The conditions for the occurrence of the electromagnetic field. Electromagnetic field
Shmelev V.E., Sbitsv S.A.
"Theoretical Basics of Electrical Engineering"
"Theory of the electromagnetic field"
Chapter 1. Basic concepts of electro theory magnetic field
§ 1.1. Definition electromagnetic field and its physical quantities.
Mathematical apparatus of the theory of electromagnetic field
Electromagnetic field(EMF) is called the type of matter that has a forceful effect on charged particles and determined in all points two pairs of vector values, which characterize two sides - electrical and magnetic fields.
Electric field - This is an EMF component, which is characterized by exposure to an electrically charged particle with a force proportional to the particle charge and does not depend on its speed.
A magnetic field - This is an EMF component, which is characterized by exposure to a moving particle with a force proportional to the particle charge and its speed.
Studied in the course theoretical foundations Electrical Equipments The main properties and methods for calculating the EMF suggest high-quality and quantifying EMF, found in electrical, radio-electronic and biomedical devices. For this, the electrodynamics equations are most suitable in integral and differential forms.
The mathematical apparatus of the theory of the electromagnetic field (TEMP) is based on the theory of scalar field, 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 mathematical apparatus of the theory of the electromagnetic field?
§ 1.2. Physical quantitiescharacterizing EMP.
Vector intensity electric field At point Q. Called vector of force acting on an electrically charged still particle placed on a point Q. If this particle has a single positive charge.
In accordance with this definition, the electric force acting on the point charge q. equal to:
where E. it is measured in per / m.
The magnetic field is characterized vector magnetic induction. Magnetic induction at some observation point Q. - This is a vector magnitude, the module of which is equal to the magnetic power acting on the charged particle located at the point Q. having a single charge and moving at a single speed, and the vectors of force, speed, magnetic induction, as well as the particle charge satisfy the condition
.
Magnetic force acting on a curvilinear conductor with a 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 recent formulas B. - magnetic induction, which is measured in Teslas (TL).
1 TL is such a magnetic induction at which a magnetic force is acting on a straight conductor with a current 1A, equal to 1N if the magnetic induction lines are directed perpendicular to the conductor with the current, and if the length of the conductor is 1M.
In addition to the tension of the electric field and magnetic induction in the theory of the electromagnetic field, the following vector quantities are considered:
1) Electrical Induction D. (electrical offset), which is measured in CL / m 2,
EMF vectors are space and time functions:
where Q. - observation point, t. - moment of time.
If the observation point Q. Located in vacuo, then the following ratios take place between the corresponding vector vapors.
where - the absolute dielectric permeability of the vacuum (the main electrical constant), \u003d 8,85419 * 10 -12;
Absolute magnetic permeability vacuum (basic magnetic constant); \u003d 4π * 10 -7.
Control 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 the conductor with the current?
5. What vector values \u200b\u200bare characterized electric field?
6. What vector values \u200b\u200bis the magnetic field?
§ 1.3. Sources of electromagnetic field
Sources of EMF are electrical charges, electric dipoles, moving electrical charges, electric currents, magnetic dipoles.
Concepts of electric charge and electric current Dases in the course of physics. Electrical currents are three types:
1. Current currents.
2. Shift currents.
3. Transfer currents.
Current conduction - The speed of passing the movable charges of the electrically conductive body through some surface.
Shift current - The rate of changes in the stream of the electrical displacement vector through some surface.
.
Transfer current Characterized by the following expression
where v. - the transfer rate of bodies through the surface S.; n. - vector single normal to the surface; - linear density of the charge of bodies flying through the surface, in the direction of normal; ρ is the volumetric density of the electric charge; ρ. v. - Transfer current density.
Electric dipolem. called a pair of point charges + q. and - q.located at a distance l.from each other (Fig. 1).
The point electric dipole is characterized by an electrical dipole moment:
Magnetic dipole called flat circuit with electric shock I. Magnetic dipole is characterized by a magnetic dipole moment vector
where S. - Vector square of a flat surface stretched on the outline with a current. Vector S. directed perpendicular to this flat surface, and if you look out of the end of the vector S. The movement along the contour in the direction that coincides with the direction of the current will occur counterclockwise. This means that the direction of the dipole magnetic moment vector is associated with the direction of the current according to the rule of the right screw.
Atoms and molecules of the substance are electrical and magnetic dipoles, so each point of the real type in EMF can be characterized by the bulk density of the electrical and magnetic dipole moment:
P. - Electric polarity substance:
M. - magnetization of matter:
Electric polarity of matter - This is a vector magnitude equal to the volumetric density of the electrical dipole moment at some point of the real body.
Magnetization of matter - This is a vector magnitude equal to the bulk density of the magnetic dipole moment at some point of the real body.
Electrical displacement - This is a vector value that for any point of observation, regardless of whether it is in vacuo or in a substance, is determined from the ratio:
(for vacuum or substance),
(only for vacuum).
Magnetic field tension - Vector magnitude, which for any observation point, regardless of whether it is in vacuo or in the substance is determined from the ratio:
,
where the magnetic field strength is measured in a / m.
In addition to polarity and magnetization, there are other volume-distributed sources of EMF:
- volume Density of Electric Charge ; ,
where the volumetric density of the electric charge is measured in CL / m 3;
- electric current density vector, the normal component of which is equal to
In a more general case, the current flowing through an unclosed surface S.is equal to the flow of current density vector through this surface:
where the electric current density vector is measured in a / m 2.
Control questions
1. What is the sources of the electromagnetic field?
2. What is conduction current?
3. What is the shift current?
4. What is a transfer current?
5. What is an electric dipole and electric dipole moment?
6. What is a magnetic dipole and magnetic dipole moment?
7. What is called electrical polarity and magnetization of matter?
8. What is called electrical displacement?
9. What is called the voltage of the magnetic field?
10. What is the volume density of the electrical charge and the current density?
An example of MATLAB application
A task.
Dano: Electric current contour I. The space is the perimeter of the 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 are lower indexes - vertices numbers. The vertices are numbered in the direction of electric current.
Required Matlab function computing the dipole magnetic torque vector. When making a M-file, it can be assumed that the spatial coordinates are measured in meters, and the current in amperes. An arbitrary organization of input and output parameters is allowed.
Decision
% m_dip_moment - calculation of the magnetic dipole moment of the triangular circuit with a current in space
% PM \u003d M_DIP_MOMENT (TOK, NODES)
% INPUT PARAMETERS
% tok - current in the circuit;
% nodes - square matrix View. ", In each row of which the coordinates of the corresponding vertex are recorded.
% Output parameter
% PM - Matrix-line of the Cartesian components of the magnetic dipole moment.
function PM \u003d M_DIP_MOMENT (TOK, NODES);
pM \u003d TOK *)]) DET ()]) DET ()])] / 2;
% In the last operator vector of the triangle square is multiplied by the current
\u003e\u003e NODES \u003d 10 * RAND (3)
9.5013 4.8598 4.5647
2.3114 8.913 0.18504
6.0684 7.621 8.2141
\u003e\u003e PM \u003d M_DIP_MOMENT (1, NODES)
13.442 20.637 -2.9692
In this case, it turned out P. M \u003d (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 the theory of electromagnetic field
Gradient scalar field φ ( Q.) = Φ( x, Y, Z) The vector field is called the formula:
,
where V. 1 - area containing a point Q.; S. 1 - closed surface limiting region V. 1 , Q. 1 - point belonging to the surface S. one ; Δ - the greatest distance From the point Q.to dots on the surface S. 1 (Max | Q Q. 1 |).
Divergence Vector field F. (Q.)=F. (x, Y, Z) It is called a scalar field defined by the formula:
Rotor(swirl) vector field F. (Q.)=F. (x, Y, Z) It is called a vector field defined by the formula:
rot. F.
= 
Operator Nabyl - This is a vector differential operator, which in the Cartesian coordinates is determined by the formula:
Imagine Grad, Div and Rot through the operator named:
We write these operators in the Cartesian coordinates:
; 
;
Laplace operator in Cartesian coordinates is determined by the formula:
Differential operators of second order:
Integral theorems
Gradient theorem 
;
Theorem on divergence 
Rotor Theorem 
In the theory of EMP, one of the integral theorems is also used:
.
Control questions
1. What's called a scalar field gradient?
2. What is called vector field divergence?
3. What's called the vector field rotor?
4. What is the operator recruit and how is the differential first-order differential operators express?
5. What are the integral theorems are valid for scalar and vector fields?
An example of MATLAB application
A task.
Dano: In the volume of the tetrahedra, the scalar and vector fields are changed according to the linear law. The coordinates of the vertices of the tetrahedron are given by the 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 \u200b\u200bof the scalar field in the vertices are set by the matrix [F 1; F 2; F 3; F 4]. Cartesian components of vector field in vertices are set by a 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.].
Determine In the volume of the tetrahedron gradient of the scalar field, as well as the divergence and rotor of the vector field. Matlab function for this.
Decision. Below is the text of the M-function.
% grad_div_rot - gradient calculation, divergence and rotor ... in the volume of tetrahedra
% \u003d GRAD_DIV_ROT (NODES, SCALAR, VECTOR)
% INPUT PARAMETERS
% Nodes - Tetrahedron vertex coordinate matrix:
% rows correspond to vertices, columns - coordinates;
% SCALAR - a column matrix of the values \u200b\u200bof the scalar field in the vertices;
% vector - matrix components of vector field in vertices:
% Output parameters
% GRAD - Matrix-line of the Cartesian components of the gradient of the scalar field;
% div - the value of the divergence of the vector field in the volume of the tetrahedron;
% Rot - Matrix-line of the Cartesian components of the vector field rotor.
% In case of calculations, it is assumed that in the volume of the tetrahedron
% Vector and scalar fields change in space by linear law.
function \u003d grad_div_rot (NODES, SCALAR, Vector);
a \u003d inv (); % Matrix coefficients linear interpolation
gRAD \u003d (A (2: End, :) * Scalar). ";% The components of the gradient of the scalar field
div \u003d * vector (:); % Vector field divergence
rot \u003d Sum (Cross (A (2: End, :), vector. "), 2).";
An example of starting the developed M-function:
\u003e\u003e NODES \u003d 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
\u003e\u003e SCALAR \u003d RAND (4,1)
\u003e\u003e Vector \u003d 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
\u003e\u003e \u003d GRAD_DIV_ROT (NODES, SCALAR, Vector)
0.16983 -0.03922 -0.17125
0.91808 0.20057 0.78844
Assuming that spatial coordinates are measured in meters, and the vector and scalar fields are dimensionless, then in this example happened:
gRAD F \u003d (-0.16983 * 1 X. - 0.03922*1 Y. - 0.17125*1 Z.) M -1;
div F. \u003d -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 the theory of electromagnetic field
EMF equations in integrated form
Complete current:
or 
Magnetic field tension vector circulation along contour l.equal to the full electric current flowing through the surface S., stretched on the contour l.If the current direction is formed with the direction of circuit bypass the projection system.
Electromagnetic Induction Act:
,
where E. C is a third-party electric field strength.
EMF electromagnetic induction e. And in the contour l.equal to the rate of change of magnetic flux through the surface S., stretched on the contour l., and the direction of the rate of change of magnetic flux forms with the direction e. and the left-hand system.
Gauss theorem in integrated form:
Stream of an electrical displacement vector through a closed surface S. equal to the amount of free electrical charges in a limited surface S..
The law of continuity of magnetic induction lines:
Magnetic flow through any closed surface is zero.
The direct use of equations in the integral form allows the calculation of the simplest electromagnetic fields. To calculate electromagnetic fields more complex form Apply equations in differential form. These equations are called Maxwell equations.
Maxwell equations for fixed media
These equations are directly followed from the corresponding equations in the integral form and from mathematical definitions of spatial differential operators.
Complete current law in differential form:
,
Full electric current density
Third-party density,
Condency current density
Displacement current density :,
Transfer current density :.
This means that the electric current is a vortex source of the vector field of 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.
Continuity equation of magnetic induction lines:
This means that the field of magnetic induction vector does not have sources, i.e. In nature, there are no magnetic charges (magnetic monopoles).
Gauss theorem in differential form:
This means that the sources of the vector field of electrical displacement are electrical charges.
To ensure the uniqueness of the solution of the problem of analysis of EMF, it is necessary to supplement Maxwell equations with the equations of material communication between 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 under the action of the electric field. All magnetics are magnetized under the action of a magnetic field. Static dielectric properties of the substance can be fully described by the functional dependence of the polarization vector P. From electric field strength vector E. (P. =P. (E. )). Static magnetic properties of the substance can be fully described by the functional dependence of the magnetization vector M. from magnetic field strength vector H. (M. =M. (H. )). In general, such dependencies are ambiguous (hysteresis). This means that the vector of polarity or magnetization at the point Q. determined not only by the value of the vector E. or H. At this point, but also the prehistory of the change of the vector E. or H. At this point. Experimentally explore and model these dependencies are extremely difficult. Therefore, in practice it often assumes that vectors P. and E. , as well as M. and H. Collinear, and the electrophysical properties of the substance describe scalar hysteresis features (| P. |=|P. |(|E. |), |M. |=|M. |(|H. |). If the hysteresis characteristics of the above functions can be neglected, the electrophysical properties are described by unambiguous functions. P.=P.(E.), M.=M.(H.).
In many cases, these functions can be approximately linear, i.e.
Then considering the relation (1) you can record the following
| , | (4) |
Accordingly, the relative dielectric and magnetic permeability of the substance:
Absolute dielectric constant of the substance:
Absolute magnetic permeability of the substance:
Relations (2), (3), (4) characterize the dielectric and magnetic properties of the substance. The electrically conductive properties of the substance can be described by the Ohm law in differential form.
where - the specific electrical conductivity of the substance measured in cm / m.
In a more general case, the dependence between conduction current density and the electric field strength vector is non-linear vector-hysteresis.
Energy of electromagnetic field
The volumetric energy density of the electric field is equal
,
where W. Eh is measured in J / m 3.
The bulk energy density of the magnetic field is equal to
,
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 the substance, the bulk energy density of EMF is equal to
This expression is valid for instant values. specific energy and emp vectors.
Specific power of thermal losses from conductivity currents
Specific power of third-party sources
Control questions
1. How is the full current law in integral form?
2. How is the law of electromagnetic induction in integrated form?
3. How is the Gauss theorem and the law of continuity of the magnetic flux in integral form formulad?
4. How is the full current law in differential form?
5. How is the law of electromagnetic induction in differential form?
6. How is the Gauss theorem and the law of continuity of magnetic induction lines in integral form?
7. What ratios are the electrophysical properties of the substance describe?
8. How is the energy of an electromagnetic field through vector magnitudes, which determines it?
9. How is the specific power of thermal loss and the specific power of third-party sources?
Examples of Matlab
Task 1..
Dano: Inside the volume of tetrahedra magnetic induction and the magnetization of the substance varies according to the linear law. The coordinates of the tetrahedra vertices are given, the values \u200b\u200bof the magnetic induction vectors and the magnetization of the substance in the vertices are also specified.
Calculate The electric current density in the tetrahedron volume, using the M-function, compiled by solving the problem in the previous paragraph. The calculation is made in the command window MATLAB, assuming that spatial coordinates are measured in millimeters, magnetic induction - in Teslas, the tension of the magnetic field and magnetization - in ka / m.
Decision.
Specify the source data in the format compatible with the M-function GRAD_DIV_ROT:
\u003e\u003e nodes \u003d 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
\u003e\u003e B \u003d 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
\u003e\u003e MU0 \u003d 4E-4 * PI% Absolute Magnetic Vacuum permeability, ICHN / mm
\u003e\u003e m \u003d 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
\u003e\u003e \u003d 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 full current density vector in the volume under consideration turned out to be equal (-914.2 * 1 X. + 527.76*1 Y. - 340.67*1 Z.) A / mm 2. To determine the current density module, execute the following statement:
\u003e\u003e CUR_D \u003d 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 a purely educational. And now check the correctness of the task of the distribution of magnetic induction in the volume of the tetrahedron. To do this, do the following operator:
\u003e\u003e \u003d GRAD_DIV_ROT (NODES, ONES (4,1), B)
0-3.0358E-017 0
0.38115 0.37114 -0.55567
Here we got the value of div B. \u003d -0.34415 TL / mm, which cannot be in accordance with the law of continuity of magnetic induction lines in differential form. It follows from this that the distribution of magnetic induction in the volume of the tetrahedron is defined correctly.
Task 2..
Let the tetrahedron, the coordinates of the vertices of which are set, is in the air (measurement units - meters). Let the tension of the electric field in its vertices (units of measurement - kV / m) are specified.
Required Calculate the volumetric density of the electrical charge inside the tetrahedron.
Decision You can do the same:
\u003e\u003e nodes \u003d 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
\u003e\u003e EPS0 \u003d 8.854E-3% Absolute dielectric permeability of vacuum, NF / M
\u003e\u003e E \u003d 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
\u003e\u003e \u003d GRAD_DIV_ROT (NODES, ONES (4,1), E * EPS0)
0.076467 0.21709 -0.015323
In this example, the volume density of charge turned out to be 0.10685 μl / m 3.
§ 1.6. Boundary conditions for EMF vectors.
The law of saving charge. Theorem Umova-Pointing
or 
Here is indicated: H. 1 - vector of the tension of the magnetic field on the surface of the media partition in medium No. 1; H. 2 - the same in Wednesday number 2; H. 1t. - tangential (tangent) component of the tension of the magnetic field on the surface of the media partition in Wednesday No. 1; H. 2t. - the same in Wednesday number 2; E. 1 vector of complete voltage of the electric field on the surface of the media partition in medium No. 1; E. 2 - the same in Wednesday number 2; E. 1 C is a third-party component of the tension of the electric field on the surface of the media partition in Wednesday No. 1; E. 2c - the same in Wednesday number 2; E. 1t. - the tangential component of the vector of tension of the electric field on the surface of the media partition in Wednesday No. 1; E. 2t. - the same in Wednesday number 2; E. 1C. t. - the tangential third-party component of the tension of the electric field on the surface of the media in Wednesday No. 1; E. 2t. - the same in Wednesday number 2; B. 1 - vector of magnetic induction on the surface of the media partition in medium No. 1; B. 2 - the same in Wednesday number 2; B. 1n. - the normal component of the magnetic induction vector on the surface of the media in Wednesday No. 1; B. 2n. - the same in Wednesday number 2; D. 1 - vector of electrical displacement on the surface of the media in medium No. 1; D. 2 - the same in Wednesday number 2; D. 1n. - the normal component of the electrical displacement vector on the surface of the media in Wednesday No. 1; D. 2n. - the same in Wednesday number 2; σ is the surface density of the electrical charge at the interface interface, measured in CL / m 2.
The law of saving charge
If there are no third-party current sources, then
,
and in the general case, i.e., the full current density vector does not have sources, i.e. the full current lines are always closed
Theorem Umova-PointingThe volumetric power density consumed by the material point in EMF is equal to
In accordance with the identity (1)
This is the capacity balance equation for volume V.. In the general case, in accordance with equality (3), the electromagnetic power generated by sources inside the volume V., It goes to thermal losses, on the accumulation of EMF energy and to radiation into the surrounding space through a closed surface that limits this volume.
The integrated expression in the integral (2) is called Pointing Vector:
,
where P Measured in W / m 2.
This vector is equal to the density of the electromagnetic power flow at some observation point. Equality (3) - there mathematical expression Melova-Pointing theorems.
Electromagnetic power emitted area V. In the surrounding space is equal to the flow of the Pointing vector through a closed surface S.Limiting area V..
Control questions
1. What expressions describe the boundary conditions for the electromagnetic field vectors on the surfaces of the media section?
2. How is the law of saving charge in differential form?
3. How is the order of saving the charge in integral form?
4. What expressions describe the boundary conditions for the current density on the surfaces of the media section?
5. What is the volumetric power density consumed by the material point in the electromagnetic field?
6. How is the electromagnetic power balance equation written for some volume?
7. What is Pointing vector?
8. How is the Umova-Pointing theorem formulad?
An example of MATLAB application
A task.
Dano: There is a triangular surface in space. The coordinates of the vertices are set. The values \u200b\u200bof the voltage vectors of the electric and magnetic field in the vertices are also specified. The third-party component of the voltage of the electric field is zero.
Required Calculate the electromagnetic power passing through this triangular surface. Make a MATLAB function that performs this calculation. When calculations assume that the vector of positive standards is directed so that if you look from its end, the movement in the order of increasing the vertices will occur counterclockwise.
Decision. Below is the text of the M-function.
% EM_POWER_TRI - calculation of electromagnetic power passing through
% triangular surface in space
% P \u003d EM_POWER_TRI (NODES, E, H)
% INPUT PARAMETERS
% nodes - square matrix of type. ",
% In each row of which the coordinates of the corresponding vertex are recorded.
% E - Matrix of the components of the voltage vector of the electric field in the vertices:
% rows correspond to the vertices, columns - Cartesian components.
% H - Matrix components of the magnetic field voltage vector in vertices.
% Output parameter
% P - electromagnetic power passing through a triangle
% In calculations, it is assumed that on a triangle
% Field voltage vectors are changed in space by linear law.
fUNCTION P \u003d EM_POWER_TRI (NODES, E, H);
% Calculate Vector Double Square Triangle
S \u003d)]) det ()]) det ()])];
P \u003d SUM (Cross (E, (ONES (3.3) + EYE (3)) * H, 2)) * s. "/ 24;
An example of starting the developed M-function:
\u003e\u003e nodes \u003d 2 * Rand (3,3)
0.90151 0.5462 0.4647
1.4318 0.50954 1.6097
1.7857 1.7312 1.8168
\u003e\u003e E \u003d 2 * Rand (3,3)
0.46379 0.15677 1.6877
0.47863 1.2816 0.3478
0.099509 0.38177 0.34159
\u003e\u003e H \u003d 2 * Rand (3,3)
1.9886 0.62843 1.1831
0.87958 0.73016 0.23949
0.6801 0.78648 0.076258
\u003e\u003e P \u003d EM_POWER_TRI (NODES, E, H)
It is assumed that the spatial coordinates are measured in meters, the electric field strength vector is in the volts per meter, the magnetic field strength vector - in amps 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 this type of matter that occurs around moving charges. It consists of electric, as well as magnetic fields. Their existence is interconnected, as they can not be separate and independently of each other, because, one field creates another.
Now let's try to approach the topic of the electromagnetic field in more detail. From the definition, it can be concluded that in the event of a change in the electric field, the prerequisites for the occurrence of the magnetic field appear. And since the electric field has a property with time to change and cannot be called unchanged, the magnetic field is also variable.
When one field changes, another is generated. And no matter what the subsequent field is, the source will serve the previous field, that is, a conductor with a current, and not its original source.
And even if the current will turn off in the conductor, the electromagnetic field will not disappear anyway, but will continue to exist and distribute in space.
Properties of electromagnetic waves
Maxwell theory. Vortex electric field
James Clerk Maxwell, a famous British physicist in 1857, a work was written in 1857, in which he led evidence that the fields such as electrical and magnetic are closely related to each other.
According to his theory, it was necessary that the variable magnetic field had a property to create such a new EP, which differs from the previous electric field created using the current source, since this new electric field is vortex.
And here we see that the vortex electric field is a field that the power lines are closed. That is, it should be noted that the electric field has the same closed lines as the magnetic field.
From this it follows that the alternating magnetic field can create a vortex electric field, and the vortex electric field has the ability to make the charges move. And in the end we get an induction electric current. Maxwell follows that fields such as electric and magnetic closely exist with each other.
That is, a moving electric charge is needed for the existence of a magnetic field. Well, the electric field is created thanks to the resting electrical charge. This is such a transparent relationship exists between the fields. From this we can make another conclusion that different systems The reference can be observed different kinds Fields.
If you follow Maxwell's theory, then we can sum up that the variables electrical and magnetic fields are not able to exist separately, because with a change, the magnetic field generates an electric field, and the changing electric field generates magnetic.
Natural sources of electromagnetic fields
For a modern person is not a secret, the fact that electromagnetic fields although they remain invisible to our eye, but they surround us everywhere.
Natural sources of EMF include:
First, it is a constant electric and magnetic polo of the Earth.
Secondly, such sources include radio waves that transform such space sourceslike the sun, stars, etc.
Thirdly, these sources are atmospheric processes as lightning discharges, etc.
Anthropogenic (artificial) sources of electromagnetic fields
Besides natural sources The appearance of EMF, they still arise and thanks to anthropogenic sources. Such sources include X-rays that are used in medical institutions. They are used to transmit information using various radio stations, mobile stations and also TV antennas. Yes, and electricity that is in every rosette also forms EMF, but truth, lower frequency.
Effect of EMF on human health
Modern society is currently not thinking of his life, without such benefits of civilization as the presence of various household appliances, computers, mobile communications. Of course, they facilitate our lives, but create electromagnetic fields around us. Naturally, we can not see EMF with you, but they surround us everywhere. They are present in our homes, at work and even in transport.
We can safely say that modern man Lives in a solid electromagnetic field, which, unfortunately, has a huge effect on human health. With a long-term effect of the electromagnetic field on the human body, such unpleasant symptoms appear as chronic fatigue, irritability, sleep disruption, attention and memory. Such prolonged effects of EMF can cause human headache, infertility, violations in the work of nervous and cardiac systems, as well as the emergence of oncological diseases.
The electromagnetic field is such a type of matter that occurs around moving charges. For example, around the conductor with a current. The electromagnetic field consists of two components of this electric and magnetic field. Regardless of each other, they cannot exist. One generates another. When changing the electric field, magnetic occurs immediately.
Electromagnetic Wave Spread Speed V \u003d C / EM
Where e. and m. Accordingly, the magnetic and dielectric permeability of the medium in which the wave is distributed.
The electromagnetic wave in the vacuum applies at the speed of light, that is, 300,000 km / s. Since the dielectric and magnetic permeability of the vacuum is considered to be equal to 1.
When changing the electric field, a magnetic field occurs. Since the electrical field that caused it is not unchanged (that is, it changes in time) then 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 (it does not matter whether it is an electric or magnetic) source will serve the previous field, and not the original source, that is, a conductor with a current.
Thus, even after turning off the current in the conductor, the electromagnetic field will continue to exist and distribute in space.
The electromagnetic wave spreads in space in all directions from its source. You can imagine a light bulb, the rays of light from it spread in all directions.
The electromagnetic wave in propagation transfers energy in space. The stronger the current in the conductor called the field, the greater the energy tolerant of the wave. Also, energy depends on the frequency of radiated waves, with an increase in it 2.3.4 times the energy of the wave will increase by 4.9.16 times, respectively. That is, the spread energy of the wave is proportional to the square of the frequency.
The best conditions for the spread of waves are created when the conductor is long, equal to the wavelength.
The power lines of the magnetic and electric flying mutually perpendicularly. Magnetic power lines cover the conductor with current and always closed.
Electric power lines go from one charge to another.
Electromagnetic wave is always a transverse wave. That is, the power lines both magnetic and electrical lie in the perpendicular plane to the distribution direction.
Electromagnetic field strength Power characteristics of the field. Also tension, vector magnitude that is, it has the beginning and direction.
Field voltage is aimed at tangent to power lines.
Since the voltage of the electric and magnetic field is perpendicular to each other, that is, the rule by which you can determine the direction of propagation of the wave. When rotating the screw along the shortest path from the tension vector of the electric field to the magnetic field voltage vector, the progressive movement of the screw will indicate the direction of the wave propagation.
What is an electromagnetic field, as 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 about the useful devices - indicators of the electromagnetic field (EMF). They can be used both in enterprises and in everyday life.
What is an electromagnetic field?
The modern world is unthinkable without household appliances, mobile phones, electricity, trams and trolley buses, televisions and computers. We are accustomed to them and absolutely not thinking about the fact that any electrical device creates an electromagnetic field around itself. It is invisible, but affects any living organisms, including a person.
The electromagnetic field is a special form of matter that occurs when the interaction of moving particles with electrical charges. The electrical and magnetic field are interconnected with each other and can generate one other - that is why, as a rule, they speak together as a single, electromagnetic field.
The main sources of electromagnetic fields include:
- power lines;
- transformer substations;
- wiring, telecommunications, television and internet cables;
- Ties of cellular communication, radio and broadcasters, amplifiers, cellular antennas and satellite phones, Wi-Fi Routers;
- computers, televisions, displays;
- household electrical appliances;
- induction and microwave (microwave) furnaces;
- electric transport;
- Radars.
Effect of electromagnetic fields on human health
Electromagnetic fields affect any biological organisms - on plants, insects, animals, people. Scientists studying the effect of EMF per person came to the conclusion that the long-term and regular effect of electromagnetic fields can lead to:
- increased fatigue, sleep disorders, headaches, pressure reduction, reduction in the pulse rate;
- disorders in immune, nervous, endocrine, sex, hormonal, cardiovascular systems;
- development of oncological diseases;
- Development of diseases of the Central nervous system;
- Allergic reactions.
Protection against EMF.
Exist sanitary normsestablishing the maximum allowable levels of electromagnetic field strength depending on the time of stay in the danger zone - for residential premises, jobs, places near the sources of a strong field. If there is no possibility to reduce the radiation structurally, for example, from the line of electromagnetic gear (EMF) or cellular tower, then official instructions are being developed, protective equipment for working personnel, sanitary quarantine areas of limited access.
Different instructions regulate the time of the person's stay in the danger zone. Screening grids, films, glazing, suits made of metallized tissue based on polymer fibers are able to reduce the intensity of electromagnetic radiation thousands of times. At the request of the GOST, the EMF radiation zone is protected and are supplied with warning signs "Not to enter, dangerous!" and sign danger electromagnetic field.
Special services with devices constantly monitor the level of EMF tension at workplaces and in residential areas. You can independently take care of your health by buying portable device "Impulse" or pulse Kit + SOEKS Nitrate Tester.
Why do we need household instruments for measuring the electromagnetic field strength?
The electromagnetic field negatively affects human health, so it is useful to know which places where you are (at home, in the office, on panstoneIn the garage) may be dangerous. You should understand that an increased electromagnetic background can create not only your electrical devices, phone numbers, televisions and computers, but also faulty wiring, electrical appliances of neighbors, industrial facilities located nearby.
Experts found out that the short-term impact of the EMF per person is almost harmlessly, but long-term foundation in the zone with an increased electromagnetic background is dangerous. These are such zones and can be detected using a "impulse" type instruments. So, you can check the places where you spend the most time; Children's and her bedroom; study. The device is listed, set regulatory documentsSo you can immediately estimate the degree of danger to you and your loved ones. It is possible that after the examination you decide to push the computer from the bed, get rid of cell phone With an enhanced antenna, change the old microwave oven to a new one, replace the insulation of the refrigerator door with the No Frost mode.
