Along with Coulomb's law, another description of the interaction of electric charges is also possible.
Long range and close range. Coulomb's law, like the law gravity, interprets the interaction of charges as "action at a distance", or "long-range action". Indeed, the Coulomb force depends only on the magnitude of the charges and on the distance between them. Coulomb was convinced that the intermediate medium, that is, the "emptiness" between the charges, does not take any part in the interaction.
Such a view was no doubt inspired by the impressive success of Newton's theory of gravity, which was brilliantly confirmed by astronomical observations. However, Newton himself wrote: “It is not clear how inanimate inert matter, without the mediation of something else that is immaterial, could act on another body without mutual contact.” Nevertheless, the concept of long-range action, based on the idea of the instantaneous action of one body on another at a distance without the participation of any intermediate medium, dominated the scientific worldview for a long time.
The idea of a field as a material medium through which any interaction of spatially distant bodies is carried out was introduced into physics in the 30s of the 19th century by the great English naturalist M. Faraday, who believed that “matter is present everywhere, and there is no intermediate space not occupied
by her." Faraday developed a consistent concept of the electromagnetic field based on the idea of a finite interaction propagation velocity. The complete theory of the electromagnetic field, clothed in a rigorous mathematical form, was subsequently developed by another great English physicist, J. Maxwell.
By modern ideas electric charges endow the space around them with special physical properties- create an electric field. The main property of the field is that a certain force acts on a charged particle in this field, i.e., the interaction of electric charges is carried out through the fields they create. The field created by stationary charges does not change with time and is called electrostatic. To study the field, it is necessary to find its physical characteristics. Consider two such characteristics - power and energy.
Electric field strength. For experimental study of the electric field, it is necessary to place a test charge in it. In practice, this will be some kind of charged body, which, firstly, must be small enough to be able to judge the properties of the field at a certain point in space, and, secondly, its electric charge must be small enough to be able to neglect the influence of this charge on the distribution of charges that create the field under study.
A test charge placed in an electric field is subjected to a force that depends both on the field and on the test charge itself. This force is greater, the larger the test charge. By measuring the forces acting on different test charges placed at the same point, one can be convinced that the ratio of the force to the test charge no longer depends on the magnitude of the charge. Hence, this relation characterizes the field itself. The power characteristic of the electric field is the intensity E - a vector quantity equal at each point to the ratio of the force acting on the test charge placed at this point to the charge
In other words, the field strength E is measured by the force acting on a single positive test charge. In general, the field strength is different at different points. A field in which the intensity at all points is the same both in absolute value and in direction is called homogeneous.
Knowing the strength of the electric field, you can find the force acting on any charge placed in given point. In accordance with (1), the expression for this force has the form
How to find the field strength at any point?
The strength of the electric field created by a point charge can be calculated using Coulomb's law. We will consider a point charge as a source of an electric field. This charge acts on a test charge located at a distance from it with a force whose modulus is equal to
Therefore, in accordance with (1), dividing this expression by we obtain the module E of the field strength at the point where the test charge is located, i.e., at a distance from the charge
Thus, the field strength of a point charge decreases with distance in inverse proportion to the square of the distance, or, as they say, according to the inverse square law. Such a field is called a Coulomb field. When approaching a point charge creating a field, the field strength of a point charge increases indefinitely: from (4) it follows that when
The coefficient k in formula (4) depends on the choice of the system of units. In CGSE k = 1, and in SI . Accordingly, formula (4) is written in one of two forms:
The unit of tension in the CGSE does not have a special name, but in SI it is called "volt per meter"
Due to the isotropy of space, i.e., the equivalence of all directions, the electric field of a solitary point charge is spherically symmetrical. This circumstance is manifested in formula (4) in that the modulus of the field strength depends only on the distance to the charge that creates the field. The intensity vector E has a radial direction: it is directed from the charge that creates the field if it is a positive charge (Fig. 6a, a), and to the charge that creates the field if this charge is negative (Fig. 6b).
The expression for the field strength of a point charge can be written in vector form. It is convenient to place the origin of coordinates at the point where the charge that creates the field is located. Then the field strength at any point characterized by the radius vector is given by the expression
This can be verified by comparing the definition (1) of the field strength vector with the formula (2) § 1, or starting from
directly from formula (4) and taking into account the above considerations about the direction of the vector E.
The principle of superposition. How to find the strength of the electric field created by an arbitrary distribution of charges?
Experience shows that electric fields satisfy the principle of superposition. The field strength created by several charges is equal to the vector sum of the field strengths created by each charge separately:
The principle of superposition actually means that the presence of other electric charges has no effect on the field created by this charge. This property, when separate sources act independently and their actions simply add up, is inherent in the so-called linear systems, and this property itself physical systems called linearity. The origin of this name is due to the fact that such systems are described linear equations(first degree equations).
We emphasize that the validity of the superposition principle for an electric field is not a logical necessity or something taken for granted. This principle is a generalization of experimental facts.
The principle of superposition makes it possible to calculate the strength of the field created by any distribution of immobile electric charges. In the case of several point charges, the recipe for calculating the resulting intensity is obvious. Any non-point charge can be mentally divided into such small parts that each of them can be considered as a point charge. The electric field strength at an arbitrary point is found as
the vector sum of the tensions created by these "point" charges. The corresponding calculations are greatly simplified in cases where there is a certain symmetry in the distribution of the charges creating the field.
Tension lines. A visual graphical representation of electric fields is given by lines of tension or lines of force.
Rice. 7. Field strength lines of positive and negative point charges
These electric field lines are drawn in such a way that at each point the tangent to the line coincides in direction with the intensity vector at that point. In other words, at any place the tension vector is directed tangentially to the line of force passing through this point. The lines of force are assigned a direction: they come from positive charges or come from infinity. They either end in negative charges or go to infinity. In the figures, this direction is indicated by arrows on the field line.
A line of force can be drawn through any point in the electric field.
The lines are drawn thicker in those places where the field strength is greater, and less often where it is less. So the density lines of force gives an idea of the modulus of tension.
Rice. 8. Lines of field strength of opposite identical charges
On fig. 7 shows the field lines of a solitary positive and negative point charge. It is obvious from the symmetry that these are radial lines distributed with the same density in all directions.
A more complex form is the picture of the lines of the field created by two charges of opposite signs. Such a field is obviously
has axial symmetry: the whole picture remains unchanged when rotated through any angle around an axis passing through the charges. When the modules of the charges are the same, the pattern of lines is also symmetrical with respect to a plane passing perpendicular to the segment connecting them through its middle (Fig. 8). In this case, the lines of force come out of the positive charge and they all terminate in the negative, although in Fig. 8 it is impossible to show how the lines going far from the charges are closed.
The electric field that surrounds the charge is a reality independent of our desire to change something and somehow influence it. From this we can conclude that the electric field is one of the forms of existence of matter, as well as matter.
The electric field of charges at rest is called electrostatic. To detect the electrostatic field of a certain charge, you need to introduce another charge into its field, on which a certain force will act in. However, without the presence of a second charge, the electrostatic field of the first charge exists, but does not manifest itself in any way.
Tension E characterize the electrostatic field. The intensity at a certain point of the electric field is a physical quantity that is equal to the force acting on a unit positive charge at rest placed at a certain point in the field, and directed in the direction of the force.
If a “trial” positive point charge q pr is introduced into the electric field created by the charge q, then, according to the Coulomb law, a force will act on it:
If different test charges q / pr, q // pr and so on are placed at one point of the field, then different forces proportional to the magnitude of the charge will act on each of them. The ratio F / q pr for all charges introduced into the field will be identical, and will also depend only on q and r, which determine the electric field at a given point. This value can be expressed by the formula:
If we assume that q pr \u003d 1, then E \u003d F. From this we conclude that the strength of the electric field is its power characteristic. From formula (2), taking into account the expression of the Coulomb force (1), it follows:
It can be seen from formula (2) that the unit of tension is taken to be the intensity at a certain point in the field, where a unit of force will act on a unit of charge. Therefore, in the CGS system, the unit of tension is dyn / CGS q, and in the SI system it will be N / Cl. The ratio between the given units is called the absolute electrostatic unit of tension (CGS E):
The intensity vector is directed from the charge along the radius with a positive charge forming the field q +, and with a negative charge q - towards the charge along the radius.
If the electric field is formed by several charges, then the forces that will act on the test charge are added according to the vector addition rule. Therefore, the strength of a system consisting of several charges at a given point in the field will be equal to the vector sum of the strengths of each charge separately:
This phenomenon is called the principle of superposition (superposition) of electric fields.
The intensity at any point of the electric field of two point charges - q 2 and + q 1 can be found using the principle of superposition:
According to the parallelogram rule, the vectors E 1 and E 2 will be added. The direction of the resulting vector E is determined by the construction, and its absolute value can be calculated using the formula below:
Where α is the angle between the vectors E 1 and E 2.
Let's consider the electric field that the dipole creates. Electric dipole - this is a system of equal in magnitude (q \u003d q 1 \u003d q 2), but opposite in sign, charges, the distance between which is very small when compared with the distance to the considered points of the electric field.
The electric dipole moment p, which is the main characteristic of the dipole and is defined as a vector directed from a negative charge to a positive one, and equal to the product of the dipole arm l and the charge q:
Also, the vector is the arm of the dipole l, directed from the negative charge to the positive, and determines the distance between the charges. The line that passes through both charges is called - dipole axis.
Let's determine the electric field strength at a point that lies on the dipole axis in the middle (figure below a)):
At point B, the intensity E will be equal to the vector sum of the intensities E / and E // , which are created by positive and negative charges but separately. Between the charges –q and +q, the intensity vectors E / and E // are directed in the same direction, therefore, in absolute value, the resulting intensity E will be equal to their sum.
If we need to find E at point A, which lies on the continuation of the dipole axis, then the vectors E / and E // will be directed in different directions, respectively, in absolute value, the resulting intensity will be equal to their difference:
Where r is the distance between the point that lies on the axis of the dipole and where the intensity is determined, and the midpoint of the dipole.
In the case of r>>l, the value (l/2) in the denominator can be neglected, then we get the following relation:
Where p is the electric dipole moment.
This formula in the CGS system will take the form:
Now you need to calculate the electric field strength at point C (figure above b)) lying on the perpendicular restored from the midpoint of the dipole.
Since r 1 \u003d r 2, then the equality will take place:
The dipole strength at an arbitrary point can be determined by the formula:
Where α is the angle between the dipole arm l and the radius vector r, r is the distance from the point at which the field strength is determined to the center of the dipole, p is the electric moment of the dipole.
Example
At a distance R \u003d 0.06 m from each other there are two identical point charges q 1 \u003d q 2 \u003d 10 -6 C (figure below):
It is necessary to determine the electric field strength at point A, which is located on the perpendicular restored in the center of the segment that connects the charges, at a distance h = 4 cm from this segment. It is also necessary to determine the tension at point B, located in the middle of the segment that connects the charges.
Decision
According to the principle of superposition (superposition of fields), the field strength E is determined. Thus, the vector (geometric) sum is determined by E created by each charge separately: E \u003d E 1 + E 2.
The electric field strength of the first point charge is:
Where q 1 and q 2 are the charges that form the electric field; r is the distance from the point at which the intensity is calculated to the charge; ε 0 - electrical constant; ε is the relative permittivity of the medium.
To determine the intensity at point B, you first need to build the electric field strength vectors from each charge. Since the charges are positive, the vectors E / and E // will be directed from point B in different directions. By condition q 1 = q 2:
This means that in the middle of the segment, the field strength is zero.
At point A, it is necessary to perform a geometric addition of the vectors E 1 and E 2. At point A, the tension will be equal to:
Forces acting at a distance are sometimes called field forces. If you charge an object, it will create an electric field - an area with changed characteristics surrounding it. An arbitrary charge that has fallen into the zone of an electric field will be subjected to the action of its forces. These forces are affected by the degree of charge of the object and the distance to it.
Forces and charges
Suppose there is some initial electric charge Q that creates an electric field. The strength of this field is measured by the electric charge in the immediate vicinity. This electric charge is called a test charge, since it serves as a test charge in determining the intensity and is too small to influence the generated electric field.
The control electric charge will be called q and have some quantitative value. When placed in an electric field, it is subjected to attractive or repulsive forces F.
As a formula for the electric field strength, indicated by the Latin letterE, serves as a mathematical notation:
Force is measured in newtons (N), charge is measured in coulombs (C). Accordingly, a unit is used for tension - N / C.
Another frequently used unit for homogeneous EP in practice is V/m. This is a consequence of the formula:
That is, E depends on the voltage of the electric field (the potential difference between its two points) and the distance.
Does the intensity depend on the quantitative value of the electric charge? It can be seen from the formula that an increase in q entails a decrease in E. But according to Coulomb's law, more charge also means more electrical force. For example, a twofold increase in electric charge will cause a twofold increase in F. Therefore, there will be no change in tension.
Important! The intensity of the electric field is not affected by the quantitative indicator of the test charge.
How is the electric field vector directed
For a vector quantity, two characteristics are necessarily applied: quantitative value and direction. The initial charge is affected by a force directed towards it or in the opposite direction. The choice of a reliable direction is determined by the charging sign. To resolve the question in which direction the lines of tension are directed, the direction of the force F acting on the positive electric charge was taken.
Important! The lines of the field strength created by the electric charge are directed from the charge with the "plus" sign to the charge with the "minus" sign. If you imagine an arbitrary positive initial charge, then the lines will come out of it in all directions. For a negative charge, on the contrary, the occurrence of lines of force from all surrounding sides is observed.
A visual display of the vector quantities of the electric field is made by means of lines of force. The simulated EP sample can consist of an infinite number of lines, which are arranged according to certain rules, giving as much information as possible about the nature of the EP.
Rules for drawing lines of force:
- Larger electric charges have the strongest electric field. In a schematic drawing, this can be shown by increasing the frequency of the lines;
- In the areas of connection with the surface of the object, the lines are always perpendicular to it. On the surface of objects regular and irregular shape there is never an electric force parallel to it. If such a force existed, any excess charge on the surface would begin to move, and there would be electricity inside an object, which is never the case in static electricity;
- When leaving the surface of an object, the force can change direction due to the influence of the EP of other charges;
- Electrical lines must not cross. If they intersect at some point in space, then at this point there should be two EPs with their own individual direction. This is an impossible condition, since each place of the EP has its own intensity and direction associated with it.
The lines of force for the capacitor will run perpendicular to the plates, but become convex at the edges. This indicates a violation of the homogeneity of the EP.
Taking into account the condition of a positive electric charge, it is possible to determine the direction of the electric field strength vector. This vector is directed towards the force acting on the electric charge with the plus sign. In situations where the electric field is created by several electric charges, the vector is found as a result of the geometric summation of all the forces that the test charge is exposed to.
At the same time, the electric field strength lines are understood as a set of lines in the EF coverage area, to which the vectors E will be tangent at any arbitrary point.
If an EP is created from two or more charges, lines appear surrounding their configuration. Such constructions are cumbersome and are performed using computer graphics. When solving practical problems, the resulting electric field strength vector for given points is used.
Coulomb's law defines the electrical force:
F = (K x q x Q)/r², where:
- F is the electric force directed along the line between two electric charges;
- K - constant of proportionality;
- q and Q are the quantitative values of the charges (C);
- r is the distance between them.
Constant proportionality is found from the ratio:
K = 1/(4π x ε).
The value of the constant depends on the medium in which the charges are located (permittivity).
Then F \u003d 1 / (4π x ε) x (q x Q) / r².
The law operates in the natural environment. For theoretical calculation, it is initially assumed that electric charges are in free space (vacuum). Then the value ε = 8.85 x 10 (to the -12th power), and K = 1/(4π x ε) = 9 x 10 (to the 9th power).
Important! Formulas describing situations where there is spherical symmetry (most cases) have 4π in their composition. If there is cylindrical symmetry, 2π appears.
To calculate the tension modulus, you need to substitute the mathematical expression for Coulomb's law into the formula for E:
E \u003d F / q \u003d 1 / (4π x ε) x (q x Q) / (r² x q) \u003d 1 / (4π x ε) x Q / r²,
where Q is the initial charge that creates the EF.
To find the electric field intensity at a particular point, it is necessary to place a test charge at this point, determine the distance to it, and calculate E using the formula.
Inverse square law
In the formulaic representation of Coulomb's law, the distance between electric charges appears in the equation as 1/r². Hence, the application of the inverse square law will be fair. Another well-known such law is Newton's law of gravity.
This expression illustrates how changing one variable can affect another. Mathematical notation of the law:
E1/E2 = r2²/r1².
The value of the field strength depends on the location of the selected point, its value decreases with distance from the charge. If we take the intensity of the EP at two different points, then the ratio of their quantitative values will be inversely proportional to the squares of the distance.
To measure the electric field strength in practical conditions, there are special devices e.g. tester VX 0100.
Video
Coulomb's law:
where F is the force of interaction of two point charges q 1 and q 2; r is the distance between charges; is the dielectric constant of the medium; 0 - electrical constant
.
The law of conservation of charge:
,
where 
is the algebraic sum of the charges included in the isolated system; n is the number of charges.
Strength and potential of the electrostatic field:
;
, or 
,
where 
is the force acting on a point positive charge q 0 placed at a given point of the field; P is the potential energy of the charge; And ∞ is the work spent on moving the charge q 0 from a given point of the field to infinity.
Tension Vector Flow 
electric field:
a) through an arbitrary surface S placed in an inhomogeneous field:
, or 
,
where is the angle between the intensity vector 
and normal 
to the surface element; dS is the area of the surface element; E n is the projection of the stress vector onto the normal;
b) through a flat surface placed in a uniform electric field:
.
Tension Vector Flow 
through a closed surface
(integration is carried out over the entire surface).
Ostrogradsky-Gauss theorem. The flow of the intensity vector through any closed surface covering the charges q1, q2, ..., qn, -
,
where 
is the algebraic sum of charges enclosed inside a closed surface; n is the number of charges.
tension electrostatic field, created by a point charge q at a distance r from the charge, –
.
The strength of the electric field created by a sphere having a radius R and carrying a charge q, at a distance r from the center of the sphere is as follows:
inside the sphere (r R) E=0;
on the surface of the sphere (r=R) 
;
outside the sphere (r R) 
.
The principle of superposition (superposition) of electrostatic fields, according to which the intensity 
of the resulting field created by two (or more) point charges is equal to the vector (geometric) sum of the strengths of the added fields, is expressed by the formula
In the case of two electric fields with strengths 
and 
the absolute value of the intensity vector is
where is the angle between the vectors 
and 
.
The intensity of the field created by an infinitely long and uniformly charged thread (or cylinder) at a distance r from its axis is
,
where is the linear charge density.
The linear charge density is a value equal to its ratio to the length of the thread (cylinder):
.
The intensity of the field created by an infinite uniformly charged plane is
,
where is the surface charge density.
The surface charge density is a value equal to the ratio of the charge distributed over the surface to its area:
.
The strength of the field created by two infinite and parallel planes, charged uniformly and differently, with the same absolute value of the surface density of the charge (the field of a flat capacitor) -
.
The above formula is valid when calculating the field strength between the plates of a flat capacitor (in its middle part) only if the distance between the plates is much less than the linear dimensions of the capacitor plates.
electrical displacement 
associated with tension 
electric field ratio
,
which is valid only for isotropic dielectrics.
The potential of an electric field is a quantity equal to the ratio of potential energy and a point positive charge placed at a given point in the field:
.
In other words, the electric field potential is a value equal to the ratio of the work of the field forces to move a point positive charge from a given point of the field to infinity to the value of this charge:
.
The potential of the electric field at infinity is conditionally taken equal to zero.
The potential of the electric field created by a point charge q on
distance r from the charge, –
.
The potential of the electric field created by a metal sphere having a radius R and carrying a charge q, at a distance r from the center of the sphere is as follows:
inside the sphere (r R) 
;
on the surface of a sphere (r = R) 
;
outside the sphere (r R) 
.
In all formulas given for the potential of a charged sphere, is the permittivity of a homogeneous infinite dielectric surrounding the sphere.
The potential of the electric field formed by a system of n point charges at a given point, in accordance with the principle of superposition of electric fields, is equal to the algebraic sum of the potentials 
, created by individual point charges 
:
.
Energy W of interaction of a system of point charges 
is determined by the work that this system can do when they are removed relative to each other to infinity, and is expressed by the formula
,
where 
- field potential created by all (n-1) charges (except for the i-th) at the point where the charge is located 
.
The potential is related to the electric field strength by the relation
.
In the case of an electric field with spherical symmetry, this relationship is expressed by the formula
,
or in scalar form
.
In the case of a homogeneous field, i.e. field, the intensity of which at each of its points is the same both in absolute value and in direction, -
,
where 1 and 2 are the potentials of the points of two equipotential surfaces; d is the distance between these surfaces along the electric line of force.
The work done by the electric field when moving a point charge q from one point of the field, having a potential 1, to another, having a potential 2, is equal to
, or 
,
where E 
is the vector projection 
to the direction of movement; 
- movement.
In the case of a homogeneous field, the last formula takes the form
,
where 
- displacement; - angle between vector directions 
and moving 
.
A dipole is a system of two point (equal in absolute value and opposite in sign) charges located at some distance from each other.
Electric moment 
dipole is a vector directed from a negative charge to a positive one, equal to the product of the charge 
per vector 
, drawn from a negative charge to a positive one, and called the dipole arm, i.e.
.
A dipole is called a point dipole if its arm 
much less than the distance r from the center of the dipole to the point at which we are interested in the action of the dipole ( 
r), see fig. one.
Field strength of a point dipole:
,
where p is the electric moment of the dipole; r is the absolute value of the radius vector drawn from the center of the dipole to the point where the field strength is of interest to us; - angle between the radius vector 
and shoulder 
dipole.
Field strength of a point dipole at a point lying on the axis of the dipole
(=0), is found by the formula
;
at a point perpendicular to the dipole arm reconstructed from its middle 
, - according to the formula
.
The field potential of a point dipole at a point lying on the dipole axis (=0) is
,
and at a point lying on the perpendicular to the dipole arm, reconstructed from its middle 
,
–
The strength and potential of a non-point dipole are determined in the same way as for a system of charges.
The mechanical moment acting on a dipole with an electric moment p, placed in a uniform electric field with a strength E, is
, or 
,
where is the angle between the directions of the vectors 
and 
.
The capacitance of a solitary conductor or capacitor is
,
where q is the charge imparted to the conductor; 
is the change in potential caused by this charge.
The capacitance of a solitary conducting sphere of radius R, located in an infinite medium with a permittivity , is
.
If the sphere is hollow and filled with a dielectric, then its capacitance does not change.
Electric capacitance of a flat capacitor:
,
where S is the area of each capacitor plate; d is the distance between the plates; - permittivity of the dielectric filling the space between the plates.
The capacitance of a flat capacitor filled with n layers of dielectric with thickness d i and permittivity i each (layered capacitor) is
.
The capacitance of a spherical capacitor (two concentric spheres with a radius R 1 and R 2, the space between which is filled with a dielectric with a permittivity ) is as follows:
.
The capacitance of series-connected capacitors is:
in general -
,
where n is the number of capacitors;
in the case of two capacitors -
;
.
The capacitance of capacitors connected in parallel is determined as follows:
in general -
C \u003d C 1 + C 2 + ... + C n;
in the case of two capacitors -
C \u003d C 1 + C 2;
in the case of n identical capacitors with electrical capacity C 1 each -
The energy of a charged conductor is expressed in terms of charge q, potential and electrical capacity C of the conductor as follows:
.
The energy of a charged capacitor is
,
where q is the charge of the capacitor; C is the capacitance of the capacitor; U is the potential difference on its plates.
A charged body constantly transfers part of the energy, transforming it into another state, one of the parts of which is an electric field. Tension is the main component that characterizes the electrical part electromagnetic radiation. Its value depends on the current strength and acts as a power characteristic. It is for this reason that high-voltage wires are placed at a greater height than wiring for less current.
Definition of the concept and calculation formula
The intensity vector (E) is the force acting on an infinitesimal current at the point under consideration. The formula for determining the parameter is as follows:
- F is the force that acts on the charge;
- q is the amount of charge.
The charge taking part in the study is called a test charge. It should be small so as not to distort the results. Under ideal conditions, the role of q is played by the positron.
It should be noted that the value is relative, its quantitative characteristics and direction depend on the coordinates and will change with a shift.
Based on the Coulomb law, the force acting on a body is equal to the product of the potentials divided by the square of the distance between the bodies.
F=q 1* q 2 /r 2
It follows from this that the intensity at a given point in space is directly proportional to the potential of the source and inversely proportional to the square of the distance between them. In the general, symbolic case, the equation is written as follows:
Based on the equation, the unit of electric field is Volts per meter. The same designation is adopted by the SI system. Having the value of the parameter, you can calculate the force that will act on the body at the point under study, and knowing the force, you can find the electric field strength.
The formula shows that the result is absolutely independent of the test charge. This is unusual since this parameter is present in the original equation. However, this is logical, because the source is the main emitter, not the test emitter. In real conditions, this parameter has an effect on the measured characteristics and produces a distortion, which leads to the use of a positron for ideal conditions.
Since tension is a vector quantity, in addition to the value, it has a direction. The vector is directed from the main source to the investigated one, or from the trial charge to the main one. It depends on the polarity. If the signs are the same, then repulsion occurs, the vector is directed towards the point under study. If the points are charged in opposite polarities, then the sources are attracted. In this case, it is customary to assume that the force vector is directed from a positive source to a negative one.
unit of measurement
Depending on the context and application in the fields of electrostatics, electric field strength [E] is measured in two units. It can be volt/meter or newton/coulomb. The reason for this confusion seems to be obtaining it from different conditions, deriving the unit of measurement from the formulas used. In some cases, one of the dimensions is used intentionally to prevent the use of formulas that work only for special cases. The concept is present in the fundamental electrodynamic laws, so the value is basic for thermodynamics.
The source can take various forms. The formulas described above help to find the electric field strength of a point charge, but the source can be in other forms:
- several independent material points;
- distributed straight line or curve (magnet stator, wire, etc.).
For a point charge, finding the tension is as follows: E=k*q/r 2 , where k=9*10 9
When several sources act on the body, the tension at the point will be equal to the vector sum of the potentials. Under the action of a distributed source, it is calculated by the effective integral over the entire distribution area.
The characteristic may change over time due to changes in charges. The value remains constant only for the electrostatic field. It is one of the main power characteristics, therefore, for a homogeneous field, the direction of the vector and the value of q will be the same in any coordinates.
From the point of view of thermodynamics
Tension is one of the main and key characteristics in classical electrodynamics. Its meaning, as well as data electric charge and magnetic induction seem to be the main characteristics, knowing which it is possible to determine the parameters of the flow of almost all electrodynamic processes. She is present and performs important role in such fundamental concepts as the Lorentz force formula and Maxwell's equations.
F-Lorenz force;
- q is the charge;
- B is the magnetic induction vector;
- C is the speed of light in vacuum;
- j - density magnetic current;
- μ 0 - magnetic constant \u003d 1.25663706 * 10 -6;
- ε 0 - electrical constant equal to 8.85418781762039 * 10 -12
Along with the value of magnetic induction, this parameter is the main characteristic of the electromagnetic field emitted by the charge. Based on this, from the point of view of thermodynamics, the intensity is much more important than the current strength or other indicators.
These laws are fundamental; all thermodynamics is based on them. It should be noted that Ampère's law and other earlier formulas are approximate or describe special cases. Maxwell's and Lorentz's laws are universal.
Practical value
The concept of tension has found wide application in electrical engineering. It is used to calculate the norms of signals, calculate the stability of the system, determine the effect of electrical radiation on the elements surrounding the source.
The main area where the concept has found wide application is cellular and satellite communications, television towers and other electromagnetic emitters. Knowing the radiation intensity for these devices allows you to calculate parameters such as:
- range of the radio tower;
- safe distance from source to person .
The first parameter is extremely important for those who install satellite television broadcasting, as well as mobile communications. The second makes it possible to determine the permissible standards for radiation, thereby protecting users from the harmful effects of electrical appliances. The application of these properties of electromagnetic radiation is not limited to communications. Power generation, household appliances, partly the production of mechanical products (for example, dyeing with electromagnetic pulses) are built on these basic principles. Thus, understanding the magnitude is also important for the production process.
Interesting experiments that allow you to see the pattern of electric field lines: video