Place the palm of your left hand in such a way that the lines of magnetic induction seem to enter it, and four extended fingers, folded parallel to each other, indicate the direction of movement of the positive. As a result, the thumb of the left hand, bent at an angle of 90, will indicate the direction of the Lorentz force. If the gimlet rule is applied to negative charges, then four outstretched fingers position the speed of movement of the charged ones.
Induction magnetic field, which is the force characteristic of the field formed by an electric current, can be found using the given formula. Here rₒ is the radius vector. It indicates the point at which we find the strength of the magnetic field. Dl is the length of the section forming the magnetic field, and I is, accordingly, the current strength. In the SI system, µₒ is a magnetic constant equal to the product of 4π by 10 v - .
Define the Lorentz force modulus as the product of the following quantities: carrier charge modulus, speed of ordered movement of the carrier along the conductor, magnetic field induction modulus, angle between the vectors of the indicated speed and magnetic induction. This is true for all values of charged speed.
Write down the expression and make the necessary calculations.
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Please note
If a charged particle moves in a magnetic field characterized by uniformity, then when the Lorentz force acts on it, the velocity vector of this particle will lie in a plane perpendicular to the magnetic induction vector. As a result, the charged object will move in a circle. In such cases, the Lorentz magnetic force becomes centripetal force.
The direction of the Lorentz force is perpendicular to the direction of the velocity and magnetic induction vectors. At the moment of motion of a charged particle in a magnetic field, this force does not do any work. Consequently, the magnitude of the velocity vector is preserved at this time, and only the direction of this vector changes.
Sources:
- Magnetic interaction of currents
Tip 2: Magnetic field strength and its main characteristics
A magnetic field is one of the forms of matter, objective reality. It is invisible to the human eye, but its existence is manifested in the form of magnetic forces that affect charged particles and permanent magnets.
Graphic representation of magnetic field
The magnetic field is invisible by nature. For convenience, a method has been developed graphic image in the form of power lines. Their direction must coincide with the direction of the magnetic field forces. Lines of force have no beginning and end: they are closed. This reflects one of Maxwell's equations in the theory of electromagnetic interaction. It is accepted by the scientific community that the lines of force “begin” at the north pole of the magnet and “end” at the south pole. This addition was made solely to conditionally specify the direction of the magnetic field force vector.
The closedness of the magnetic field lines can be verified using a simple experiment. Need to permanent magnet and the area around it with iron filings. They will be positioned in such a way that you can see the lines of force themselves.
Magnetic field strength
The magnetic field strength vector is the same vector described in the previous section. It is its direction that must coincide with the direction of the lines of force. This is the force with which the field acts on a permanent magnet placed in it. Tension characterizes the interaction of a magnetic field with surrounding matter. There is a special one with which you can determine the modulus of its vector at any point in space (Biot-Savart-Laplace law). The tension does not depend on the magnetic properties of the medium and is measured in oersteds (in the CGS system) and in A/m (SI).
Magnetic field induction and magnetic flux
The magnetic field induction characterizes its intensity, i.e. ability to produce work. The higher this ability, the stronger the field and the higher the concentration of field lines in 1 m2. Magnetic flux is the product of induction and the area affected by the field. Numerically, this value is usually equated to the number of field lines penetrating certain area. The flow is maximum if the site is located perpendicular to the direction of the tension vector. The smaller this angle, the weaker the impact.
Magnetic permeability
The effect of a magnetic field in a certain medium depends on its magnetic permeability. This value characterizes the magnitude of induction in the medium. Air and some substances have a magnetic permeability of vacuum (the value is taken from the table of physical constants). In ferromagnets it is thousands of times greater.
Along with pieces of amber electrified by friction, permanent magnets were the first material evidence for ancient people electromagnetic phenomena(at the dawn of history, lightning was definitely attributed to the sphere of manifestation of intangible forces). Explaining the nature of ferromagnetism has always occupied the inquisitive minds of scientists, but even today physical nature permanent magnetization of some substances, both natural and artificially created, has not yet been fully disclosed, leaving a considerable field of activity for modern and future researchers.
Traditional materials for permanent magnets
They have been actively used in industry since 1940 with the advent of alnico alloy (AlNiCo). Previously, permanent magnets made of various types of steel were used only in compasses and magnetos. Alnico made it possible to replace electromagnets with them and use them in devices such as motors, generators and loudspeakers.
This is their penetration into our daily life received new impetus with the creation of ferrite magnets, and since then permanent magnets have become commonplace.
The revolution in magnetic materials began around 1970, with the creation of the samarium-cobalt family of hard magnetic materials with previously unheard-of magnetic energy densities. Then a new generation of rare earth magnets was discovered, based on neodymium, iron and boron, with a much higher magnetic energy density than samarium cobalt (SmCo) and at an expectedly low cost. These two families of rare earth magnets have such high energy densities that they can not only replace electromagnets, but be used in areas that are inaccessible to them. Examples include the tiny permanent magnet stepper motor in wristwatches and the sound transducers in Walkman-type headphones.
The gradual improvement in the magnetic properties of materials is shown in the diagram below.
Neodymium permanent magnets
They represent the latest and most significant development in this field over the past decades. Their discovery was first announced almost simultaneously at the end of 1983 by metal specialists from Sumitomo and General Motors. They are based on the intermetallic compound NdFeB: an alloy of neodymium, iron and boron. Of these, neodymium is a rare earth element extracted from the mineral monazite.
The great interest that these permanent magnets have aroused arises because for the first time a new magnetic material, which is not only stronger than previous generation, but is more economical. It consists mainly of iron, which is much cheaper than cobalt, and neodymium, which is one of the most common rare earth materials and has more reserves on Earth than lead. The major rare earth minerals monazite and bastanesite contain five to ten times more neodymium than samarium.
Physical mechanism of permanent magnetization
To explain the functioning of a permanent magnet, we must look inside it down to the atomic scale. Each atom has a set of spins of its electrons, which together form its magnetic moment. For our purposes, we can consider each atom as a small bar magnet. When a permanent magnet is demagnetized (either by heating it to a high temperature or by an external magnetic field), each atomic moment is oriented randomly (see figure below) and no regularity is observed.
When it is magnetized in a strong magnetic field, all atomic moments are oriented in the direction of the field and, as it were, interlocked with each other (see figure below). This coupling allows the permanent magnet field to be maintained when removed external field, and also resist demagnetization when changing its direction. A measure of the cohesive force of atomic moments is the magnitude of the coercive force of the magnet. More on this later.
In a more in-depth presentation of the magnetization mechanism, they do not operate with the concepts of atomic moments, but use ideas about miniature (of the order of 0.001 cm) regions inside the magnet, which initially have permanent magnetization, but are randomly oriented in the absence of an external field, so that a strict reader, if desired, can refer to the above physical mechanism not to the magnet in general. but to its separate domain.
Induction and magnetization
The atomic moments are summed up and form the magnetic moment of the entire permanent magnet, and its magnetization M shows the magnitude of this moment per unit volume. Magnetic induction B shows that a permanent magnet is the result of an external magnetic force (field strength) H applied during primary magnetization, as well as an internal magnetization M due to the orientation of atomic (or domain) moments. Its value in the general case is given by the formula:
B = µ 0 (H + M),
where µ 0 is a constant.
In a permanent ring and homogeneous magnet, the field strength H inside it (in the absence of an external field) is equal to zero, since, according to the law of total current, the integral of it along any circle inside such a ring core is equal to:
H∙2πR = iw=0, whence H=0.
Therefore, the magnetization in a ring magnet is:
In an open magnet, for example, in the same ring magnet, but with an air gap of width l in a core of length l gray, in the absence of an external field and the same induction B inside the core and in the gap, according to the law of total current, we obtain:
H ser l ser + (1/ µ 0)Bl zaz = iw=0.
Since B = µ 0 (H ser + M ser), then, substituting its expression into the previous one, we get:
H ser (l ser + l zaz) + M ser l zaz =0,
H ser = ─ M ser l zaz (l ser + l zaz).
In the air gap:
H zaz = B/µ 0,
wherein B is determined by the given M ser and the found H ser.
Magnetization curve
Starting from the unmagnetized state, when H increases from zero, due to the orientation of all atomic moments in the direction of the external field, M and B quickly increase, changing along section “a” of the main magnetization curve (see figure below).
When all atomic moments are equalized, M comes to its saturation value, and a further increase in B occurs solely due to the applied field (section b of the main curve in the figure below). When the external field decreases to zero, the induction B decreases not along the original path, but along section “c” due to the coupling of atomic moments, tending to maintain them in the same direction. The magnetization curve begins to describe the so-called hysteresis loop. When H (external field) approaches zero, the induction approaches a residual value determined only by atomic moments:
B r = μ 0 (0 + M g).
After the direction of H changes, H and M act in opposite directions and B decreases (part of the curve “d” in the figure). The value of the field at which B decreases to zero is called the coercive force of the magnet B H C . When the magnitude of the applied field is large enough to break the cohesion of the atomic moments, they are oriented in the new direction of the field, and the direction of M is reversed. The field value at which this occurs is called the internal coercive force of the permanent magnet M H C . So, there are two different but related coercive forces associated with a permanent magnet.
The figure below shows the basic demagnetization curves of various materials for permanent magnets.
It can be seen from it that NdFeB magnets have the highest residual induction B r and coercive force (both total and internal, i.e., determined without taking into account the strength H, only by the magnetization M).
Surface (ampere) currents
The magnetic fields of permanent magnets can be considered as the fields of some associated currents flowing along their surfaces. These currents are called Ampere currents. In the usual sense of the word, there are no currents inside permanent magnets. However, comparing the magnetic fields of permanent magnets and the fields of currents in coils, the French physicist Ampere suggested that the magnetization of a substance can be explained by the flow of microscopic currents, forming microscopic closed circuits. And indeed, the analogy between the field of a solenoid and a long cylindrical magnet is almost complete: there is a north and South Pole permanent magnet and the same poles of the solenoid, and the patterns of their field lines are also very similar (see figure below).
Are there currents inside a magnet?
Let's imagine that the entire volume of some bar permanent magnet (with an arbitrary shape) cross section) is filled with microscopic Ampere currents. A cross section of a magnet with such currents is shown in the figure below.
Each of them has a magnetic moment. With the same orientation in the direction of the external field, they form a resulting magnetic moment that is different from zero. It determines the existence of a magnetic field in the apparent absence of ordered movement of charges, in the absence of current through any cross section of the magnet. It is also easy to understand that inside it, the currents of adjacent (contacting) circuits are compensated. Only the currents on the surface of the body, which form the surface current of a permanent magnet, are uncompensated. Its density turns out to be equal to the magnetization M.
How to get rid of moving contacts
The problem of creating a contactless synchronous machine is known. Its traditional design with electromagnetic excitation from the poles of a rotor with coils involves supplying current to them through movable contacts - slip rings with brushes. The disadvantages of such a technical solution are well known: they are difficulties in maintenance, low reliability, and large losses in moving contacts, especially when it comes to powerful turbo and hydrogen generators, the excitation circuits of which consume considerable electrical power.
If you make such a generator using permanent magnets, then the contact problem immediately goes away. However, there is a problem of reliable fastening of magnets on a rotating rotor. This is where the experience gained in tractor manufacturing can come in handy. They have long been using an inductor generator with permanent magnets located in rotor slots filled with a low-melting alloy.
Permanent magnet motor
In recent decades, DC motors have become widespread. Such a unit consists of the electric motor itself and an electronic commutator for its armature winding, which performs the functions of a collector. The electric motor is a synchronous motor with permanent magnets located on the rotor, as in Fig. above, with a stationary armature winding on the stator. Electronic switch circuitry is an inverter of direct voltage (or current) of the supply network.
The main advantage of such a motor is its non-contact nature. Its specific element is a photo-, induction or Hall rotor position sensor that controls the operation of the inverter.
Even in ancient times, people discovered unique properties certain stones - attracting metal. Nowadays, we often come across objects that have these qualities. What is a magnet? What is his strength? We will talk about this in this article.
An example of a temporary magnet is paper clips, buttons, nails, a knife and other household items made of iron. Their strength lies in the fact that they are attracted to a permanent magnet, and when the magnetic field disappears, they lose their properties.
The field of an electromagnet can be controlled using electric current. How it happens? A wire wound in turns on an iron core changes the strength of the magnetic field and its polarity when a current is supplied and changed.
Types of permanent magnets
Ferrite magnets are the most famous and actively used in everyday life. This black material can be used as fasteners for various items, such as posters, wall boards used in the office or school. They do not lose their attractive properties at temperatures not lower than 250 o C.
Alnico is a magnet consisting of an alloy of aluminum, nickel and cobalt. This gave it its name. It is very resistant to high temperatures and can be used at 550 o C. The material is lightweight, but completely loses its properties when exposed to a stronger magnetic field. Mainly used in the scientific industry.
Samarium magnetic alloys are high performance materials. The reliability of its properties allows the material to be used in military developments. It is resistant to aggressive environments, high temperatures, oxidation and corrosion.
What is a neodymium magnet? It is the most popular alloy of iron, boron and neodymium. It is also called a supermagnet, as it has a powerful magnetic field with high coercive force. By observing certain conditions during operation, a neodymium magnet can retain its properties for 100 years.
Use of neodymium magnets
It is worth taking a closer look at what a neodymium magnet is? This is a material that is capable of recording the consumption of water, electricity and gas in meters, and not only. This type of magnet belongs to permanent and rare earth materials. It is resistant to fields of other alloys and is not subject to demagnetization.
Neodymium products are used in the medical and industrial industries. Also in domestic conditions they are used for attaching curtains, decorative elements, and souvenirs. They are used in search instruments and electronics.
To extend their service life, magnets of this type are coated with zinc or nickel. In the first case, spraying is more reliable, as it is resistant to aggressive agents and can withstand temperatures above 100 o C. The strength of the magnet depends on its shape, size and the amount of neodymium included in the alloy.
Applications of Ferrite Magnets
Ferrites are considered the most popular permanent magnets. Thanks to strontium included in the composition, the material does not corrode. So what is a ferrite magnet? Where is it used? This alloy is quite fragile. That's why it is also called ceramic. Ferrite magnets are used in automotive and industrial applications. It is used in various equipment and electrical appliances, as well as household installations, generators, and acoustic systems. In automobile manufacturing, magnets are used in cooling systems, window lifters, and fans.
The purpose of ferrite is to protect equipment from external interference and prevent damage to the signal received via the cable. Thanks to this, they are used in the production of navigators, monitors, printers and other equipment where it is important to obtain a clean signal or image.
Magnetotherapy
A procedure called magnetic therapy is often used and is carried out for therapeutic purposes. The action of this method is to influence the patient's body using magnetic fields under low-frequency alternating or DC. This treatment method helps get rid of many diseases, relieve pain, strengthen immune system, improve blood flow.
It is believed that diseases are caused by disturbances in the human magnetic field. Thanks to physiotherapy, the body returns to normal and the general condition improves.
From this article you learned what a magnet is, and also studied its properties and applications.
Widely used in electrical engineering, mechanical engineering and many other industries. It should be remembered that the properties and characteristics of neodymium magnets depend on a number of factors. For their effective practical application It is important to consider the size, shape and power of the products. Their weaknesses, including operating temperature limitations, should also be considered. Only taking into account the characteristics and classes of neodymium magnets is it possible to select product options that are optimal in price and magnetic strength.
How to determine the power of a neodymium magnet
The key characteristic for a magnet is its power. This parameter should be taken into account when selecting suitable products to solve specific problems. applied problems. The easiest way to determine the power of a neodymium magnet and its compliance with the planned use is to pay attention to the following parameters:
1) Grip strength. The description of the magnets indicates the pullout force indicator. Based on this characteristic, it is possible to judge the mass of objects that can be held, as well as the required force to detach them. The power of neodymium magnets is usually indicated in kilograms and sometimes in newtons.
2) Alloy number. The properties of a material based on a compound of neodymium, iron and boron depend on additional inclusions. Based on how the demagnetization curve of neodymium magnets performs when using a certain alloy, it receives its specific number. For example, N 38 or neodymium magnets N 45. The alloy number is directly proportional to the pullout force. Thus, by this indicator one can judge the power of a neodymium magnet.
3) Induction. If you plan to use the material to solve complex technical problems, then taking into account the tear force or alloy number will not be enough. Additionally, the induction of the neodymium magnet must be known. In particular, this indicator is of key importance when choosing materials for activating Hall sensors or reed relays. The magnetic induction of neodymium magnets determines the strength and direction of the field at a specific point located near the magnet. Its measurement is carried out in Gauss and Tesla (1 Tesla=10,000 Gauss).
What parameters determine the properties of neodymium magnets
How to choose the right powerful neodymium magnet
In most cases, the power of the simplest and most inexpensive magnets is sufficient for household use. But in a situation where the adhesion force of neodymium magnets comes first, certain characteristics of the products and the conditions of their use should be taken into account:
When choosing magnets for various purposes, you should pay attention to the main characteristics that affect their performance. These characteristics include:
- Magnetic induction(IN). The units of measurement are Tesla or Gauss. This parameter is found by measuring the induction on the surface of the magnet with a gaussmeter. The measurement result depends on many factors, such as the shape of the magnet, the measuring point, the properties of the measuring sensor and others. Because of this, magnetic flux density is not a reliable way to compare the strength of magnets.
- Residual magnetic induction(Br). The units of measurement are Tesla or Gauss. This value shows the maximum magnetic field strength that a magnet can create in a closed magnetic system. Is enough in a good way compare the strength of different magnets, but you need to take into account that magnets in a closed system are practically never used anywhere
- Coercive magnetic force(NS). Units of measurement are Ampere/meter or Oersted. Coercive force characterizes the resistance of a magnet to demagnetization under the influence of an external magnetic field. The higher this indicator, the more reliably the magnetic material retains its residual magnetization.
- Magnetic energy(VN)max . Measured in MGauss*Oersted. This indicator determines the strength of the magnet. The greater the amount of magnetic energy, the more powerful the magnet. For example, neodymium magnets N45 have a strength of 45 MGse, and ferrite C8 magnets have a strength of 8 MGse.
- Temperature coefficient of residual magnetic induction(ТсBr). It is measured in %/0С. A parameter showing the degree of change in magnetic induction under the influence of temperature. For example, if a magnet has a coefficient value of -0.20, this means that with an increase in temperature by 100 degrees, the decrease in magnetic induction will be 20%.
- Maximum operating temperature(Tmax). Measured in degrees Celsius. This value indicates at what maximum temperature the magnet will temporarily and partially lose its magnetic properties. After the temperature decreases, the magnetic properties will be completely restored.
- Curie temperature(Tcur). Also measured in degrees Celsius. It represents the temperature limit at which a magnet irreversibly loses its magnetic properties.
