in terms of interacting monopoles, but then a contradiction arises, according to which the monopoles cannot be separated. That is, any attempt to divide a magnet will result in the appearance of several bipolar parts.
The properties of field lines are of great interest. We have already talked about continuity, but of practical interest is the ability to create an electric current in a conductor. The meaning of this is as follows: if the conductive contour is crossed by lines (or the conductor itself moves in a magnetic field), then additional energy is imparted to the electrons in the outer orbits of the atoms of the material, allowing them to begin independent directed movement. We can say that the magnetic field seems to “knock out” charged particles from the crystal lattice. This phenomenon is called electromagnetic induction and is currently the main way to obtain primary electrical energy. It was discovered experimentally in 1831 by the English physicist Michael Faraday.
The study of magnetic fields began back in 1269, when P. Peregrinus discovered the interaction of a spherical magnet with steel needles. Almost 300 years later, W. G. Colchester suggested that he himself was a huge magnet with two poles. Further, magnetic phenomena were studied by such famous scientists as Lorentz, Maxwell, Ampere, Einstein, etc.
