Power lines magnetic field

Magnetic fields, just like electric ones, can be represented graphically using lines of force. A magnetic field line, or magnetic field induction line, is a line whose tangent at each point coincides with the direction of the magnetic field induction vector.

A)	b)	V)

Rice. 1.2. Direct current magnetic field lines (a),

circular current (b), solenoid (c)

Magnetic power lines just like electric ones, they do not intersect. They are drawn with such density that the number of lines crossing a unit surface perpendicular to them is equal to (or proportional to) the magnitude of the magnetic induction of the magnetic field in a given location.

In Fig. 1.2, A The field lines of direct current are shown, which are concentric circles, the center of which is located on the current axis, and the direction is determined by the right-hand screw rule (the current in the conductor is directed towards the reader).

Magnetic induction lines can be “revealed” using iron filings, which become magnetized in the field under study and behave like small magnetic needles. In Fig. 1.2, b magnetic field lines of circular current are shown. The magnetic field of the solenoid is shown in Fig. 1.2, V.

The magnetic field lines are closed. Fields with closed lines of force are called vortex fields. It is obvious that the magnetic field is a vortex field. This is the significant difference between a magnetic field and an electrostatic one.

In an electrostatic field, the lines of force are always open: they begin and end at electric charges. Magnetic lines of force have neither beginning nor end. This corresponds to the fact that there are no magnetic charges in nature.

1.4. Biot-Savart-Laplace law

French physicists J. Biot and F. Savard conducted a study of magnetic fields in 1820, created by currents, flowing through thin wires various shapes. Laplace analyzed the experimental data obtained by Biot and Savart and established a relationship that was called the Biot-Savart-Laplace law.

According to this law, the magnetic field induction of any current can be calculated as a vector sum (superposition) of the magnetic field inductions created by individual elementary sections of the current. For the magnetic induction of the field created by a current element of length , Laplace obtained the formula:

, (1.3)

where is a vector, modulo equal to length conductor element and coinciding in direction with the current (Fig. 1.3); – radius vector drawn from the element to the point at which it is determined; – modulus of the radius vector.

Let's understand together what a magnetic field is. After all, many people live in this field all their lives and don’t even think about it. It's time to fix it!

A magnetic field

A magnetic field- a special type of matter. It manifests itself in the action on moving electric charges and bodies that have their own magnetic moment (permanent magnets).

Important: the magnetic field does not affect stationary charges! A magnetic field is also created by moving electric charges, or by a time-varying electric field, or by the magnetic moments of electrons in atoms. That is, any wire through which current flows also becomes a magnet!

A body that has its own magnetic field.

A magnet has poles called north and south. The designations "north" and "south" are given for convenience only (like "plus" and "minus" in electricity).

The magnetic field is represented by magnetic power lines. The lines of force are continuous and closed, and their direction always coincides with the direction of action of the field forces. If metal shavings are scattered around a permanent magnet, the metal particles will show a clear picture of the magnetic field lines coming out of the north pole and entering the south pole. Graphic characteristic of a magnetic field - lines of force.

Characteristics of the magnetic field

The main characteristics of the magnetic field are magnetic induction, magnetic flux And magnetic permeability. But let's talk about everything in order.

Let us immediately note that all units of measurement are given in the system SI.

Magnetic induction B – vector physical quantity, which is the main force characteristic of the magnetic field. Denoted by the letter B . Unit of measurement of magnetic induction – Tesla (T).

Magnetic induction shows how strong the field is by determining the force it exerts on a charge. This force is called Lorentz force.

Here q - charge, v - its speed in a magnetic field, B - induction, F - Lorentz force with which the field acts on the charge.

F- physical quantity, equal to the product magnetic induction on the contour area and the cosine between the induction vector and the normal to the plane of the contour through which the flux passes. Magnetic flux is a scalar characteristic of a magnetic field.

We can say that magnetic flux characterizes the number of magnetic induction lines penetrating a unit area. Magnetic flux is measured in Weberach (Wb).

Magnetic permeability– coefficient that determines the magnetic properties of the medium. One of the parameters on which the magnetic induction of a field depends is magnetic permeability.

Our planet has been a huge magnet for several billion years. The induction of the Earth's magnetic field varies depending on the coordinates. At the equator it is approximately 3.1 times 10 to the minus fifth power of Tesla. In addition, there are magnetic anomalies where the value and direction of the field differ significantly from neighboring areas. Some of the largest magnetic anomalies on the planet - Kursk And Brazilian magnetic anomalies.

The origin of the Earth's magnetic field still remains a mystery to scientists. It is assumed that the source of the field is the liquid metal core of the Earth. The core is moving, which means the molten iron-nickel alloy is moving, and the movement of charged particles is the electric current that generates the magnetic field. The problem is that this theory ( geodynamo) does not explain how the field is kept stable.

The Earth is a huge magnetic dipole. The magnetic poles do not coincide with the geographic ones, although they are in close proximity. Moreover, the Earth's magnetic poles move. Their displacement has been recorded since 1885. For example, over the past hundred years, the magnetic pole in the Southern Hemisphere has shifted almost 900 kilometers and is now located in the Southern Ocean. The pole of the Arctic hemisphere is moving through the Arctic Ocean to the East Siberian magnetic anomaly; its movement speed (according to 2004 data) was about 60 kilometers per year. Now there is an acceleration of the movement of the poles - on average, the speed is growing by 3 kilometers per year.

What is the significance of the Earth's magnetic field for us? First of all, the Earth's magnetic field protects the planet from cosmic rays and solar wind. Charged particles from deep space do not fall directly to the ground, but are deflected by a giant magnet and move along its lines of force. Thus, all living things are protected from harmful radiation.

Several events have occurred over the course of Earth's history. inversions(changes) of magnetic poles. Pole inversion- this is when they change places. The last time this phenomenon occurred was about 800 thousand years ago, and in total there were more than 400 geomagnetic inversions in the history of the Earth. Some scientists believe that, given the observed acceleration of the movement of the magnetic poles, the next pole inversion should be expected in the next couple of thousand years.

Fortunately, a pole change is not yet expected in our century. This means that you can think about pleasant things and enjoy life in the good old constant field of the Earth, having considered the basic properties and characteristics of the magnetic field. And so that you can do this, there are our authors, to whom you can confidently entrust some of the educational troubles with confidence! and other types of work you can order using the link.

When connecting two parallel conductors to electrical current, they will attract or repel, depending on the direction (polarity) of the connected current. This is explained by the phenomenon of the emergence of a special kind of matter around these conductors. This matter is called a magnetic field (MF). Magnetic force is the force with which conductors act on each other.

The theory of magnetism arose in ancient times, in the ancient civilization of Asia. In the mountains of Magnesia they found a special rock, pieces of which could be attracted to each other. Based on the name of the place, this rock was called “magnetic”. A bar magnet contains two poles. Its magnetic properties are especially pronounced at the poles.

A magnet hanging on a thread will show the sides of the horizon with its poles. Its poles will be turned north and south. The compass device operates on this principle. Opposite poles of two magnets attract, and like poles repel.

Scientists have discovered that a magnetized needle located near a conductor is deflected when an electric current passes through it. This indicates that an MP is formed around it.

The magnetic field affects:

Moving electric charges.
Substances called ferromagnets: iron, cast iron, their alloys.

Permanent magnets are bodies that have a common magnetic moment of charged particles (electrons).

1 - South pole of the magnet
2 - North pole of the magnet
3 - MP using the example of metal filings
4 - Magnetic field direction

Lines of force appear when a permanent magnet approaches a paper sheet on which a layer of iron filings is poured. The figure clearly shows the locations of the poles with oriented lines of force.

Magnetic field sources

• Electric field changing over time.
• Mobile charges.
• Permanent magnets.

We have been familiar with permanent magnets since childhood. They were used as toys that attracted various metal parts. They were attached to the refrigerator, they were built into various toys.

Electric charges that are in motion most often have more magnetic energy compared to permanent magnets.

Properties

• Main hallmark and the property of the magnetic field is relativity. If you leave a charged body motionless in a certain frame of reference, and place a magnetic needle nearby, then it will point to the north, and at the same time will not “feel” an extraneous field, except for the field of the earth. And if you start moving a charged body near the arrow, then an MP will appear around the body. As a result, it becomes clear that the MF is formed only when a certain charge moves.
• A magnetic field can influence and influence electric current. It can be detected by monitoring the movement of charged electrons. In a magnetic field, particles with a charge will be deflected, conductors with flowing current will move. The frame with the current supply connected will begin to rotate, and the magnetized materials will move a certain distance. The compass needle is most often colored Blue colour. It is a strip of magnetized steel. The compass always points north, since the Earth has a magnetic field. The entire planet is like a big magnet with its own poles.

The magnetic field is not perceived human organs, and can only be recorded with special devices and sensors. It comes in variable and permanent types. The alternating field is usually created by special inductors that operate on alternating current. A constant field is formed by a constant electric field.

Rules

Let's consider the basic rules for depicting the magnetic field for various conductors.

Gimlet rule

The line of force is depicted in a plane, which is located at an angle of 90 0 to the path of current flow so that at each point the force is directed tangentially to the line.

To determine the direction of magnetic forces, you need to remember the rule of a gimlet with a right-hand thread.

The gimlet must be positioned along the same axis with the current vector, the handle must be rotated so that the gimlet moves in the direction of its direction. In this case, the orientation of the lines is determined by rotating the gimlet handle.

Ring gimlet rule

The translational movement of the gimlet in a conductor made in the form of a ring shows how the induction is oriented; the rotation coincides with the flow of current.

The lines of force have their continuation inside the magnet and cannot be open.

The magnetic field of different sources is added to each other. In doing so, they create a common field.

Magnets with the same poles repel, and magnets with different poles attract. The value of the interaction strength depends on the distance between them. As the poles approach, the force increases.

Magnetic field parameters

• Flow coupling ( Ψ ).
• Magnetic induction vector ( IN).
• Magnetic flux ( F).

The intensity of the magnetic field is calculated by the size of the magnetic induction vector, which depends on the force F, and is formed by the current I along a conductor having a length l: B = F / (I * l).

Magnetic induction is measured in Tesla (T), in honor of the scientist who studied the phenomena of magnetism and worked on their calculation methods. 1 T is equal to the magnetic flux induction force 1 N at length 1m straight conductor at an angle 90 0 to the direction of the field, with a flowing current of one ampere:

1 T = 1 x H / (A x m).

Left hand rule

The rule finds the direction of the magnetic induction vector.

If the palm of the left hand is placed in the field so that the magnetic field lines enter the palm from the north pole at 90 0, and 4 fingers are placed along the current flow, thumb will show the direction of the magnetic force.

If the conductor is at a different angle, then the force will directly depend on the current and the projection of the conductor onto the plane at a right angle.

The force does not depend on the type of conductor material and its cross-section. If there is no conductor, and the charges move in a different medium, then the force will not change.

When the magnetic field vector is directed in one direction of one magnitude, the field is called uniform. Different environments affect the size of the induction vector.

Magnetic flux

Magnetic induction passing through a certain area S and limited by this area is a magnetic flux.

If the area is inclined at a certain angle α to the induction line, the magnetic flux is reduced by the size of the cosine of this angle. Its greatest value is formed when the area is at right angles to the magnetic induction:

F = B * S.

Magnetic flux is measured in a unit such as "weber", which is equal to the flow of induction of magnitude 1 T by area in 1 m2.

Flux linkage

This concept is used to create general meaning magnetic flux, which is created from a certain number of conductors located between the magnetic poles.

In the case where the same current I flows through a winding with a number of turns n, the total magnetic flux formed by all turns is the flux linkage.

Flux linkage Ψ measured in Webers, and equals: Ψ = n * Ф.

Magnetic properties

Magnetic permeability determines how much the magnetic field in a certain medium is lower or higher than the field induction in a vacuum. A substance is called magnetized if it produces its own magnetic field. When a substance is placed in a magnetic field, it becomes magnetized.

Scientists have determined the reason why bodies acquire magnetic properties. According to scientists' hypothesis, there are substances inside electric currents microscopic size. An electron has its own magnetic moment, which is of a quantum nature, and moves along a certain orbit in atoms. It is these small currents that determine magnetic properties.

If the currents move randomly, then the magnetic fields caused by them are self-compensating. The external field makes the currents ordered, so a magnetic field is formed. This is the magnetization of the substance.

Various substances can be divided according to the properties of their interaction with magnetic fields.

They are divided into groups:

Paramagnets– substances that have magnetization properties in the direction of an external field and have a low potential for magnetism. They have positive field strength. Such substances include ferric chloride, manganese, platinum, etc.
Ferrimagnets– substances with magnetic moments unbalanced in direction and value. They are characterized by the presence of uncompensated antiferromagnetism. Field strength and temperature affect their magnetic susceptibility (various oxides).
Ferromagnets– substances with increased positive susceptibility, depending on tension and temperature (crystals of cobalt, nickel, etc.).
Diamagnets– have the property of magnetization in the opposite direction of the external field, that is, negative meaning magnetic susceptibility, independent of tension. In the absence of a field, this substance will not have magnetic properties. These substances include: silver, bismuth, nitrogen, zinc, hydrogen and other substances.
Antiferromagnets – have a balanced magnetic moment, resulting in a low degree of magnetization of the substance. When heated, a phase transition of the substance occurs, during which paramagnetic properties appear. When the temperature drops below a certain limit, such properties will not appear (chromium, manganese).

The magnets considered are also classified into two more categories:

Soft magnetic materials . They have low coercivity. In low-power magnetic fields they can become saturated. During the magnetization reversal process, they experience minor losses. As a result, such materials are used for the production of cores of electrical devices operating on alternating voltage (, generator,).
Hard magnetic materials. They have an increased coercive force. To remagnetize them, a strong magnetic field is required. Such materials are used in the production of permanent magnets.

The magnetic properties of various substances find their use in engineering projects and inventions.

Magnetic circuits

A combination of several magnetic substances is called a magnetic circuit. They are similar and are determined by similar laws of mathematics.

Electrical devices, inductances, etc. operate on the basis of magnetic circuits. In a functioning electromagnet, the flux flows through a magnetic circuit made of ferromagnetic material and air, which is not ferromagnetic. The combination of these components is a magnetic circuit. Many electrical devices contain magnetic circuits in their design.

> Magnetic field lines

How to determine magnetic field lines: diagram of the strength and directions of magnetic field lines, using a compass to determine the magnetic poles, drawing.

Magnetic field lines Useful for visually displaying the strength and direction of a magnetic field.

Learning Objective

• Relate the magnetic field strengths to the density of magnetic field lines.

Main points

• Magnetic field direction displays compass needles touching magnetic field lines at any specified point.
• The strength of the B-field is inversely proportional to the distance between the lines. It is also exactly proportional to the number of lines per unit area. One line never crosses another.
• The magnetic field is unique at every point in space.
• The lines are not interrupted and create closed loops.
• The lines stretch from the north to the south pole.

Terms

• Magnetic field lines are a graphical representation of the magnitude and direction of a magnetic field.
• B-field is a synonym for magnetic field.

Magnetic field lines

It is said that as a child, Albert Einstein loved to look at a compass, thinking about how the needle sensed force without direct physical contact. Deep thinking and serious interest led to the child growing up and creating his own revolutionary theory of relativity.

Since magnetic forces affect distances, we calculate magnetic fields to represent these forces. Line graphics are useful for visualizing the strength and direction of a magnetic field. The elongation of the lines indicates the north orientation of the compass needle. Magnetic is called the B-field.

(a) – If a small compass is used to compare the magnetic field around a bar magnet, it will show the correct direction from the north pole to the south pole. (b) – Adding arrows creates continuous magnetic field lines. The strength is proportional to the proximity of the lines. (c) – If you can examine the inside of a magnet, the lines will appear as closed loops

There is nothing difficult in comparing the magnetic field of an object. First, calculate the strength and direction of the magnetic field at several locations. Mark these points with vectors pointing in the direction of the local magnetic field with a magnitude proportional to its strength. You can combine the arrows to form magnetic field lines. The direction at any point will be parallel to the direction of the nearest field lines, and the local density can be proportional to the strength.

Magnetic field lines resemble contour lines on topographic maps, because they show something continuous. Many of the laws of magnetism can be formulated using simple concepts, such as the number of field lines through a surface.

Direction of magnetic field lines represented by the alignment of iron filings on paper placed above a bar magnet

The display of lines is affected by various phenomena. For example, iron filings on a magnetic field line create lines that correspond to magnetic ones. They are also visually displayed in auroras.

A small compass sent into a field will align itself parallel to the field line, with the north pole pointing E.

Miniature compasses can be used to demonstrate fields. (a) – The magnetic field of a circular current loop resembles a magnetic one. (b) – A long and straight wire forms a field with magnetic field lines creating circular loops. (c) – When the wire is in the plane of the paper, the field protrudes perpendicular to the paper. Note which symbols are used for the box pointing in and out

A detailed study of magnetic fields helped to derive a number of important rules:

• The direction of the magnetic field touches the field line at any point in space.
• The field strength is proportional to the proximity of the line. It is also exactly proportional to the number of lines per unit area.
• Magnetic field lines never collide, which means that at any point in space the magnetic field will be unique.
• The lines remain continuous and run from the north to the south pole.

The last rule is based on the fact that the poles cannot be separated. And it's different from the lines electric field, in which the end and beginning are marked by positive and negative charges.