The main values \u200b\u200bof electrostatics. Electrostatics

In electrostatics, one of the fundamental is the law of Coulomb. It is used in physics to determine the interaction force of two fixed point charges or distances between them. This is the fundamental law of nature, which does not depend on any other laws. Then the form of the real body does not affect the magnitude of the forces. In this article we will tell us a simple language of the law of Kulon and its application in practice.

History opening

Sh.O. Pendant in 1785 for the first time experimentally proved the interaction of the law described. In their experiments, he used special tweeted scales. However, in 1773, it was proved by Cavendis, on the example of a spherical capacitor, which within the sphere there is no electrical field. This said that the electrostatic forces vary depending on the distance between the bodies. To be more accurate - the square square. Then his studies were not published. Historically, this discovery was named after the coulon, the same name is and the value in which the charge is measured.

Formulation

Definition of the Culon Law reads: In vacuumF interaction of two charged bodies is directly proportional to the product of their modules and inversely in proportion to the square of the distance between them.

It sounds brief, but may not be all clear. Simple words: The greater charge has the body and the closer they are to each other, the more power.

And vice versa: If you increase the distance between the charges - the force will become less.

Formula Rules of Coulomb looks like this:

Designation of letters: Q is the value of the charge, R is the distance between them, K - the coefficient depends on the selected system of units.

The value of the charge q may be conditionally positive or conventionally negative. This division is very conditional. When contacting bodies, it can be transmitted from one to another. It follows that one and the same body can have a different value and a charge sign. The point is called such a charge or body, the dimensions of which are much less than the distance of possible interaction.

It is worth considering that the medium in which the charges are located, affects F interaction. Since in the air and in vacuum it is almost equal, the opening of the coulon is applicable only for these environments, this is one of the conditions for the application of this type of formula. As already mentioned, in the system SI, the unit of charge is a pendant, reduced CL. It characterizes the amount of electricity per unit of time. It is derived from major SI units.

1 cl \u003d 1 A * 1 with

It is worth noting that the dimension of 1 CL is redundant. Due to the fact that the carriers are repelled from each other they are difficult to hold in a small body, although the current itself in 1a is small, if it occurs in the conductor. For example, in the same incandescent lamp by 100 W flow flows at 0.5 A, and in the electrical heater and more than 10 A. Such strength (1 CL) is approximately equal to the body by weight of 1 ton from the ground side.

You could see that the formula is practically the same as in gravitational interaction only if the masses appear in Newtonian mechanics, then in electrostatics - charges.

Cool formula for dielectric medium

The coefficient, taking into account the magnitudes of the SI system, is determined in H 2 * m 2 / CL 2. It is equal:

In many textbooks, this coefficient can be found in the form of a fraction:

Here e 0 \u003d 8.85 * 10-12 CL2 / N * M2 is an electrical constant. E - dielectric permeability of the medium is added to dielectric, then the law of the coulon can be used to calculate charge interaction for vacuum and medium.

Taking into account the effect of the dielectric is:

From here we see that the administration of dielectric between the bodies reduces the power of F.

How the forces are directed

The charges interact with each other depending on their polarity - the same repel, and the variepetes (opposite) are attracted.

By the way, this is the main difference from such a law of gravitational interaction, where the bodies are always attracted. The forces are directed along the line conducted between them, called the radius vector. In physics, it is designated as R 12 and as a radius-vector from the first to the second charge and vice versa. The forces are directed from the charge center to the opposite charge along this line, if the charges are opposite, and in the opposite direction, if they are the same (two positive or two negative). Vector:

The force applied to the first charge from the second side is denoted as F 12. Then in vector form, the law of the coulon looks like this:

To determine the force applied to the second charge, the designations F 21 and R 21 are used.

If the body has a complex shape and it is quite large, that at a given distance can not be considered point, then it is broken into small sections and consider each site as a point charge. After the geometric addition of all the resulting vectors, the resulting force is obtained. Atoms and molecules interact with each other through the same law.

Application in practice

Coulomb works are very important in electrostatics, in practice they are used in a number of inventions and devices. A bright example can be distinguished by a lightning conduction. With it, they protect buildings and electrical installations from thunderstorms, thereby preventing the fire and failure of the equipment. When it rains with a thunderstorm on Earth, an induced charge of a large magnitude appears, they are attracted towards the cloud. It turns out that a large electric field appears on the surface of the Earth. It has a greater value, as a result of this, the crown discharge (from the ground, through the lightning loss to the cloud) is ignited from the tip. The charge from the Earth is attracted to the opposite charge of the clouds, according to the law of the coulon. The air is ionized, and the electric field strength decreases near the end of the lightning conduction. Thus, charges do not accumulate on the building, in this case the probability of lightning strike is small. If the blow to the building and happens, then through the lightning resulting all the energy will go to the ground.

In serious scientific research, the greatest structure of the 21st century is used - particle accelerator. In it, the electric field performs work to increase the particle energy. Considering these processes in terms of exposure to the point charge of a group of charges, then all the relationships of the law are valid.

Useful

Encyclopedic YouTube.

• 1 / 5

  The foundation of electrostatics laid the work of Coulomb (although ten years before him, the same results, even with even greater accuracy, received Cavendish. The results of the works of Cavendish were kept in the family archive and were published only after a hundred years); The law of electrical interactions found by the latest law enabled Green, Gauss and Poisson to create elegant in mathematically theory. The most significant part of electrostatics is the theory of potential created by the Green and Gauss. A very many experienced research on electrostatics was produced by the rice of the book of which were at the same time the main allowance in the study of these phenomena.

  The dielectric constant

  Finding the values \u200b\u200bof the dielectric coefficient K of any substance, the coefficient incoming in almost all formulas with which it is necessary to deal with electrostatics can be produced very different ways. The most common ways are the essence of the following.

  1) Comparison of the electrical dispensers of two capacitors having the same dimensions and shape, but in which one insulating layer is a layer of air, in the other - a layer of the dielectric test.

  2) Comparison of attractions between the surfaces of the condenser when this surfaces are reported to a certain potential difference, but in one case the air is located between them (the force of attraction \u003d F 0), in another case, the test liquid insulator (attraction force \u003d f). The dielectric coefficient is in the formula:

  K \u003d f 0 f. (\\ displaystyle k \u003d (\\ FRAC (F_ (0)) (F)).)

  3) observations of electrical waves (see electrical oscillations) propagating along the wire. By the theory of Maxwell, the speed of distribution of electrical waves along the wire is expressed by the formula

  V \u003d 1 k μ. (\\ DisplayStyle V \u003d (\\ FRAC (1) (\\ SQRT (K \\ MU))).)

  in which K denotes the dielectric coefficient of the medium surrounding the wire, μ denotes the magnetic permeability of this medium. Can be put for a huge majority of tel μ \u003d 1, and therefore it turns out

  V \u003d 1 k. (\\ DisplayStyle V \u003d (\\ FRAC (1) (\\ SQRT (K))).)

  It is usually compared the lengths of standing electrical waves arising in parts of the same wire in the air and in the test dielectric (liquid). Having determined these lengths λ 0 and λ, they obtain k \u003d λ 0 2 / λ 2. According to Maxwell theory, it follows that when the electrical field is excited in any insulating substance, special deformations arise within this substance. Along the induction tubes, an insulating medium is polarized. It occurs in it, electrical displacements occur, which can be moved by the movements of positive electricity in the direction of the axes of these tubes, and through each cross-section of the tube passes the amount of electricity equal to

  D \u003d 1 4 π k f. (\\ DisplayStyle D \u003d (\\ FRAC (1) (4 \\ PI)) kf.)

  Maxwell's theory makes it possible to find the expressions of those internal forces (tension and pressure forces), which are in dielectrics when the electric field is excited. This question was first reviewed by Maxwell himself, and later and more thoroughly with Helmholz. Further development of the theory of this issue and closely connected with this theory of electricaltrix (that is, the theories that considering phenomena, depending on the occurrence of special stresses in dielectrics during the excitation of the electric field in them) belongs to the works of Lorberg, Kirchhoff, P. Duhmama, N. N. Schiller and Some dr.

  Border conditions

  We will finish a summary of the most significant of the electro-crushing department by considering the refraction of induction tubes. We present it in the electric field two dielectrics separated from each other by some surface S, with dielectric coefficients to 1 and K 2.

  Let at points p 1 and p 2, located infinitely close to the surface S along the other side, the values \u200b\u200bof the potentials are expressed by V 1 and V 2, and the values \u200b\u200bof the forces tested placed at these points by the unit of positive electricity through F 1 and F 2. Then, for the point p lying on the surface S must be 1 \u003d v 2,

  d v 1 d s \u003d d v 2 d s, (30) (\\ displaystyle (\\ FRAC (DV_ (1)) (DS)) \u003d (\\ FRAC (DV_ (2)) (DS)), \\ Qquad (30))

  if DS is infinitely small moving along the intersection line of the tangent plane to the surface S at the point P with a plane passing through the normal surface at this point and through the direction of electrical strength in it. On the other hand, must be

  K 1 d v 1 dn 1 + k 2 d v 2 dn 2 \u003d 0. (31) (\\ displaystyle k_ (1) (\\ FRAC (DV_ (1)) (DN_ (1))) + k_ (2) ( \\ FRAC (DV_ (2)) (DN_ (2))) \u003d 0. \\ QQuad (31))

  Denote by ε 2 angle, component of the force F2 with a normal N2 (inside the second dielectric), and through ε 1 angle, designed by force F 1 with the same normal N 2 then, using formulas (31) and (30), we will find

  T g ε 1 T g ε 2 \u003d k 1 k 2. (\\ displaystyle (\\ FRAC (\\ MathRM (TG) (\\ Varepsilon _ (1))) (\\ MathRM (TG) (\\ Varepsilon _ (2)))) \u003d (\\ FRAC (K_ (1)) (K_ ( 2))).)

  So, on the surface separating two dielectrics from each other, the electrical force undergoes a change in its direction like a light beam incoming from one medium to another. This consequence of theory is justified by experience.

  Even in ancient Greece, it was noticed that the amber-sided fur begins to attract small particles - dust and crumbs. For a long time (up to mid-18th century) could not give a serious substantiation of this phenomenon. Only in 1785, the pendant, observing the interaction of charged particles, brought the basic law of their interaction. After about half a century, Faradays studied and systematized the effect of electric currents and magnetic fields, and after another thirty years, Maxwell substantiated the theory of the electromagnetic field.

  Electric charge

  For the first time, the term "electric" and "electrification", as derivatives from the Latin word "Electri" - amber, were introduced in 1600. English scientists W. Hilbert to explain the phenomena that arise when rubbing amber fur or glass of leather. Thus, the bodies that have electrical properties have become electrically charged, that is, they were transmitted electrical charge.

  From the above it follows that an electrical charge is a quantitative characteristic showing the degree of possible body participation in electromagnetic interaction. The charge is denoted by q or q and has a discharge pendant (CL)

  As a result of numerous experiments, the main properties of electrical charges were derived:

  • there are charges of two types that are conditionally named positive and negative;
  • electrical charges can be transmitted from one body to another;
  • the electrical charges of the same name are repelled from each other, and the relevant - attract each other.

  

  In addition, the law of saving charge was established: the algebraic amount of electrical charges in a closed (isolated) system remains constant

  In 1749, the American inventor Benjamin Franklin puts forward the theory of electrical phenomena, according to which electricity is a charged fluid, the lack of which it determined as a negative electricity, and excess - positive electricity. Thus, the famous paradox of electrical engineering appeared: according to the theory of B. Franklin, electricity flows from a positive to the negative pole.

  According to the modern theory of the structure of substances, all substances consist of molecules and atoms, which in turn consist of an atom kernel and electrons rotating around it ". The kernel is inhomogeneous and consists in turn from protons "P" and neutron "n". Moreover, electrons are negatively charged particles, and the protons are positively charged. Since the distance between the electrons and the atom core significantly exceeds the dimensions of the particles themselves, the electrons can be cleaved from the atom, thereby determining the movement of electrical charges between the bodies.

  

  In addition to the properties described above, the electric charge has a property of division, but there is a value of the minimum possible indivisible charge equal to the absolute value of the electron charge (1.6 * 10 -19 CL), also called an elementary charge. Currently, the existence of particles with an electric charge is less than the elementary, which are called quarks, but the time of their existence is slightly and in the free state they are not detected.

  The law of the coulon. Superposition principle

  The interaction of fixed electrical charges is studied by the section of physics named electrostatic, which actually actually lies the law of the coulon, which was derived from numerous experiments. This law, as well as the unit of electric charge, was named after the French Chall Physics.

  Pendant Conducting his experiments found that the strength of the interaction between two small electric charges is subject to the following rules:

  • the force is proportional to the magnitude of each charge;
  • the force is inversely proportional to the square of the distances between them;
  • the direction of force is essential along the direct connecting charge;
  • the force is an attraction if the bodies are charged opposite, and repulsion in the case of the same charges.

  Thus, the law of the coulon is expressed by the following formula

  

  where Q1, Q2 is the magnitude of electric charges,

  r is the distance between two charges,

  k is a proportionality coefficient equal to k \u003d 1 / (4πε 0) \u003d 9 * 10 9 kL 2 / (H * m 2), where ε 0 is the electrical constant, ε 0 \u003d 8.85 * 10 -12 CL 2 / ( N * m 2).

  I note that the previously electrical constant ε0 was called the dielectric constant or dielectric permeability of the vacuum.

  

  The law of Culon manifests itself, not only when the interaction of two charges, but also that the system is more common from several charges. In this case, the law of Kulon is complemented by another significant factor called "the principle of overlays" or the principle of superposition.

  The principle of superposition is based on two rules:

  • impact on a charged particle of several forces is the vector sum of the effects of these forces;
  • any complex movement consists of several simple movements.

  The principle of superposition, in my opinion, is the easiest to portray graphically

  

  The figure shows three charges: -q 1, + Q 2, + Q 3. In order to calculate the strength of the F total, which acts on charge -q 1, it is necessary to calculate according to the law of the coolement of the interaction force F1 and F2 between -Q 1, + Q 2 and -q 1, + Q 3. Then, the resulting forces are folded according to the rule of the formation of vectors. In this case, F was calculated as a diagonal of the parallelogram according to the following expression

  where α is the angle between the vectors F1 and F2.

  Electric field. Electric field tension

  Any interaction between charges, called the Coulomb interaction (by the name of the Culon law), occurs with the help of an electrostatic field, which is immutable in time by the electric field of fixed charges. The electrical field is part of the electromagnetic field and it is created by electrical charges or charged bodies. The electric field affects charges and charged bodies, regardless of whether they are moving or are at rest.

  One of the fundamental concepts of the electric field is its tension, which is defined as the ratio of the strength of the current in the electric field to the magnitude of this charge. To disclose this concept, it is necessary to introduce such a concept as a "trial charge".

  "Trial charge" is called such a charge that does not participate in the creation of an electric field, and also has a very small amount and therefore its presence does not cause the redistribution of charges in space, thereby not distorting the electric field created by electrical charges.

  

  Thus, if you make a "trial charge" Q 0 to a point, which is at some distance from the charge Q, then some force F, due to the presence of the charge q, will act on the "trial charge". The ratio of the power of F 0 acting on a trial charge, in accordance with the law of the coulon, to the magnitude of the "test charge" is called the electric field strength. The electric field strength is indicated by E and has the bittenness of N / CL

  

  The potential of the electrostatic field. Potential difference

  As you know, if any power acts on the body, then such a body makes a certain job. Consequently, the charge placed in the electric field will also perform work. In the electric field, the work performed does not depend on the trajectory of motion, but is determined only by the position that occupies a particle at the beginning and end of movement. In the physics of the field like an electric field (where work does not depend on the trajectory of the body movement) are called potential.

  

  The work performed by the body is determined by the following expression

  

  where F is the force acting not the body,

  S - the distance traveled by the power body F,

  α is the angle between the direction of the body movement and the direction of force F.

  Then the work performed by the "test charge" in the electric field created by the charge Q 0 will be determined from the law of the coulon

  

  where Q p - "Trial charge",

  q 0 - a charge creating an electric field,

  r 1 and R 2 - respectively, the distance between Q P and Q 0 in the initial and final position of the "test charge".

  Since the performance is associated with the change in the potential energy W p, then

  

  And the potential energy of the "test charge" in each hotel point of the trajectory of movement will be determined from the following expression

  

  As can be seen from the expression with a change in the magnitude of the "test charge" Q n value of the potential energy W P will be changed in proportion to Q P, therefore, another parameter was introduced to the characteristic of the electric field, which is the potential of the electric field φ, which is the energy characteristic and is determined by the following expression

  

  where k is the proportionality coefficient equal to k \u003d 1 / (4πε 0) \u003d 9 * 10 9 kL 2 / (H * m 2), where ε 0 is the electrical constant, ε 0 \u003d 8,85 * 10 -12 KL 2 / (N * m 2).

  Thus, the potential of the electrostatic field is an energy characteristic that characterizes the potential energy, which has a charge, placed at this point of the electrostatic field.

  From the above, we can conclude that the work performed when moving the charge from one point to another can be determined from the following expression

  That is, the work performed by the electrostatic field with the movement of the charge from one point to another is equal to the charge of the charge on the potential difference in the initial and endpoints of the trajectory.

  When calculating the most convenient to know the potential difference between the points of the electric field, and not the specific values \u200b\u200bof the potentials in these points, therefore, speaking about the potential of any point of the field, the potential difference between this point and the other point of the field, the potential of which was to be considered equal to zero.

  The potential difference is determined from the following expression and has a volt dimension (B)

  

  

  Continued read in the next article

  The theory is good, but without practical application it is just words.

  Electric charge - This is a physical quantity characterizing the ability of particles or tel to enter into electromagnetic interactions. Electric charge is usually indicated by letters q. or Q.. In the SI system, the electrical charge is measured in the cabins (CL). The free charge of 1 CL is a gigantic amount of charge, practically not found in nature. As a rule, you will have to deal with microcolehons (1 μl \u003d 10 -6 CL), nanocoles (1 NNK \u003d 10 -9 CL) and picocoleons (1 PPC \u003d 10 -12 CL). Electrical charge has the following properties:

  1. Electrical charge is a type of matter.

  2. The electrical charge does not depend on the movement of the particle and from its speed.

  3. Charges can be transmitted (for example, with direct contact) from one body to another. Unlike body weight, an electrical charge is not an integral characteristic of this body. The same body in different conditions may have a different charge.

  4. There are two kinds of electric charges, conditionally mentioned positive and negative.

  5. All charges interact with each other. At the same time, the charges of the same name are repelled, the variepetes are attracted. The interaction forces are central, that is, they lie on a straight line connecting charge centers.

  6. There is a minimum possible (module) electrical charge called elementary charge. Its value:

  e. \u003d 1,602177 · 10 -19 CL ≈ 1.6 · 10 -19 CB.

  Electric charge of any body is always keen elementary charge:

  where: N. - integer. Note, the existence of a charge is not possible 0.5 e.; 1,7e.; 22,7e. etc. Physical quantities that can only take a discrete (not continuous) range of values \u200b\u200bare called quantized. Elementary charge E is a quantum (smallest portion) of an electric charge.

  In an isolated system, the algebraic amount of charges of all bodies remains permanent:

  The law of conservation of an electric charge argues that in a closed system of bodies, the processes of birth or the disappearance of charges of only one sign can not be observed. From the law of saving the charge also follows, if two bodies of the same size and shapes with charges q. 1 I. q. 2 (absolutely no matter what sign of charges), lead to contact, and then distribute back, then the charge of each body will be equal to:

  From a modern point of view, elementary particles are carriers of charges. All ordinary bodies consist of atoms, which includes positively charged protonsnegatively charged electrons and neutral particles - neutron. Protons and neutrons are part of atomic nuclei, electrons form an electron sheath of atoms. Electrical charges of proton and electron modulo are exactly the same and equal to elementary (that is, the minimum possible) charge e..

  In a neutral atom, the proton number in the core is equal to the number of electrons in the shell. This number is called an atomic number. Atom of this substance may lose one or more electrons, or to purchase an excess electron. In these cases, the neutral atom turns into a positive or negatively charged ion. Note that the positive protons are part of the atomic core, so their number can change only under nuclear reactions. Obviously, when electrifying bodies of nuclear reactions does not occur. Therefore, in any electrical phenomena, the number of protons does not change, only the number of electrons changes varies. Thus, the message of the body of a negative charge means the transmission of unnecessary electrons. A message of a positive charge, contrary to a frequent error, means not the addition of protons, but torn electron. The charge can be transmitted from one body to another only portions containing an integer electrons.

  Sometimes in the tasks, the electrical charge is distributed over some body. To describe this distribution, the following values \u200b\u200bare introduced:

  1. Linear charge density. Used to describe the distribution of the thread charge:

  where: L. - The length of the thread. Measured in CL / m.

  2. Surface charge density. Used to describe the charge distribution over the body surface:

  where: S. - Body surface area. Measured in CL / m 2.

  3. Volume density charge. Used to describe the distribution of charge by volume of the body:

  where: V. - body volume. It is measured in CL / m 3.

  Note that electron mass equal to:

  m E. \u003d 9.11 ∙ 10 -31 kg.

  The law of Kulon.

  Point charge Called the charged body, the sizes of which in the conditions of this task can be neglected. Based on numerous experiments, the pendant established the following law:

  The strengths of interaction of fixed point charges are directly proportional to the product of charge modules and inversely proportional to the square of the distance between them:

  

  where: ε - Dielectric permeability of the medium - a dimensionless physical value showing how many times the power of electrostatic interaction in this medium will be less than in vacuum (that is, how many times the medium weakens the interaction). Here k. - coefficient in the law of the coulon, the value that determines the numerical value of the power of the interaction of charges. In the system of the system it is taken equal to:

  k. \u003d 9 ∙ 10 9 m / f.

  The interaction forces of point fixed charges are subject to the third Newton's law, and are repulsion from each other with the same signs of charges and attraction for each other with different signs. The interaction of fixed electrical charges is called electrostatic or Coulomb interaction. The section of electrodynamics studying the Coulomb interaction is called electrostatics.

  The law of the coulon is fair for point charged bodies, uniformly charged spheres and balls. In this case for distances r. Take the distance between the centers of spheres or balls. In practice, the law of Kulon is well done if the size of charged bodies is much less than the distance between them. Coefficient k. In the system SI, sometimes written in the form:

  

  where: ε 0 \u003d 8.85 ∙ 10 -12 F / M - electrical constant.

  Experience shows that the forces of Coulomb interaction are subject to the principle of superposition: if the charged body interacts simultaneously with several charged bodies, then the resulting force acting on this body is equal to the vector sum of the forces acting on this body from all other charged bodies.

  Remember also two important definitions:

  Conditions - Substances containing free electrical charge carriers. Inside the conductor, the free movement of electrons - charge carriers is possible (electrical current can occur according to conductors). Conductors include metals, solutions and melts of electrolytes, ionized gases, plasma.

  Dielectrics (insulators) - Substances in which there are no free charge carriers. The free movement of electrons inside dielectrics is impossible (electric current cannot flow). It is dielectrics that have some no equal unit dielectric constant ε .

  For the dielectric constant of the substance, the following is true (about what an electric field is slightly lower):

  

  Electric field and its tension

  According to modern ideas, electrical charges do not act directly. Each charged body creates in the surrounding space. electric field. This field has a power action on other charged bodies. The main property of the electric field is an effect on electrical charges with some force. Thus, the interaction of charged bodies is carried out not directly by their impact on each other, but through electrical fields surrounding charged bodies.

  The electric field surrounding the charged body can be explored using the so-called test charge - a small in the magnitude of a point charge that does not make a noticeable redistribution of the studied charges. For the quantitative determination of the electric field, the power characteristic is introduced - electric field tension E..

  The electric field tension is called a physical value equal to the ratio of power with which the field acts on a test charge, placed at this point point, to the magnitude of this charge:

  

  Electric field strength - vector physical value. The direction of the vector of tension coincides at each point of space with the direction of force acting on a positive test charge. The electrical field of fixed and non-varying charges is called electrostatic.

  For a visual representation of the electric field use power lines. These lines are carried out so that the direction of the tension vector at each point coincided with the direction of tangent to the power line. Power lines have the following properties.

  • The power lines of the electrostatic field never intersect.
  • The power lines of the electrostatic field are always directed from positive charges to negative.
  • When an electric field is depicted using power lines, their thickness must be proportional to the field strength vector module.
  • Power lines begin on a positive charge or infinity, and end on negative or infinity. The lines thickness are the greater the greater the tension.
  • At this point, only one power line can pass, because The voltage of the electric field at this point is set to definitely.

  The electrical field is called homogeneous if the voltage vector is the same in all points of the field. For example, a homogeneous field creates a flat capacitor - two plates charged to equal in size and opposite by the sign, separated by a dielectric layer, and the distance between the plates is much less than the size of the plates.

  At all points of a homogeneous field for charge q., entered in a homogeneous field with tension E., acts the same in size and direction force equal F. = EQ.. And if the charge q. Positive, the direction of force coincides with the direction of the voltage vector, and if the charge is negative, then the vector of force and tension is oppositely directed.

  Positive and negative point charges are shown in Figure:

  

  Superposition principle

  If the electrical field created by several charged bodies is investigated using a test charge, then the resulting force is equal to the geometric sum of forces acting on a test charge from each charged body separately. Consequently, the tension of the electric field created by the charge system at this point of space is equal to the vector sum of the tension of the electric fields created at the same charges of charges separately:

  

  This property of the electric field means that the field is subordinate superposition principle. In accordance with the law of the coulon, the tension of the electrostatic field created by a point charge Q. on distance r. From him, equal to module:

  

  This field is called Coulomb. In the Coulomb field, the direction of tension vector depends on the charge sign Q.: if a Q. \u003e 0, then the tension vector is directed from charge if Q. < 0, то вектор напряженности направлен к заряду. Величина напряжённости зависит от величины заряда, среды, в которой находится заряд, и уменьшается с увеличением расстояния.

  The electric field strength, which the charged plane creates near its surface:

  So, if the task requires to determine the intensity of the field of the charge system, then you need to act at the following algorithm:

  1. Draw a drawing.
  2. Picture the field strength of each charge separately at the desired point. Remember that tensions are aimed at negative charge and from a positive charge.
  3. Calculate each of the tensions according to the corresponding formula.
  4. Fold tension vector geometrically (i.e. vector).

  Potential energy interaction energy

  Electrical charges interact with each other and with an electric field. Any interaction describes potential energy. Potential energy interaction of two point electric charges Calculated by the formula:

  Pay attention to the lack of modules at charges. For variety charges, the interaction energy has a negative value. The same formula is also valid for the energy of the interaction of uniformly charged spheres and balls. As usual, in this case, the distance R is measured between the centers of the balls or spheres. If the charges are not two, but more, then the energy of their interaction should be considered as follows: break the system of charges for all possible couples, calculate the energy of the interaction of each pair and sum up all the energies for all pairs.

  The tasks on this topic are solved, as well as the tasks of the law of conservation of mechanical energy: first is the initial interaction energy, then the final one. If the task is asked to find work on the movement of charges, it will be equal to the difference between the initial and final total energy of the interaction of charges. The energy of the interaction can also switch to kinetic energy or other types of energy. If the bodies are at a very long distance, the energy of their interaction relies equal to 0.

  Please note: if the task is required to find the minimum or maximum distance between the bodies (particles) when moving, this condition is completed at that time when the particles move in one direction at the same speed. Therefore, the decision should be started with the record of the law of preserving the impulse, from which this same speed is located. And then you should write the law of conservation of energy, taking into account the kinetic energy of the particles in the second case.

  Potential. Potential difference. Voltage

  The electrostatic field has an important property: the operation of the power of the electrostatic field when the charge is moved from one point of the field to another does not depend on the form of the trajectory, but is determined only by the position of the initial and endpoint and the charge value.

  The result of the independence of the work on the form of the trajectory is the following statement: the work of the power of the electrostatic field when the charge is moving along any closed trajectory is zero.

  The property of the potential (independence of work on the form of the trajectory) of the electrostatic field allows you to enter the concept of potential charge energy in the electric field. And the physical quantity equal to the ratio of the potential energy of an electric charge in the electrostatic field to the magnitude of this charge is called potential φ Electric field:

  Potential φ It is the energy characteristic of the electrostatic field. In the international system of units (s), the unit of potential (and therefore the difference of potentials, i.e. voltages) is volt [B]. The potential is a scalar value.

  In many tasks of electrostatics, when calculating the potentials for a support point, where the values \u200b\u200bof potential energy and potential are applied to zero, it is convenient to take an infinitely remote point. In this case, the concept of potential can be determined as follows: the field potential at this point of space is equal to the work that electrical forces perform when removing a single positive charge from this point to infinity.

  Recalling the formula for the potential energy of the interaction of two point charges and separating it by one of the charges in accordance with the determination of the potential, we obtain that potential φ fields of point charge Q. on distance r. From it relative to an infinitely remote point is calculated as follows:

  The potential calculated by this formula can be positive and negative depending on the charge sign created it. The same formula expresses the potential of the field of a uniformly charged ball (or sphere) at r. ≥ R. (outside the ball or sphere), where R. - Balloon radius, and the distance r. It is counted from the center of the ball.

  For a visual representation of the electric field, along with power lines use equipotential surfaces. The surface, in all points of which the potential of the electric field has the same values, is called the equipotential surface or the surface of equal potential. The power lines of the electric field are always perpendicular to the equipotential surfaces. Equipotential surfaces of the Coulomb field of point charge are concentric spheres.

  Electrical voltage This is just the difference of potentials, i.e. Definition of electrical voltage can be specified by the formula:

  

  In a homogeneous electric field, there is a connection between the field strength and voltage:

  Electrical field work It can be calculated as the difference in the initial and ultimate potential energy of the charge system:

  The operation of the electric field in the general case can also be calculated by one of the formulas:

  In a uniform field, when the charge is moving along its power lines, the field operation can also be calculated by the following formula:

  In these formulas:

  • φ - Electric field potential.
  • ∆φ - Potential difference.
  • W. - Potential charge energy in an external electric field.
  • A. - The work of the electric field to move charge (charges).
  • q. - The charge that is moved in an external electric field.
  • U. - Voltage.
  • E. - Electric field strength.
  • d. or Δ. l. - The distance to which is moved along the power lines.

  In all previous formulas, it was about the work of the electrostatic field, but if the task states that "work must be done", or we are talking about "work of external forces", then this work should be considered the same as the field work, but with opposing sign.

  Principle of superposition potential

  From the principle of superposition of the tensions of fields created by electric charges, the principle of superposition for potentials is followed (with the field potential sign depends on the charge sign that created the field):

  Please note how easier to apply the principle of superposition of the potential than tensions. The potential is a scalar value that does not have directions. Potentials are simply summed up numerical values.

  Electrical container. Flat condenser

  When the charge conductor is reported, there is always a certain limit, which is no longer able to charge the body. For the characteristics of the body's ability to accumulate the electrical charge introduce the concept electrical capacity. The capacity of a secluded conductor calls the ratio of its charge to the potential:

  In the system, the container is measured in the Farades [F]. 1 Farad - extremely large capacity. For comparison, the capacity of the entire globe is significantly less than one Faraday. The capacitance of the conductor does not depend on its charge or on the potential of the body. Similarly, the density does not depend on the mass or on the volume of the body. The capacity depends only on the body shape, its size and properties of its environment.

  Electricity Systems of two conductors are called a physical value, as defined as the ratio of charge q. One of the conductors to the potential difference Δ φ Between them:

  

  The magnitude of the electrical conditioner depends on the shape and size of the conductors and the properties of the dielectric separating the conductors. There are such configurations of conductors in which the electric field is concentrated (localized) only in a certain area of \u200b\u200bspace. Such systems are called condensers, and conductors constituting the capacitor are called planmarks.

  The simplest condenser is a system of two flat conductive plates located in parallel to each other in small compared to the size of the distances of the distance and separated by a dielectric layer. Such a condenser is called flat. The electrical field of a flat condenser is mainly localized between the plates.

  Each of the charged plates of the flat capacitor creates a electric field near its surface, the tension module of which is expressed by the ratio of the above. Then the tension module of the outcome field inside the condenser created by two plates is equal to:

  

  Outside the condenser, the electric fields of two plates are directed in different directions, and therefore the resulting electrostatic field E. \u003d 0. It can be calculated by the formula:

  Thus, the electrical capacity of the flat condenser is directly proportional to the area of \u200b\u200bthe plates (plates) and inversely proportional to the distance between them. If the space between the plates is filled with a dielectric, the electrical capacity of the capacitor increases into ε time. note that S. In this formula, there is an area of \u200b\u200bonly one condenser plated. When the task is talking about "Planlates", they mean this amount. You never need to multiply or share it.

  Let us give a formula once again for charge condenser. Under the charge of the capacitor, only the charge of its positive attack is understood:

  The force of attraction of the plates of the condenser. The force acting on each plane is determined by the non-complete capacitor field, and the field created by the opposite clamp (the occurrence itself does not work). The tension of this field is equal to half the tension of the full field, and the power of the interaction of the plates:

  The energy of the condenser. It is called the energy of the electric field inside the condenser. Experience shows that the charged condenser contains a stock of energy. The energy of the charged capacitor is equal to the work of the external forces that must be expeked to charge the capacitor. There are three equivalent forms of recording of the formula for the energy of the condenser (they follow one of the other if you take advantage of the ratio q. = Cu.):

  

  Pay special attention to the phrase: "The condenser is connected to the source." This means that the voltage on the condenser does not change. And the phrase "the capacitor charged and turned off from the source" means that the capacitor charge will not change.

  Electric field energy

  Electrical energy should be considered as potential energy stored in a charged condenser. According to modern ideas, the electrical energy of the condenser is localized in the space between the capacitor plates, that is, in the electric field. Therefore, it is called the energy of the electric field. The energy of charged bodies is concentrated in the space in which there is an electric field, i.e. You can talk about the energy of the electric field. For example, the capacitor has energy concentrated in space between its plates. Thus, it makes sense to introduce a new physical characteristic - the volumetric energy density of the electric field. On the example of a flat capacitor, you can get such a formula for the volumetric energy density (or the energy of the unit of the electric field volume):

  Constressor connections

  Parallel condenser connection - To increase the tank. Capacitors are connected by the same name-charged plates, as if by increasing the area of \u200b\u200bequally charged plates. The voltage on all capacitors is the same, the total charge is equal to the sum of the charges of each of the capacitors, and the total capacity is also equal to the amount of the containers of all capacitors connected in parallel. Drink out formulas for parallel condenser connection:

  

  For consecutive condenser connection The total capacity of the battery of the capacitors is always less than the container of the smallest capacitor included in the battery. A sequential connection is used to increase the voltage of the condenser breakdown. We will divert the formula for a consistent condenser connection. The total capacity of sequentially connected capacitors is from the ratio:

  

  From the law of preserving the charge it follows that charges on neighboring plates are equal:

  The voltage is equal to the amount of stresses on separate capacitors.

  For two successively connected condensers, the formula above will give us the following expression for a total capacity:

  For N. Same consistently connected capacitors:

  Conductive sphere

  The field strength inside the charged conductor is zero. Otherwise, electric power would operate on free charges inside the conductor, which would force these charges to move inside the conductor. This movement, in turn, would lead to warming up the charged conductor, which does not actually happen.

  The fact that inside the conductor there is no electric field can be understood differently: if it were, the charged particles would move again, and they would move exactly so as to reduce this field to noise in their own field, because In general, they would not want to move, because any system is committed to equilibrium. Sooner or later, all the engined charges would stop in that place so that the field inside the conductor becomes no longer.

  On the surface of the conductor, the voltage of the electric field is maximum. The magnitude of the tension of the electric field of the charged ball beyond its limits as it removes from the conductor and is calculated by the formula, similar to the formulas for the intensity of the point charge field, in which distances are counted from the center of the ball.

  Since the field strength inside the charged conductor is zero, the potential at all points inside and on the surface of the conductor is the same (only in this case the potential difference, and therefore the tension is zero). The potential inside the charged bowl is equal to the potential on the surface. The potential outside the ball is calculated by the formula, similar to the formulas for the potential of a point charge, in which distances are counted from the center of the ball.

  Radius R.:

  If the ball is surrounded by a dielectric, then:

  Properties of the conductor in the electric field

  1. Inside the conductor, the field strength is always zero.
  2. The potential inside the conductor at all points is the same and equal to the potential of the surface of the conductor. When the task says that "the conductor is charged to potential ... in", then they mean the potential of the surface.
  3. Outside from the conductor near its surface, the field strength is always perpendicular to the surface.
  4. If the conductor inform the charge, then it will be all distributed on a very thin layer near the surface of the conductor (usually it is said that the entire charge of the conductor is distributed on its surface). It is easily explained: the fact is that the charge of the body is informed, we convey to him the charge carriers of one sign, i.e. The charges of the same name, which are repelled. So they will strive to spread apart from each other at the maximum distance from all possible, i.e. Squake the very edges of the conductor. As a result, if from the conductor to remove the core, then its electrostatic properties will not change in any way.
  5. Outside the conductor, the field strength is the greater than the curve surface of the conductor. The maximum value of tension is achieved near the edges and sharp fesoms of the surface of the conductor.

  Remarks to solve complex tasks

  1. Grounding something means the connection of the conductor of this object with the Earth. At the same time, the potentials of the Earth and the existing object are aligned, and the charges necessary for this charge on the conductor from the ground to the object or vice versa. It must be taken into account by several factors that follow the fact that the earth is incommensurable more than any object that is not here:

  • The total charge of the Earth is conditionally equal to nulo, therefore its potential is also equal to the nul, and it will remain equal to the nul after connecting the object with the Earth. In short, ground - means to reset the potential of the object.
  • To zeroing the potential (and therefore, the own charge of an object that could be both positive and negative), the object will have to either accept either the land (perhaps even very large) charge, and the Earth will always be able to provide such an opportunity.

  2. Repeat again: the distance between the repellent bodies is minimally at the moment when their speeds become equal in size and directed in one direction (the relative speed of charges is zero). At this point, the potential energy of the interaction of charges is maximum. The distance between the attractive bodies is maximally, also at the time of equality of speeds directed in one direction.

  3. If the task is a system consisting of a large number of charges, then it is necessary to consider and paint forces acting on the charge that is not in the center of symmetry.

• To learn all the formulas and laws in physics, and formulas and methods in mathematics. In fact, it is also very simple to perform this, the necessary formulas in physics is only about 200 pieces, but in mathematics even a little less. In each of these items there are about a dozen standard methods for solving the problems of the basic level of complexity, which, too, can well learn, and thus completely on the machine and without difficulty solve at the right moment most of the Central Ts. After that, you will just think about the most difficult tasks.
• Visit all three stages of rehearsing testing in physics and mathematics. Each RT can be visited twice to break both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and knowledge of formulas and methods, it is also necessary to be able to correctly plan the time, distribute forces, and the main thing is to correctly fill out the answer form, without confuseing the number of responses and tasks, no surname. Also during the Republic of Tatarstan, it is important to get used to the issue of formulation of issues in tasks, which on the CT may seem very unusual person.

Successful, diligent and responsible implementation of these three points will allow you to show a great result to the CT, the maximum of what you are capable of.

Found a mistake?

If you, as you think, have found a mistake in training materials, please write about it by mail. You can also write about the error in the social network (). In the letter, specify the subject (physics or mathematics), the name or number the topic or test, the task number, or a place in the text (page) where you think there is an error. Also describe what is the estimated error. Your letter will not remain unnoticed, the error either will be fixed, or you will explain why this is not a mistake.