Electric charge (number of electricity) - This is a physical scalar value that determines the ability of bodies to be the source of electromagnetic fields and take part in electromagnetic interaction. For the first time, the electric charge was introduced in the law of Coulomb in 1785.

The unit for measuring the charge in the international system of units (C) is a pendant - an electrical charge passing through a cross-section of the conductor at a current of 1 and for the time 1 s. One pendant is very large. If two charge carriers ( q. 1 = q. 2 \u003d 1 CL) were located in a vacuum at a distance of 1 m, then they would interact with force 9 · 10 9 H, that is, with force with which the gravity of the Earth would attract the object with a weighing of about 1 million tons. The electrical charge of a closed system is preserved in time and quantum - changes in portions, multiple elementary electrical charge, that is, in other words, the algebraic amount of electrical charges of bodies or particles forming an electrically isolated system does not change with any processes occurring in this system.

Interaction charges The simplest and most daily phenomenon in which the fact of existence in the nature of electrical charges is detected is the electroity of the bodies when contacting. The ability of electrical charges both to mutual attraction and to a mutual repulsion is explained by the existence of two different types of charges. One type of electrical charge is called positive, and the other is negative. The variestly charged bodies are attracted, and the charged eponymoids - repel each other.

With the contact of two electrically neutral bodies, as a result of friction, charges go from one body to another. Each of them violates the equality of the amount of positive and negative chargesAnd the bodies charge variestly.

With the electrification of the body through the effect in it, the uniform distribution of charges is disturbed. They are redistributed so that in one part of the body an excess of positive charges arise, and in the other - negative. If two parts are disconnected, they will be charged variestically.

The law of conservation of EL. Charge In the system under consideration, new electrically charged particles may form, for example, electrons - due to the phenomenon of ionization of atoms or molecules, ions - due to the phenomenon of electrolithic dissociation, etc. However, if the system is electrically isolated, the algebraic amount of charges of all particles, including again Appeared in such a system, always zero.

The law of conservation of an electric charge is one of the fundamental laws of physics. He was first experimentally confirmed in 1843 by the English scientist Michael Faraday and is considered to be one of the fundamental laws of preservation in physics (similar to the laws of preserving the impetus of the Iennergy). An increasingly sensitive experimental checks of the law of preservation of charge, ongoing and today, have not yet revealed deviations from this law.

. Electric charge and its discreteness. The law of saving charge. The law of conservation of an electric charge states that the algebraic amount of charges of an electrically closed system is preserved. Q, Q, E - Electric charge designation. Charge units in C [Q] \u003d CL (pendant). 1MK \u003d 10-3 CL; 1 μKl \u003d 10-6 CL; 1NKl \u003d 10-9 CL; E \u003d 1.6 ∙ 10-19 CL - elementary charge. Elementary charge, e is a minimum charge found in nature. Electron: QE \u003d - E - electron charge; M \u003d 9.1 ∙ 10-31 kg - the mass of the electron and the positron. Positron, Proton: QP \u003d + E - Positron and Proton charge. Any charged body contains an integer elementary charges: Q \u003d ± NE; (1) Formula (1) expresses the principle of discreteness of an electrical charge, where n \u003d 1,2,3 ... is an integer positive number. The law of conservation of an electric charge: the charge of an electrically isolated system over time does not change: q \u003d const. The law of Kulon. - One of the main laws of electrostatics, which determines the strength of the interaction between two point electrical charges.

The law was established in 1785 by sh. Cylonary with the help of spokes invented by them. The pendant was interested not so much by electricity as manufacturing, devices. The invention is an extremely sensitive device for measuring force - the twist scales he was looking for the possibilities for its use.

For the suspension, the pendant used a silk filament with a length of 10 cm, which rotated for 1 ° at 3 * 10 -9 GS. With this device, it found that the interaction force between two electrical charges and between two poles of magnets is inversely proportional to the square square between charges or poles.

Two point charges interact with each other in vacuum with force F. whose value is proportional to the work of charges e. 1 and e. 2 and inversely proportional to the square of the disturbance r. between them:

Proportionality coefficient k. Depends on the choice of the system of units of measurements (in the system of Gauss units k.\u003d 1, in si

ε 0 - Electric constant).

Force F. Directed in a straight line, connecting charges, and corresponds to an attraction for multi-charged charges and repulsion for the same name.

If the interacting charges are located in a homogeneous dielectric, with dielectric constant ε , then the strength of the interaction decreases in ε time:

The law of the coulon is also called the law that determines the strength of the interaction of two magnetic poles:

where m. 1 and m. 2 - magnetic charges,

μ - Magnetic permeability of the medium,

f. - proportionality coefficient, depending on the choice of units.

Electric field - A separate form of manifestation (along with a magnetic field) of the electromagnetic field.

In the process of physics, physics existed two approaches to explaining the reasons for the interaction of electrical charges.

According to the first version, the power action between individual charged bodies was due to the presence of intermediate links transmitting this action, i.e. The presence of the environment of the medium in which the action is transmitted from the point to the point at the final speed. This theory was named theories of closestream .

According to the second version, the action is transmitted instantly at any distances, while the intermediate environment may be absent at all. One charge instantly "feels" the presence of another, and no changes in the surrounding space occurs. This theory was called theory of long-range theory .

The concept of "electric field" was introduced by M. Faraday in the 1930s of the XIX century.

According to Faraday, each resting charge creates an electric field in the surrounding space. The field of one charge acts on another charge and on the turn (concept of closestream).

Electrical field created by stationary charges and not changing over time, called electrostatic. The electrostatic field characterizes the interaction of fixed charges.

Electric field tension - Vector physical quantity characterizing the electric field at a given point and numerically equal to the ratio of the force acting on a fixed point, placed at this field, to the magnitude of this charge:

From this definition you can see why tensions electric field Sometimes called silence characteristic The electric field (indeed, all the difference from the vector of the force acting on the charged particle is only in a constant multiplier).

At each point of space, at the moment there is its value of the vector (generally speaking - different in different points of space), therefore, the ecto-sector field. Formally, this is expressed in the record

representing the tension of the electric field as a function of spatial coordinates (and time, as it can change with time). This field, together with a magnetic induction, is an electromagnetic field, and the laws that it obeys is the subject of electrodynamics.

The voltage of the electric field in the international system of units (SI) is measured in volts per meter [V / M] or in Newton to the pendant [N / CL].

The force with which the electromagnetic field is valid for charged particles[

The complete force with which the electromagnetic field (including generally speaking the electrical and magnetic components) acts on a charged particle, expressed in the Lorentz force formula:

where q. - Electric particle charge - its speed - vector image induction (basic characteristic magnetic field), oblique cross indicated aware of the work. The formula is given in units of C.

Charges that create an electrostatic field can be distributed in space or a discretion or continuously. In the first case, the field strength: n e \u003d σ ei₃ i \u003d T, where EI - tension at a certain point of the field of the field created by one i-M charge Systems, and n - the total number of discretion charges, which are part of the system. An example of solving the problem, which is based on the principle of superposition of electric fields. So to determine the intensity of the electrostatic field, which is created in vacuo by fixed point charges q₁, q₂, ..., qn, we use the formula: n e \u003d (1 / 4πε₀) σ (qi / r³i) Ri i \u003d T, where Ri - radius-vector conducted point charge QI in the field under consideration. We give another example. Determination of the electrostatic field strength, which is created in a vacuum by an electric dipole. Electric dipole is a system of two identical in absolute value and, at the same time, opposite by the signs of charges q\u003e 0 and -q, the distance I between which is relatively small in comparison with the distance of the points under consideration. The shoulder of the dipole will be called the vector L, which is directed along the axis of the dipole to the positive charge from the negative and numerically equal to the distance I between them. Vector Pₑ \u003d QL - Dipole electric moment.

The tension E of the dipole field at any point: E \u003d E₊ + E₋, where E₊ and E₋ are the intensities of the fields of electrical charges Q and -q. Thus, at a point A, which is located on the axis of the dipole, the intensity of the dipole field in vacuo will be E \u003d (1 / 4πε₀) (2pₑ / r³) at the point in the point in the perpendicular restored to the dipole axis from its middle: E \u003d (1 / 4πε₀) (Pₑ / R³) in an arbitrary point M, sufficiently removed from the dipole (r≥L), the intensity module of its field is E \u003d (1 / 4πε₀) (Pₑ / R³) √3cosθ + 1 The principle of superposition of electric fields consists of two statements: the Coulomb force of the interaction of two charges does not depend on the presence of other charged bodies. Suppose that Q is interacting with the charge system Q1, Q2 ,. . . , Qn. If each of the charges of the system acts on the charge Q with the force of F₁, F₂, ..., Fn, respectively, then the resulting force F, applied to the charge q from the side of this system, is equal to the vector sum of the individual forces: F \u003d F₁ + F₂ + ... + Fn. Thus, the principle of superposition of electric fields allows you to come to one important statement.

Power lines Electric field

The electric field is depicted using power lines.

Power lines indicate the direction of force acting on a positive charge at this point point.

Properties of power lines of the electric field

The power lines of the electric field have the beginning and end. They begin on positive charges and end on negative.

The power lines of the electric field are always perpendicular to the surface of the conductor.

The distribution of power lines of the electric field determines the nature of the field. The field may be radial (if the power lines come out of one point or converge at one point), uniform(if the power lines are parallel) and inhomogeneous (If the power lines are not parallel).

Density charge - This is the amount of charge per unit length, area or volume, thus define linear, surface and volumetric charge density, which are measured in the SI system: in culs per meter (CL / m), in the square meter (CL / m² ) and in the cubes on the cubic meter (CL / m³), \u200b\u200brespectively. Unlike the density of the substance, the charge density can have both positive and negative values, this is due to the fact that there are positive and negative charges.

The linear, surface and volumetric charge density is usually indicated by functions, and, accordingly, where- Thisradius vector. Knowing these functions we can determine the full charge:

§5 stream of tension vector

We define the flow of the vector through an arbitrary surface DS, is normal to the surface.α - the angle between the normal and the vector line of the vector. You can enter the vector area. Thread vector called scalar value Equal Scalar Tension Vector Square Vector

For uniform field

For an inhomogeneous field

where is the projection - projection.

In the case of a curvilinear surface S, it must be divided into elementary surfaces ds., calculate the flow through the elementary surface, and the total thread will be equal to the amount or in the limit of the integral from the elementary streams

where is the integral on the closed surface S (for example, on the sphere, cylinder, cube, etc.)

Vector stream is an algebraic value: it depends not only on the field configuration, but also from the choice of direction. For closed surfaces for the positive direction of normal, external normal is received, i.e. Normal directed by the outside area covered by the surface.

For a homogeneous field, the flow through a closed surface is zero. In the case of an inhomogeneous field

3. The intensity of the electrostatic field created by a uniformly charged spherical surface.

Let the spherical surface of the radius R (Fig. 13.7) bearing a uniformly distributed charge Q, i.e. surface density Charge at any point of the sphere will be the same.

We conclude our spherical surface into a symmetric surface S with a radius R\u003e R. Thread stream through the surface s will be equal

According to Theorem Gauss

Hence

Comparing this ratio with the formula for the intensity of the point charge field, it can be concluded that the field strength outside the charged sphere is as if the entire sphere is focused in its center.

2. The electrostatic field of the ball.

Let we have a Radius RF, evenly charged with a bulk density.

Any point A lying outside the ball at the distance R from its center (R\u003e R), its field is similar to the field of point charge located in the center of the ball. Then outside the ball

and on its surface (r \u003d r)

At the point in the insertion of the ball on the distance R from its center (R\u003e R), the field is determined only by the charge enclosed within the sphere by the R radius R. The stream of tension through this sphere is equal

on the other hand, in accordance with Theorem Gauss

From the comparison of the latest expressions should

where- the dielectric constant Inside the ball. The dependence of the field strength created by the charged sphere, from the distance to the center of the ball is shown on (Fig.13.10)

3. The field strength of a uniformly charged endless straight filament (or cylinder).

Suppose that the hollow cylindrical surface of the radius R is charged with a constant linear density.

We carry out the coaxial cylindrical surface of the radius stream of the vector of tension through this surface

According to Theorem Gauss

Of the last two expressions, we determine the intensity of the field created by a uniformly charged thread:

Let the plane have an infinite length and charge per unit area equal to σ. From the laws of symmetry it follows that the field is directed everywhere perpendicular to the plane, and if there are no other external charges, the fields on both sides of the plane should be the same. We limit the part of the charged plane by an imaginary cylindrical box, so that the box will cut off in half and its formulations were perpendicular, and two bases having an area s each parallel to the charged plane (Fig. 1.10).

The total stream of the vector; Tension is equal to the vector multiplied by the first base area, plus the flow vector perfectly the opposite basis. The stream of tension through the side surface of the cylinder is zero, because The lines of tension do not intersect. Thus, on the other hand, the Gaussian Theorem

Hence

but then the field strength of an infinite uniformly charged plane will be equal to

This expression does not include coordinates, therefore the electrostatic field will be homogeneous, and its tension at any point of the field is the same.

5. The field strength created by two infinite parallel planes charged varies with the same densities.

As can be seen from Figure 13.13, the field strength between two endless parallel planes having surface densities of charges and are equal to the sum of the intensities of the fields created by the plates, i.e.

In this way,

Outside the plate, the vectors from each of them are directed in opposite sides and are mutually destroyed. Therefore, the field strength in the space surrounding the plates will be zero e \u003d 0.

Electric field - one of the two components electromagnetic field, which is a vector field that exists around bodies or particles with an electric charge, as well as an arising from the magnetic field change (for example, in electromagnetic waves). The electric field is directly invisible, but can be detected due to its power influence on charged bodies

Electric field tension - vector physical quantity, characterizing the electric field at a given point and numerically equal to the ratio of the power acting on a fixed point charge, placed at this point of the field, to the magnitude of this charge:

It can be seen from this definition, why the electric field strength is sometimes referred to as the power characteristic of the electric field (indeed, all the difference from the power vector acting on the charged particle, only in a constant multiplier).

At this point of space, at the moment there is a vector of the vector (generally speaking - different in different points of space), therefore, this is a vector field. Formally, this is expressed in the record

representing the electric field strength as a function of spatial coordinates (and time, because it may vary with time). This field together with the magnetic induction vector field is an electromagnetic field, and the laws that it obeys is the subject of electrodynamics.

The voltage of the electric field in the international system of units (SI) is measured in volts per meter [V / M] or in Newton to the pendant [N / CL].

The power line, or the integral curve is a curve, which is a tangent to which at any point coincides in the direction with a vector that is the element of the vector field at the same point. It is used to visualize vector fields that are difficult to visually portray in any other way. Sometimes (not always) on these curves, arrows are set, showing the direction of the vector along the curve. For vectors physical fieldforming the power lines is usually used by the term "tension".

Different kinds Real physical fields have their own characteristics that are manifested in the image of integral curves. In particular, the electrical charge is centerin which the power lines converge. Electrical field according to Maxwell equations and, it can be both potential (due to the presence of electrical charges) and vortex (arising from the phenomenon electromagnetic induction), or a combination of these two cases. According to Maxwell equations and, and so far, magnetic monopolis are unknown, the magnetic field can only occur as a result of the change electric induction (The first term in the left side of the 2nd equation) and the flow electric current (the second term in the left side of the 2nd equation)

If the field is formed not by one charge, but a few, then the forces acting on the trial charge are consisted by the rule of the formation of vectors. Therefore, the tensions of the charge system at a given point, the fields are equal to the vector sum of field tensions from each charge separately.

For the characteristics of the electric field created by charges, two magnitudes are introduced - the electric field strength and its potential. Tensions characterizes the force acting on the side of the field to the trial charge made into it. If at some point of the field, the power acts on the charge, then the electric field strength at this point is equal to

where - the charge that we took to "try" the field at this point. This charge is called "trial". The trial charge should not distort the distribution of charges, creating a field, and therefore should be small enough. In formula (18.1), the trial charge is included with his sign (not a module), therefore, as follows from (18.1), the field strength vector at some point is directed the same as the vector of force acting at this point on a positive test charge.

We find the electric field strength created by a point charge. To do this, take an arbitrary trial charge and put it on a point at a distance from charge. The force acting on the test charge from charge is determined by the Coulomb law (17.1), (17.2). Therefore, according to (18.1) we have

where . Directed vector of tension from charge if and to him if .

Let the field be created by several charges ... In this case, its tension is equal to the vector sum of the tensions of those fields that are created by each charge separately. Indeed, from the principle of superposition it follows that the force in this case is powerful

..., where ... - Forces acting on the test charge from each charge ... Therefore, from (18.1) we get

where ... - the tensions of those fields that would be created by each charge separately in the absence of other charges. Approval (18.3) is called the principle of superposition for fields. Formula (18.2) and the principle of superposition allow you to calculate the field created by any charged body - using a mental splitting of it to point parts and summation of the tensions created by all such parts. However, due to the mathematical complexity of such a procedure, it is not included in the physics school program. The schoolboy should know without withdrawing the result of its use to charged areas and planes. From formulas (17.4), (17.5) We obtain for the field strength of the field of radius, evenly charged charge, at a point at a distance from the center of the sphere:

where - the charge of the plane, is the area, the surface density of the plane charges.

The electric field can be depicted graphically (in modern Russian - visualize) With the help of power lines. Power lines are such imaginary lines due to which at each point coincide in the direction with the vector of tension at this point. Generally speaking, the power lines pass through each field of the field (except for those points where ), But since it is impossible to draw them, it was agreed to carry out them with a certain degree depending on the size of the field: the thick of the power lines, the greater the field strength.

The second characteristic of the electric field is its potential. The main idea of \u200b\u200bintroducing this magnitude is as follows. If the electrical charge moves in an electric field (created by other charges), then the field has forces, and, therefore, the field does work. Field potential is such a field point function. that the work performed by the field above the point test charge when it is moved from the point with a radius-vector to a point with a radius-vector is equal to

(It is in such a sequence). From formula (18.6) it follows that the work that the field performs when the charge is moving does not depend on the form of the trajectory, but is determined only by the initial and ultimate points. In particular, when moving the body on a closed trajectory, the field makes zero.

Since in formula (18.6), the difference of potentials of two points of the field is included, the potential is determined up to constant. This constant can always be chosen so that the potential of any specified point of the field can be made equal to zero. As a rule, as such a point, the point of the field is infinitely removed from charges, considering its potential to zero. From formula (18.6) it follows that the potential of any point of the field is equal to the attitude of the electrical field when moving the test charge from this point to the point, the potential of which is selected with zero, to the trial charge.

It can be proved that if the field is created by a point charge, then the potential at a distance from charge, provided that the potential of an infinitely remote point is taken for zero, is equal to

It is important to note that in formula (18.7) includes a charge with a sign (not a module!), I.e. The potential of the field created by a positive charge is positive, negative - negative.

For potentials, the principle of superposition is valid: if the field is created by several point charges, the potential of any point is equal to the algebraic amount of potentials (18.7), created at this point by each point charge. This rule allows you to find the potential of the field created by an extended charged body: you need to mentally divide the body into small ("spot") parts, according to formula (18.7) to find the potential of the field created by each such part, and then fold the results obtained.

To solve the tasks of the EGE, you need to know (without output) the formula of the potential of the field of a uniformly charged sphere. Let there be a sphere of radius, evenly charged with charge. Then the potential of the point of the field located at the distance of the center of the sphere is equal to

(The point of zero potential is chosen at infinity).

Often, in the tasks of the exam in physics, the connection of the tension of a homogeneous electric field and the difference in the potentials of two points of the field lying on one power line is used. To find this connection, take a positive trial charge, we take it from the first point in the second along the power line and find the work that the electric field does. Since the field acts on a charge with a constant force, the angle between the movement and this force is zero (the charge moves along the power line), so the operation of the field forces is equal where - the distance between the test points. On the other hand, by definition of the potential, the operation of the field is equal . Equating these works, find

We emphasize that Formula (18.9) is valid only for a homogeneous field, and points 1 and 2 must lie on the same power line.

Consider now the tasks.

The magnitude of the electric field strength created by a point charge ( task 18.1.1) is determined by the formula (18.2)

where (answer 1 ).

The dimension of the electric field strength ( task 18.1.2) It can be found from the field strength and potential (see formula (18.9)). And since the dimensionality of the potential in the international system of SI-Volt units, from formula (18.9) we have:

where square brackets denote dimension (answer 3 ).

To determine the field strength, a test charge is used (see formula (18.1)). However, tensions (18.1) are not dependent on the sign, nor from the value of the test charge ( task 18.1.3.). This is due to the fact that the force in (18.1) linearly depends on the trial charge, and it is reduced in (18.1). If you take a trial charge negative, then the vector direction of the numerator (18.1) will change compared with the case of a positive test charge, but the attitude will be sent to the opposite vector, i.e. Vector direction will not change (answer 4 ).

To find a field created by two point charges ( task 18.1.4.), We use the principle of superposition. The intensity of the fields created at the point by each charge separately, is shown by thin vectors and are marked as. Since the modules of these vectors are equal, the vector of their sum is directed vertically down (answer 4 ).

By definition, power lines are such imaginary lines tangents that at each point coincide in the direction with the vector of tension at this point ( task 18.1.5. - answer 4 ).

Since the power lines of the field in task 18.1.6 The direction of tension at each point is directed to the right, the right direction and the vector of tension at each point. Therefore, the right to right and the vector of force acting on the part of this field on the positive point charge (answer 2 ).

Since all charge trajectories I, II and III in task 18.1.7 Start and end at the same points, the work of the field above the charge when it moves in all three trajectories the same (answer 4 ).

The difference in the potentials of two points of the uniform electric field ( task 18.1.8) We will find according to the formula (18.9):

(answer 1 ).

Since the vector of electric field strength at any point is directed from charge, the fields of fields are diverted radially, being directly directly (see. Sync). Thus, the correct answer in task 18.1.9 - 1 .

By definition of the potential, we have to work the field in task 18.1.10

(answer 3 ).

The power lines of the electric field are built so that their thickness is proportional to the size of the field: the thick of the power lines, the greater the magnitude of the tension. Therefore B. task 18.2.1 (answer 2 ).

Figure B. task 18.2.2 - The same as in the previous task, however, the logic of getting a response is completely different. To compare the potentials at points 1 and 2, we move from the first point to the second positive trial charge and find the work of the field. Because , and if the work is positive, then if negative is the opposite. Obviously, the operation of the field when moving positive charge From point 1 to point 2 positive. Indeed, the arrows on the power lines are directed to the right, consequently, the force acting on a positive charge is directed to the right, the vector of charge movement is also directed there, so the cosine of the angle between force and movement is positive on all elementary trajectory sites, so the work is positive. In this way (answer 1 ), and this result is a consequence of the direction of the shooters on the power lines, and not a variable thickness of power lines.

Lord, a great greeting! Today we will consider the topic of interaction of charges, get acquainted with culon law, learn what is tension Electric field, as well as learn how to draw power lines. We start right now!

Gentlemen, the modern theory of physics claims that the charges act on each other not directly, but through the electric field. That is, every charge around him in space creates the field and through this field has an impact on other charges.

What is the electric field at all? Yes, in fact, no one knows this. There is an opinion that it is such a type of matter. That it is created by electrical charges. If somewhere there is an electric charge - there will be an electric field around it in any way. And this field will act on other charges. The charges act on each other are not otherwise, as through an electric field, which every charge creates.

So, the charges act in each other are not directly, but through the fact that each of them creates an electric field around itself. But, probably, there must be laws, there may be even mathematical formulas that formally describe this process and allow you to calculate the forces with which these the most charges interact. Indeed, such a law is also called the law of Kulon.

Let us have two charges Q 1 and Q 2. Formally they should be point.Then the strength of their interaction in vacuum is directly proportional to the product of these two charges and is inversely proportional to the square of the distance between them.

Here, actually, and all the law of the coulon. A reasonable question - and where did it all come from and why should I believe?! Gentlemen, the law is experimental, mathematically, it is not northworth anywhere. Well, i.e. Dear Mr. Pendon conducted a number of experiments on the interaction of charges on the so-called twist scales. And on the basis of generalizing experienced data, he received this expression. Whoever believes - Google to help. Find the installation scheme and you can repeat the path of the coolement itself.

Gentlemen, remember that we have a coefficient there k, About which has not yet been told a word. He is equal

where ε 0 \u003d 8,85⋅10 -12 - electric constant.

A completely expected question - what is so complicated?!

Gentlemen, all because of confusion with a calculus system. There is such a system of calculating the SGSE - such where the forces are measured in dina And other obsolences in the opinion of fans of the SI Orthodox system. So, initially the law was written under this system and in her k.=1. And when transferring to the SI system, all this disgrace and promoted. Divide the same k.on 4π I. ε 0 It is useful in the future, they are much when they are used by separately.

Still, gentlemen, you probably noticed that when recording the law of Culon, it was about a vacuum? And what will be in any environment? If the charges interact in the water? Or in oil? Or where else?

Gentlemen, the power of interaction will be less than several times! At what time? ATε time. Yes, a special coefficient is introduced ε called dielectric permeability of the environment And just shows how many times the strength of the interaction of charges in this medium is less than in vacuum. This is a tabletable. So, gentlemen, if I'm interested in Google and there will find for your substance what kind of dielectric permeability of the medium.

So, the law of coulon for the incidence of charges in the environment will look like this:

Now let's do the phint ears. From the course of mechanics, which, I hope you remember, power - vector magnitude. And for us while everywhere appeared scalar. How to go to vectors? For example, like this:

Now everything is honest, we have vectors. - Vector radius from one charge to another. Such a record is convenient because it allows you to calculate the case of the interaction of several charges in arbitrary spaces. Then the forces add up by the law of the addition of vectors. However, for the simplest case one r. Reduced and everything remains still.

Well, the electric field is created by charges, it is understandable. But how to characterize this the field? The answer is very obvious on the one hand and maybe a little unexpected on the other. Gentlemen, I ask you to look at the formula of the law of Kulon a little bit at a different angle. Imagine that the Q1 charge is the source of the electric field and in its field we put trial Charge Q2. Changing the Q2 charge, we will change and the force F (we consider it under the law of the coulon), with which the charge Q1 is valid for it. The attitude of this force to the trial chargeq.2 All the time constantly. And can be used as a characteristic of the charge fieldq.1. it tension electric field.

Yes, it is also a vector magnitude. Because power - vector magnitude. However, in many simple cases, everything is easily reduced to the scalars according to the principles described above.

Gentlemen, from the written formula it is clear that the tension of the electric field depends on the charge, which creates it from the distance to the charge source. Well, that is, what more charge And what we closer to it, the intensity of the field is more.

Knowing the electric field strength is easy to determine how power the field is valid for the charge placed in this field:

If we have several fields in space, it is similar to how the forces are folded, field strengths will also be formed:

So it turned out that a person perceives the material much better if he draw a beautiful picture. I am so at all on a rumor, without the pictures, in general, very badly caught. Also with the field. We talked like this is a special form of matter and all that. And now, it turns out, we can draw the field! Well, it is, of course, a very bold expression. In fact, we will graphically characterize the field using the so-called power lines.Gentlemen, attention. A little ending brain definition. Power lines are such lines, tangents that everywhere coincide with the intensity of tension. Well, that is, it is necessary to draw such a line, so that the vector of tension was to it tangent to each point of the field. Power lines have a direction. They go from the plus to minus. In addition, the power lines never intersect with each other.

I give examples of drawings, for the identification of which I killed a couple of hours! All for you, gentlemen!

Figure 1 shows the power lines of a single positive charge. They come from him and go far, far into the surrounding space. With increasing distance, the number of lines per square meter is becoming less and less, the lines go more caught.This is equivalent to a decrease in field strength. The same confirms the formula.

Figure 1 - Positive charge strength lines

Figure 2 shows the picture of the power lines of two charges of one sign. In our example for negative. For example, two electrons. Sheet lines are not between charges, they repel each other.

Figure 2 - Power lines of two negative charges near each other

Figure 3 shows the field of field strength for two charges of different characters. The power lines are densely concentrated between them - there is a high field intensity.

Figure 3 - Power lines of positive and negative charges.

So, the power lines are an excellent tool for a better understanding of the field.

Gentlemen, today we defined as interacting with each other electric charges, I got acquainted with the law of Kulon, learned about the tension of the electric field and posed the power lines. I think it is quite enough. So far and huge success!

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