Conditions for the emergence of an electromagnetic field. Electromagnetic field
Shmelev V.E., Sbitnev S.A.
"THEORETICAL FOUNDATIONS OF ELECTRICAL ENGINEERING"
"ELECTROMAGNETIC FIELD THEORY"
Chapter 1 magnetic field
§ 1.1. Definition electromagnetic field and its physical quantities.
Mathematical apparatus of the electromagnetic field theory
electromagnetic field(EMF) is a type of matter that has a force effect on charged particles and is determined at all points by two pairs of vector quantities that characterize its two sides - electric and magnetic fields.
Electric field- this is a component of the EMF, which is characterized by the impact on an electrically charged particle with a force proportional to the charge of the particle and independent of its speed.
A magnetic field- this is a component of the EMF, which is characterized by the impact on a moving particle with a force proportional to the charge of the particle and its speed.
Learned in the course theoretical foundations electrical engineering, the main properties and methods for calculating EMF involve a qualitative and quantitative study of EMF found in electrical, radio-electronic and biomedical devices. For this, the equations of electrodynamics in integral and differential forms are most suitable.
The mathematical apparatus of the electromagnetic field theory (TEMF) is based on the scalar field theory, vector and tensor analysis, as well as differential and integral calculus.
1. What is an electromagnetic field?
2. What is called an electric and magnetic field?
3. What is the basis of the mathematical apparatus of the electromagnetic field theory?
§ 1.2. Physical quantities characterizing EMF
Tension vector electric field at the point Q is called the vector of the force acting on an electrically charged stationary particle placed at a point Q if this particle has a unit positive charge.
According to this definition, the electric force acting on a point charge q is equal to:
where E measured in V/m.
The magnetic field is characterized magnetic induction vector. Magnetic induction at some observation point Q is a vector quantity, the modulus of which is equal to the magnetic force acting on a charged particle located at a point Q, which has a unit charge and moves with a unit velocity, and the vectors of force, velocity, magnetic induction, and also the charge of the particle satisfy the condition
.
The magnetic force acting on a curvilinear conductor with current can be determined by the formula
.
On a straight conductor, if it is in a uniform field, the following magnetic force acts
.
In all the latest formulas B - magnetic induction, which is measured in tesla (Tl).
1 T is such a magnetic induction at which a magnetic force equal to 1N acts on a straight conductor with a current of 1A if the lines of magnetic induction are directed perpendicular to the conductor with current, and if the length of the conductor is 1 m.
In addition to the electric field strength and magnetic induction, the following vector quantities are considered in the electromagnetic field theory:
1) electrical induction D (electric displacement), which is measured in C / m 2,
The EMF vectors are functions of space and time:
where Q- observation point, t- moment of time.
If the observation point Q is in vacuum, then the following relations hold between the corresponding pairs of vector quantities
where is the absolute permittivity of vacuum (basic electrical constant), = 8.85419 * 10 -12;
Absolute magnetic permeability of vacuum (basic magnetic constant); \u003d 4π * 10 -7.
test questions
1. What is the electric field strength?
2. What is called magnetic induction?
3. What is the magnetic force acting on a moving charged particle?
4. What is the magnetic force acting on a conductor with current?
5. What are the vector quantities characterized by electric field?
6. What vector quantities characterize the magnetic field?
§ 1.3. Sources of electromagnetic field
The sources of EMF are electric charges, electric dipoles, moving electric charges, electric currents, magnetic dipoles.
The concepts of electric charge and electric current given in physics. Electric currents are of three types:
1. Conduction currents.
2. Displacement currents.
3. Transfer currents.
Conduction current- the speed of passage of mobile charges of an electrically conductive body through a certain surface.
Bias current- the rate of change of the electric displacement vector flow through a certain surface.
.
Transfer current characterized by the following expression
where v - the speed of transfer of bodies through the surface S; n - vector of the unit normal to the surface; - linear charge density of bodies flying through the surface in the direction of the normal; ρ is the volume density of the electric charge; p v - transfer current density.
electric dipole is called a pair of point charges + q and - q located at a distance l from each other (Fig. 1).
A point electric dipole is characterized by the electric dipole moment vector:
magnetic dipole called a flat circuit with electric current I. The magnetic dipole is characterized by the magnetic dipole moment vector
where S is the area vector of the flat surface stretched over the circuit with current. Vector S directed perpendicular to this flat surface, moreover, if viewed from the end of the vector S , then the movement along the contour in the direction coinciding with the direction of the current will occur counterclockwise. This means that the direction of the dipole magnetic moment vector is related to the direction of the current according to the right screw rule.
Atoms and molecules of matter are electric and magnetic dipoles, so each point of the real type in the EMF can be characterized by the bulk density of the electric and magnetic dipole moment:
P - electrical polarization of the substance:
M - the magnetization of the substance:
Electrical polarization of matter is a vector quantity equal to the bulk density of the electric dipole moment at some point of a real body.
Matter magnetization is a vector quantity equal to the bulk density of the magnetic dipole moment at some point of a real body.
electrical displacement- this is a vector quantity, which for any point of observation, regardless of whether it is in a vacuum or in a substance, is determined from the relation:
(for vacuum or matter),
(only for vacuum).
Magnetic field strength- a vector quantity, which for any point of observation, regardless of whether it is in a vacuum or in a substance, is determined from the relation:
,
where the magnetic field strength is measured in A/m.
In addition to polarization and magnetization, there are other volume-distributed EMF sources:
- bulk electric charge density ; ,
where the volume density of the electric charge is measured in C/m 3 ;
- electric current density vector, whose normal component is equal to
In a more general case, the current flowing through an open surface S, is equal to the flux of the current density vector through this surface:
where the electric current density vector is measured in A/m 2 .
test questions
1. What are the sources of the electromagnetic field?
2. What is conduction current?
3. What is bias current?
4. What is transfer current?
5. What is an electric dipole and an electric dipole moment?
6. What is a magnetic dipole and magnetic dipole moment?
7. What is called the electrical polarization and magnetization of a substance?
8. What is called electrical displacement?
9. What is called the strength of the magnetic field?
10. What is the volumetric electric charge density and current density?
MATLAB Application Example
A task.
Given: Circuit with electric current I in space is the perimeter of a triangle, the Cartesian coordinates of the vertices of which are given: x 1 , x 2 , x 3 , y 1 , y 2 , y 3 , z 1 , z 2 , z 3 . Here the subscripts are the vertex numbers. The vertices are numbered in the direction of electric current flow.
Required compose a MATLAB function that calculates the dipole magnetic moment vector of the loop. When compiling the m-file, it can be assumed that the spatial coordinates are measured in meters, and the current is measured in amperes. Arbitrary organization of input and output parameters is allowed.
Solution
% m_dip_moment - calculation of the magnetic dipole moment of a triangular circuit with current in space
%pm = m_dip_moment(tok,nodes)
% INPUT PARAMETERS
% current - current in the circuit;
% nodes - square matrix of the form ." , each line of which contains the coordinates of the corresponding vertex.
% OUTPUT PARAMETER
% pm is a row matrix of the Cartesian components of the magnetic dipole moment vector.
function pm = m_dip_moment(tok,nodes);
pm=tok*)]) det()]) det()])]/2;
% In the last statement, the area vector of the triangle is multiplied by the current
>> nodes=10*rand(3)
9.5013 4.8598 4.5647
2.3114 8.913 0.18504
6.0684 7.621 8.2141
>> pm=m_dip_moment(1,nodes)
13.442 20.637 -2.9692
In this case it turned out P M = (13.442* 1 x + 20.637*1 y - 2.9692*1 z) A * m 2 if the current in the circuit is 1 A.
§ 1.4. Spatial differential operators in electromagnetic field theory
Gradient scalar field Φ( Q) = Φ( x, y, z) is called a vector field defined by the formula:
,
where V 1 - area containing point Q; S 1 - closed surface bounding area V 1 , Q 1 - point belonging to the surface S one ; δ- greatest distance from the point Q to points on the surface S 1 (max| QQ 1 |).
Divergence vector field F (Q)=F (x, y, z) is called a scalar field defined by the formula:
Rotor(vortex) vector field F (Q)=F (x, y, z) is a vector field defined by the formula:
rot F
= 
Nabla operator is a vector differential operator, which in Cartesian coordinates is defined by the formula:
Let's represent grad, div and rot via the nabla operator:
We write these operators in Cartesian coordinates:
; 
;
The Laplace operator in Cartesian coordinates is defined by the formula:
Second order differential operators:
Integral theorems
gradient theorem 
;
Divergence theorem 
Rotor theorem 
In the theory of EMF, one more of the integral theorems is also used:
.
test questions
1. What is called the gradient of a scalar field?
2. What is called the divergence of a vector field?
3. What is called the rotor of a vector field?
4. What is the nabla operator and how are first-order differential operators expressed in terms of it?
5. What integral theorems are valid for scalar and vector fields?
MATLAB Application Example
A task.
Given: In the volume of the tetrahedron, the scalar and vector fields change according to a linear law. The coordinates of the vertices of the tetrahedron are given by a matrix of the form [ x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x 3 , y 3 , z 3 ; x 4 , y 4 , z four ]. The values of the scalar field at the vertices are given by the matrix [Ф 1 ; F 2; F 3; F 4]. The Cartesian components of the vector field at the vertices are given by the matrix [ F 1 x, F 1y, F 1z; F 2x, F 2y, F 2z; F 3x, F 3y, F 3z; F 4x, F 4y, F 4z].
Define in the volume of the tetrahedron, the gradient of the scalar field, as well as the divergence and curl of the vector field. Write a MATLAB function for this.
Solution. Below is the text of the m-function.
% grad_div_rot - Calculate gradient, divergence and curl... in the volume of a tetrahedron
%=grad_div_rot(nodes,scalar,vector)
% INPUT PARAMETERS
% nodes - matrix of tetrahedron vertex coordinates:
% lines correspond to vertices, columns - coordinates;
% scalar - columnar matrix of scalar field values at vertices;
% vector - matrix of vector field components at vertices:
% OUTPUT PARAMETERS
% grad - row matrix of Cartesian gradient components of the scalar field;
% div - divergence value of the vector field in the volume of the tetrahedron;
% rot - row matrix of Cartesian components of the vector field rotor.
% In calculations, it is assumed that in the volume of a tetrahedron
% vector and scalar fields vary in space according to a linear law.
function =grad_div_rot(nodes,scalar,vector);
a=inv(); % Coefficient Matrix linear interpolation
grad=(a(2:end,:)*scalar)."; % Scalar field gradient components
div=*vector(:); % Divergence of a vector field
rot=sum(cross(a(2:end,:),vector."),2).";
An example of running the developed m-function:
>> nodes=10*rand(4,3)
3.5287 2.0277 1.9881
8.1317 1.9872 0.15274
0.098613 6.0379 7.4679
1.3889 2.7219 4.451
>> scalar=rand(4,1)
>>vector=rand(4,3)
0.52515 0.01964 0.50281
0.20265 0.68128 0.70947
0.67214 0.37948 0.42889
0.83812 0.8318 0.30462
>> =grad_div_rot(nodes,scalar,vector)
0.16983 -0.03922 -0.17125
0.91808 0.20057 0.78844
If we assume that the spatial coordinates are measured in meters, and the vector and scalar fields are dimensionless, then in this example happened:
grad Ф = (-0.16983* 1 x - 0.03922*1 y - 0.17125*1 z) m -1 ;
div F = -1.0112 m -1;
rot F = (-0.91808*1 x + 0.20057*1 y + 0.78844*1 z) m -1 .
§ 1.5. Basic laws of electromagnetic field theory
EMF Equations in Integral Form
Full current law:
or 
Circulation of the magnetic field strength vector along the contour l is equal to the total electric current flowing through the surface S, stretched over the contour l, if the direction of the current forms a right-handed system with the direction of bypassing the circuit.
Law of electromagnetic induction:
,
where E c is the strength of the external electric field.
EMF of electromagnetic induction e and in the circuit l equal to the rate of change of the magnetic flux through the surface S, stretched over the contour l, and the direction of the rate of change of the magnetic flux forms with the direction e and left handed system.
Gauss' theorem in integral form:
Electric displacement vector flow through a closed surface S is equal to the sum of free electric charges in the volume bounded by the surface S.
The law of continuity of magnetic induction lines:
The magnetic flux through any closed surface is zero.
The direct application of equations in integral form makes it possible to calculate the simplest electromagnetic fields. To calculate electromagnetic fields over complex shape apply equations in differential form. These equations are called Maxwell's equations.
Maxwell's Equations for Stationary Media
These equations follow directly from the corresponding equations in integral form and from the mathematical definitions of spatial differential operators.
Total current law in differential form:
,
Total electric current density,
External electric current density,
Conduction current density,
Displacement current density: ,
Transfer current density: .
This means that the electric current is a vortex source of the vector field of the magnetic field strength.
The law of electromagnetic induction in differential form:
This means that the alternating magnetic field is a vortex source for the spatial distribution of the electric field strength vector.
The equation of continuity of magnetic induction lines:
This means that the field of the magnetic induction vector has no sources, i.e. in nature there are no magnetic charges (magnetic monopoles).
Gauss's theorem in differential form:
This means that the sources of the electric displacement vector field are electric charges.
To ensure the uniqueness of the solution of the EMF analysis problem, it is necessary to supplement the Maxwell equations with the equations of the material connection between the vectors E and D , as well as B and H .
Relations between field vectors and electrophysical properties of the medium
It is known that
| (1) |
All dielectrics are polarized by an electric field. All magnets are magnetized by a magnetic field. The static dielectric properties of a substance can be completely described by the functional dependence of the polarization vector P from the electric field strength vector E (P =P (E )). The static magnetic properties of a substance can be completely described by the functional dependence of the magnetization vector M from the magnetic field strength vector H (M =M (H )). In the general case, such dependences are ambiguous (hysteresis) in nature. This means that the polarization or magnetization vector at the point Q is determined not only by the value of the vector E or H at this point, but also the history of the change in the vector E or H at this point. It is extremely difficult to experimentally investigate and model these dependences. Therefore, in practice it is often assumed that the vectors P and E , as well as M and H are collinear, and the electrophysical properties of matter are described by scalar hysteresis functions (| P |=|P |(|E |), |M |=|M |(|H |). If the hysteresis characteristics of the above functions can be neglected, then the electrical properties are described by single-valued functions P=P(E), M=M(H).
In many cases, these functions can be approximately considered linear, i.e.,
Then, taking into account relation (1), we can write the following
| , | (4) |
Accordingly, the relative dielectric and magnetic permeability of the substance:
Absolute permittivity of a substance:
Absolute magnetic permeability of a substance:
Relations (2), (3), (4) characterize the dielectric and magnetic properties of the substance. The electrically conductive properties of a substance can be described by Ohm's law in differential form
where is the specific electrical conductivity of the substance, measured in S/m.
In a more general case, the dependence between the conduction current density and the electric field strength vector has a non-linear vector-hysteresis character.
Electromagnetic field energy
The volumetric energy density of the electric field is
,
where W e is measured in J / m 3.
The volumetric energy density of the magnetic field is
,
where W m is measured in J / m 3.
The volumetric energy density of the electromagnetic field is equal to
In the case of linear electrical and magnetic properties of matter, the volume energy density of the EMF is equal to
This expression is valid for instantaneous values specific energy and EMF vectors.
Specific power of heat losses from conduction currents
Specific power of third-party sources
test questions
1. How is the total current law formulated in integral form?
2. How is the law of electromagnetic induction formulated in integral form?
3. How is the Gauss theorem and the law of magnetic flux continuity formulated in integral form?
4. How is the law of total current formulated in differential form?
5. How is the law of electromagnetic induction formulated in differential form?
6. How is the Gauss theorem and the law of continuity of magnetic induction lines formulated in integral form?
7. What relationships describe the electrical properties of matter?
8. How is the energy of an electromagnetic field expressed in terms of the vector quantities that determine it?
9. How is the specific power of heat losses and the specific power of third-party sources determined?
MATLAB Application Examples
Task 1.
Given: Inside the volume of a tetrahedron, magnetic induction and magnetization of a substance change according to a linear law. The coordinates of the vertices of the tetrahedron are given, the values of the vectors of magnetic induction and the magnetization of the substance at the vertices are also given.
Calculate electric current density in the volume of the tetrahedron, using the m-function compiled in the solution of the problem in the previous paragraph. Perform the calculation in the MATLAB command window, assuming that the spatial coordinates are measured in millimeters, the magnetic induction is in teslas, the magnetic field strength and magnetization are in kA/m.
Solution.
Let's set the source data in a format compatible with the grad_div_rot m-function:
>> nodes=5*rand(4,3)
0.94827 2.7084 4.3001
0.96716 0.75436 4.2683
3.4111 3.4895 2.9678
1.5138 1.8919 2.4828
>> B=rand(4,3)*2.6-1.3
1.0394 0.41659 0.088605
0.83624 -0.41088 0.59049
0.37677 -0.54671 -0.49585
0.82673 -0.4129 0.88009
>> mu0=4e-4*pi % absolute vacuum magnetic permeability, μH/mm
>> M=rand(4,3)*1800-900
122.53 -99.216 822.32
233.26 350.22 40.663
364.93 218.36 684.26
83.828 530.68 -588.68
>> =grad_div_rot(nodes,ones(4,1),B/mu0-M)
0 -3.0358e-017 0
914.2 527.76 -340.67
In this example, the vector of the total current density in the considered volume turned out to be equal to (-914.2* 1 x + 527.76*1 y - 340.67*1 z) A/mm 2 . To determine the modulus of current density, execute the following statement:
>> cur_d=sqrt(cur_dens*cur_dens.")
The calculated value of the current density cannot be obtained in highly magnetized media in real technical devices. This example is purely educational. And now let's check the correctness of setting the distribution of magnetic induction in the volume of the tetrahedron. To do this, execute the following statement:
>> =grad_div_rot(nodes,ones(4,1),B)
0 -3.0358e-017 0
0.38115 0.37114 -0.55567
Here we got the div value B \u003d -0.34415 T / mm, which cannot be in accordance with the law of continuity of magnetic induction lines in differential form. From this it follows that the distribution of magnetic induction in the volume of the tetrahedron is set incorrectly.
Task 2.
Let the tetrahedron, whose vertex coordinates are given, be in the air (measurement units are meters). Let the values of the electric field strength vector at its vertices be given (measurement units - kV/m).
Required calculate the volumetric electric charge density inside the tetrahedron.
Solution can be done similarly:
>> nodes=3*rand(4,3)
2.9392 2.2119 0.59741
0.81434 0.40956 0.89617
0.75699 0.03527 1.9843
2.6272 2.6817 0.85323
>> eps0=8.854e-3 % absolute vacuum permittivity, nF/m
>> E=20*rand(4,3)
9.3845 8.4699 4.519
1.2956 10.31 11.596
19.767 6.679 15.207
11.656 8.6581 10.596
>> =grad_div_rot(nodes,ones(4,1),E*eps0)
0.076467 0.21709 -0.015323
In this example, the volumetric charge density turned out to be 0.10685 μC/m 3 .
§ 1.6. Boundary conditions for EMF vectors.
The law of conservation of charge. Umov-Poynting theorem
or 
It is marked here: H 1 - the vector of the magnetic field strength on the interface between the media in the environment No. 1; H 2 - the same in environment No. 2; H 1t- tangential (tangential) component of the magnetic field strength vector on the media interface in medium No. 1; H 2t- the same in environment No. 2; E 1 is the vector of the total electric field strength on the media interface in medium No. 1; E 2 - the same in environment No. 2; E 1 c - third-party component of the electric field strength vector on the media interface in medium No. 1; E 2c - the same in environment No. 2; E 1t- tangential component of the electric field strength vector on the media interface in medium No. 1; E 2t- the same in environment No. 2; E 1s t- tangential third-party component of the electric field strength vector on the media interface in medium No. 1; E 2t- the same in environment No. 2; B 1 - vector of magnetic induction at the interface between media in medium No. 1; B 2 - the same in environment No. 2; B 1n- the normal component of the vector of magnetic induction on the interface between media in medium No. 1; B 2n- the same in environment No. 2; D 1 - electric displacement vector on the media interface in medium No. 1; D 2 - the same in environment No. 2; D 1n- normal component of the electric displacement vector on the media interface in medium No. 1; D 2n- the same in environment No. 2; σ is the surface density of the electric charge at the interface between media, measured in C/m 2 .
Law of conservation of charge
If there are no third-party current sources, then
,
and in the general case, i.e., the total current density vector has no sources, i.e., the total current lines are always closed
Umov-Poynting theoremThe volumetric power density consumed by a material point in the EMF is equal to
According to identity (1)
This is the power balance equation for the volume V. In the general case, in accordance with equality (3), the electromagnetic power generated by sources inside the volume V, goes to heat losses, to the accumulation of EMF energy and to radiation into the surrounding space through a closed surface that limits this volume.
The integrand in the integral (2) is called the Poynting vector:
,
where P measured in W / m 2.
This vector is equal to the electromagnetic power flux density at some observation point. Equality (3) - yes mathematical expression the Umov-Poynting theorem.
Electromagnetic power radiated by the area V into the surrounding space is equal to the flow of the Poynting vector through a closed surface S, bounding area V.
test questions
1. What expressions describe the boundary conditions for the electromagnetic field vectors on the media interfaces?
2. How is the law of conservation of charge formulated in differential form?
3. How is the law of conservation of charge formulated in integral form?
4. What expressions describe the boundary conditions for the current density at the media interfaces?
5. What is the volume density of power consumed by a material point in an electromagnetic field?
6. How is the electromagnetic power balance equation written for a certain volume?
7. What is the Poynting vector?
8. How is the Umov-Poynting theorem formulated?
MATLAB Application Example
A task.
Given: There is a triangular surface in space. The vertex coordinates are set. The values of the electric and magnetic field strength vectors at the vertices are also given. The third-party component of the electric field strength is zero.
Required calculate the electromagnetic power passing through this triangular surface. Compose a MATLAB function that performs this calculation. When calculating, consider that the positive normal vector is directed in such a way that if you look from its end, then the movement in ascending order of vertex numbers will occur counterclockwise.
Solution. Below is the text of the m-function.
% em_power_tri - calculation of the electromagnetic power passing through
% triangular surface in space
%P=em_power_tri(nodes,E,H)
% INPUT PARAMETERS
% nodes - square matrix like ." ,
% in each line of which the coordinates of the corresponding vertex are written.
% E - matrix of components of the electric field strength vector at the vertices:
% Rows correspond to vertices, columns correspond to Cartesian components.
% H - matrix of components of the magnetic field strength vector at the vertices.
% OUTPUT PARAMETER
%P - electromagnetic power passing through the triangle
% The calculations assume that on the triangle
% field strength vectors change in space according to a linear law.
function P=em_power_tri(nodes,E,H);
% Calculate the double area vector of the triangle
S=)]) det()]) det()])];
P=sum(cross(E,(ones(3,3)+eye(3))*H,2))*S."/24;
An example of running the developed m-function:
>> nodes=2*rand(3,3)
0.90151 0.5462 0.4647
1.4318 0.50954 1.6097
1.7857 1.7312 1.8168
>> E=2*rand(3,3)
0.46379 0.15677 1.6877
0.47863 1.2816 0.3478
0.099509 0.38177 0.34159
>> H=2*rand(3,3)
1.9886 0.62843 1.1831
0.87958 0.73016 0.23949
0.6801 0.78648 0.076258
>> P=em_power_tri(nodes,E,H)
If we assume that the spatial coordinates are measured in meters, the electric field strength vector is in volts per meter, the magnetic field strength vector is in amperes per meter, then in this example, the electromagnetic power passing through the triangle turned out to be 0.18221 W.
Electromagnetic field
The electromagnetic field refers to the kind of matter that occurs around moving charges. It consists of electric as well as magnetic fields. Their existence is interconnected, since they cannot exist separately and independently of each other, because one field gives rise to another.
And now let's try to approach the topic of the electromagnetic field in more detail. From the definition, we can conclude that in the case of a change in the electric field, prerequisites for the emergence of a magnetic field appear. And since the electric field tends to change over time and cannot be called constant, the magnetic field is also variable.
When one field changes, another is generated. And no matter what the next field will be, the source will be the previous field, that is, the conductor with current, and not its original source.
And even in the case when the current is turned off in the conductor, the electromagnetic field will still not disappear anywhere, but will continue to exist and spread in space.
Properties of electromagnetic waves
Maxwell's theory. Vortex electric field
James Clerk Maxwell, a famous British physicist, wrote a work in 1857 in which he provided evidence that fields such as electric and magnetic are closely related.
According to his theory, it followed that an alternating magnetic field tends to create such a new electric field, which differs from the previous electric field created using a current source, since this new electric field is vortex.
And here we see that a vortex electric field is a field in which the lines of force are closed. That is, it should be noted that the lines of the electric field are as closed as those of the magnetic field.
From this follows the conclusion that an alternating magnetic field is capable of creating a vortex electric field, and a vortex electric field has the ability to make charges move. And as a result, we get an induction electric current. It follows from Maxwell's work that such fields as electric and magnetic closely exist with each other.
That is, a moving electric charge is necessary for the existence of a magnetic field. Well, the electric field is created due to the resting electric charge. Here such transparent interrelation exists between fields. From this we can draw another conclusion, that in different systems readings can be observed different kinds fields.
If we follow Maxwell's theory, then we can conclude that alternating electric and magnetic fields are not able to exist separately, because when a magnetic field changes, it generates an electric field, and a changing electric field generates a magnetic one.
Natural sources of electromagnetic fields
For a modern person, it is not a secret that electromagnetic fields, although they remain invisible to our eyes, surround us everywhere.
Natural sources of EMF include:
First, it is the permanent electric and magnetic field of the Earth.
Secondly, such sources include radio waves that convert such space sources like the sun, stars, etc.
Thirdly, these sources are also such atmospheric processes as lightning discharges, etc.
Anthropogenic (artificial) sources of electromagnetic fields
Except natural sources appearance of EMF, they also arise due to anthropogenic sources. These sources include x-rays, which are used in medical institutions. They are also used to transmit information using various radio stations, mobile communication stations and also TV antennas. Yes, and the electricity that is in every outlet also forms an EMF, but it is true, at a lower frequency.
The impact of EMF on human health
Modern society currently cannot imagine its life without such benefits of civilization as the presence of various household appliances, computers, mobile communications. They, of course, make our lives easier, but they create electromagnetic fields around us. Naturally, you and I cannot see EMF, but they surround us everywhere. They are present in our homes, at work and even in transport.
It is safe to say that modern man lives in a continuous electromagnetic field, which, unfortunately, has a huge impact on human health. With prolonged influence of the electromagnetic field on the human body, such unpleasant symptoms appear as chronic fatigue, irritability, sleep disturbance, attention and memory. Such prolonged exposure to EMF can cause headaches, infertility, disorders in the functioning of the nervous and cardiac systems, as well as the appearance of oncological diseases in a person.
An electromagnetic field is a kind of matter that arises around moving charges. For example, around a conductor with current. The electromagnetic field consists of two components - electric and magnetic fields. They cannot exist independently of each other. One begets the other. When the electric field changes, a magnetic field immediately arises.
Electromagnetic wave propagation speed V=C/EM
Where e and m respectively, the magnetic and dielectric permittivities of the medium in which the wave propagates.
An electromagnetic wave in a vacuum travels at the speed of light, that is, 300,000 km/s. Since the dielectric and magnetic permeability of the vacuum is considered equal to 1.
When the electric field changes, a magnetic field is created. Since the electric field that caused it is not constant (that is, it changes over time), the magnetic field will also be variable.
The changing magnetic field in turn generates an electric field, and so on. Thus, for the subsequent field (whether it is electric or magnetic), the source will be the previous field, and not the original source, that is, a current-carrying conductor.
Thus, even after the current is turned off in the conductor, the electromagnetic field will continue to exist and spread in space.
An electromagnetic wave propagates in space in all directions from its source. You can imagine turning on a light bulb, the rays of light from it spread in all directions.
An electromagnetic wave during propagation carries energy in space. The stronger the current in the conductor that caused the field, the greater the energy carried by the wave. Also, the energy depends on the frequency of the emitted waves, with an increase in it by 2.3.4 times, the energy of the wave will increase by 4.9.16 times, respectively. That is, the propagation energy of the wave is proportional to the square of the frequency.
The best conditions for wave propagation are created when the length of the conductor is equal to the wavelength.
The lines of force of magnetic and electric will fly mutually perpendicular. Magnetic lines of force envelop a current-carrying conductor and are always closed.
Electric lines of force go from one charge to another.
An electromagnetic wave is always a transverse wave. That is, the lines of force, both magnetic and electric, lie in a plane perpendicular to the direction of propagation.
The intensity of the electromagnetic field is the power characteristic of the field. Also tension is a vector quantity, that is, it has a beginning and a direction.
The field strength is directed tangentially to the lines of force.
Since the strength of the electric and magnetic fields are perpendicular to each other, there is a rule by which the direction of wave propagation can be determined. When the screw rotates along the shortest path from the electric field strength vector to the magnetic field strength vector, the translational movement of the screw will indicate the direction of wave propagation.
What is an electromagnetic field, how it affects human health and why measure it - you will learn from this article. Continuing to acquaint you with the assortment of our store, we will tell you about useful devices - indicators of electromagnetic field strength (EMF). They can be used both in businesses and at home.
What is an electromagnetic field?
The modern world is unthinkable without household appliances, mobile phones, electricity, trams and trolleybuses, televisions and computers. We are used to them and do not think at all that any electrical device creates an electromagnetic field around itself. It is invisible, but affects any living organisms, including humans.
An electromagnetic field is a special form of matter that occurs when moving particles interact with electric charges. The electric and magnetic fields are interconnected with each other and can give rise to one another - which is why, as a rule, they are spoken of together as a single, electromagnetic field.
The main sources of electromagnetic fields include:
- power lines;
— transformer substations;
– electrical wiring, telecommunications, TV and Internet cables;
– cell towers, radio and TV towers, amplifiers, cell and satellite phone antennas, WiFi routers;
— computers, TVs, displays;
- household electrical appliances;
– induction and microwave (MW) ovens;
— electric transport;
- radars.
Effect of electromagnetic fields on human health
Electromagnetic fields affect any biological organisms - plants, insects, animals, people. Scientists studying the effect of electromagnetic fields on humans have come to the conclusion that prolonged and regular exposure to electromagnetic fields can lead to:
- increased fatigue, sleep disturbances, headaches, decreased pressure, decreased heart rate;
- disorders in the immune, nervous, endocrine, sexual, hormonal, cardiovascular systems;
- the development of oncological diseases;
- the development of diseases of the central nervous system;
- allergic reactions.
EMI protection
Exist sanitary norms, which establish the maximum allowable levels of electromagnetic field strength depending on the time spent in the hazardous area - for residential premises, workplaces, places near sources of a strong field. If it is not possible to reduce the radiation structurally, for example, from an electromagnetic transmission line (EMF) or a cell tower, then service instructions, protective equipment for working personnel, and sanitary-quarantine restricted access zones are developed.
Various instructions regulate the time a person stays in the danger zone. Shielding nets, films, glazing, suits made of metallized fabric based on polymer fibers can reduce the intensity of electromagnetic radiation by thousands of times. At the request of GOST, EMF radiation zones are fenced off and equipped with warning signs “Do not enter, it is dangerous!” and sign of danger electromagnetic field.
Special services with the help of devices constantly monitor the level of EMF intensity at workplaces and in residential premises. You can take care of your own health by buying portable device "Impulse" or kit "Impulse" + nitrate tester "SOEKS".
Why do we need household devices for measuring the strength of the electromagnetic field?
The electromagnetic field negatively affects human health, so it is useful to know which places you visit (at home, in the office, on personal plot, in a garage) can be hazardous. You must understand that an increased electromagnetic background can be created not only by your electrical devices, telephones, televisions and computers, but also faulty wiring, electrical appliances of neighbors, industrial facilities located nearby.
Experts have found that a short-term exposure to EMF on a person is practically harmless, but a long stay in an area with an increased electromagnetic background is dangerous. These are the zones that can be detected using devices of the “Impulse” type. So, you can check the places where you spend the most time; nursery and your bedroom; study. The instrument contains the values set normative documents so that you can immediately assess the degree of danger to you and your loved ones. It is possible that after the examination you decide to move the computer away from the bed, get rid of cell phone with a reinforced antenna, change the old microwave oven to a new one, replace the refrigerator door insulation with the No Frost mode.
