The concept of electrical charge will be considered not subject to definition. The course of general physics gives an idea of \u200b\u200bthe facts on the basis of which the concept of charge is formed. Charge as physical quantity It is denoted by the Q symbol and is measured in the coulons (CL).

It is known that the charge is discretened, the smallest in the absolute value belongs to the elementary particle - the electron. Classical electrodynamics is macroscopic, that is, considers the effect of huge - "practically infinite" volumes of charged particles. The medium is solid, and currents and charges are continuously distributed in the amount.

The distribution of charge Q in volume V is characterized by the value of ρ, which determines the amount of charge per unit volume and is called the volumetric density of charge (17):

The charge distributed in the amount is determined by the integral through bulk density:

Figure 17 - to the definition of volumetric charge density

In theory electronic magnetic field The concept of the surface density density is also applied. In many cases, especially when the frequency of changes in the field is large, the charge focuses in a very thin layer at the body surface. In mathematical models, it is believed that the charge becomes purely surface (the thickness of the layer tends to zero). The charge in this case is defined as (Figure 18)

where ξ is the surface density of charge

.

Figure 18 - Surface Density of Charge

Finally, linear charge, i.e. distributed along line L (for example, the charge of wires of infinitely small radius, 19) is calculated as

where τ -linear charge density

.

Figure 19 - Linear Density of Charge

An experimental way is installed one of the basic laws of nature: the law of conservation of an electric charge: an electric charge is not destroyed and is not created from nothing, it can only be redistributed between the bodies when they are direct contact.

Current, current density

Electric current (conductivity current) is an ordered movement of free charges under the influence of an electric field.

Consider the system in which two electrodes connected to the source of the electric current (Figure 20) are connected to the interface between the vacuum and conductive substance. Obviously, the current lines inside the substance are distributed in such a way that the largest part will be held in the region representing the smallest resistance for current; A much smaller part will be increasing deep into the body.

Figure 20 - to determine the concept of current density

It can be seen from the figure that for the exhaustive characteristics of the state of this system, it is not enough to indicate only the value of the current flowing in the outer chain. Here it is necessary to have information about the intensity and direction of the movement of charge carriers at each point of the region. To this end, it is customary to introduce the concept of the conductivity current density, determining it as follows (Figure 21): the volumetric current density is equal to the charge passing per unit of time through the unit of the surface area, perpendicular to the current lines.

Figure 21 - current flow through the surface s

I highlight inside the body, according to which the current flows, the tube, the side surface of which consists of current lines. Charged particles when moving do not intersect the tube wall. Consider the charge carried by particles through the transverse perpendicular cross section of the tube. The speed is a particle we denote the vector, and its charge is. Let the total number of particles in the amount of equal. Then from the volume through the platform during all particles tolerate the charge equal to , where - single vector normal to the surface. Then where - Vector volumetric current density. If the speed of charge carriers are equal to the average, then where is the bulk density of the charge in volume. Thus, per unit of time through a single surface, perpendicular to the current lines, a charge is transferred as the volumetric current density. Unit of measurement is a / m 2: .

General

We live in the era of synthesized materials. Starting with the invention, viscose and nylon, the chemical industry generously supplies us with synthetic tissues and we no longer think our existence without them. Truly, thanks to them, mankind managed to fully satisfy the need for clothing: from openwork ladies and tights to light and warm sweaters and comfortable and beautiful jackets with synthetic insulation. Synthetic fabrics have a lot of other advantages, among which, for example, consistency in the sock and water-repellent properties, or a property for a long time to preserve the form after ironing.

Unfortunately, in a barrel with honey, there will always be a place for a spoon of fun. Synthesized materials easily electrified that we literally feel our own skin. Each of us, tightening a sweater from artificial wool in the dark, could watch sparkles and hear the cracks of electrical discharges.

Doctors refer to such a synthetic property is awesome enough, recommending to use at least for underwear of natural fibers with a minimum amount of added synthetics.

Technologists seek to create tissues with high antistatic properties using various methods Reduced electrification, but the complication of technologies leads to an increase in production costs. To control the antistatic properties of polymers various methods Measurements of the surface density of the charge, which, along with the electrical resistance, serves as a characteristic of antistatic properties.

It should be noted that the antistatic properties of clothing and shoes are very important for a certain part of pure industrial premises, for example, in the microelectronic industry, where electrostatic chargesaccumulated by friction of tissues or footwear materials on their surfaces can destroy chips.

Extremely high demands on the antistatic properties of clothing tissues and for the materials of the shoe presents the oil and gas industry - after all, a sufficiently small spark in order to initiate an explosion or a fire in such industries. Sometimes with very hard consequences in the material plan and even with human victims.

Historical reference

The concept of the surface density of the charge is directly related to the concept of electrical charges.

Another Charles Dafe, a scientist from France, in 1729 expressed and proved the assumption of the existence of the charges of various types, called "glass" and "smolyan", as they were obtained when rubbing the glass with silk and amber (that is, the resins of trees) wool. Benjamin Franklin, who investigated the thunder discharges and created the threshold, introduced the modern names of such charges - positive (+) and negative (-) charges.

The law of interaction of electrical charges opened the French scientist Charles Pendant in 1785; Now, in honor of his merit in front of science, this law carries his name. For the sake of justice, it should be noted that the same law of interaction 11 years earlier than Kulon opened the British scientist Henry Cavendish, which used for experiments the same sponsored scales, which subsequently applied the pendant. Unfortunately, the work of Cavendish under the law of interaction of charges for a long time (over a hundred years) was unknown. Manuscripts Cavendish were published in only 1879.

The next step in the study of charges and calculations by the electrical fields created by them was made by the British scientist James Clerk Maxwell, which united the law of Culon and the principle of the superposition of fields with its electrostatics equations.

Surface density charge. Definition

The superficial charge density is a scalar value that characterizes the charge per unit surface of the object. Its physical illustration in the first approximation can be a charge on a condenser from flat conductive plates of some area. Since charges can be both positive and negative, the values \u200b\u200bof their surface density of charge can be expressed by positive and negative values. It is indicated by the Greek letter Σ (pronounced as Sigma) and is calculated on the basis of the formula:

σ \u003d q / s

σ \u003d Q / S where q is a surface charge, S is a surface area.

The dimension of the surface density of the charge in the international system of SI units is expressed in the coulutes per square meter (CL / m²).

In addition to the main unit of the surface density of the charge, a multiple unit is used (CL / cm2). In another measurement system, the SGSM is used an abpaulon unit per square meter (ABKKKL / m²) and a multiple unit abpaulon per square centimeter (ABKL / CM²). 1 Abclonon is 10 cabins.

In countries where metric units of the area are not used, the surface density of charge is measured in the squares per square inch (CL / inC) and the abclones per square inch (abkkl / inch).

Surface density charge. Physics phenomena

The surface charge density is used to carry out physical and engineering calculations of electric fields when designing and using various electronic experimental installations, physical instruments and electronic components. As a rule, such installations and appliances have planar electrodes from the conductive material of sufficient area. Since charges in the conductor are located on its surface, its other sizes and edge effects can be neglected. Calculations of electric fields of such objects are carried out using Maxwell Elektrostatics equations.

Surface Density of Earth

Few of us remembers the fact that we live on the surface of a giant capacitor, one of the plates of which represents the surface of the Earth, and the second occurrence is formed by ionized atmospheric layers.

That is why the Earth and behaves like a condenser - accumulates the electrical charge and in this capacitor, from time to time, even arise the samples of the interelectrode space when the "working" voltage is exceeded, more well-known as lightning. The electric field of the Earth is similar to the electric field of a spherical capacitor.

Like any condenser, the earth can be characterized by a surface density of charge, the value of which, in the general case, can change. With clear weather, the superficial charge density on a specific section of the Earth approximately corresponds to the average value on the planet. Local values \u200b\u200bof the surface density of the charge of the earth in the mountains, on the hills, in places of occurrence of metal ores and during electrical processes in the atmosphere may differ from the average values \u200b\u200bup to the zoom.

We estimate its average value under normal conditions. As you know, the land radius is 6371 kilometers.

Experimental study of the electric field of the Earth and the corresponding calculations show that the land as a whole has a negative charge, the mean value of which is estimated at 500,000 pendants. This charge is supported in approximately one level due to a number of processes in the Earth's atmosphere and in the nearest space.

According to the famous of the school year, the formula will calculate the surface area globeIt is approximately equal to 500,000,000 square kilometers.

From here, the average surface density of the charge of the Earth will be approximately 1 10 ° C / m² or 1 NL / m².

Kinescope and oscillographic tube

Television would be impossible without the appearance of devices that ensure the formation of a narrow beam of electrons with high charge density - electron guns. More recently, one of the main elements of TVs and monitors was a kinescope, or, otherwise, an electron beam tube (CRT). The production of CRT on an annualized basis was in the near future hundreds of millions of units.

The kinescope is an electron-vacuum device designed to convert electrical signals into light to dynamic image formation on a luminophore-covered screen, which can be monochrome or polychrome.

The design of the kinescope consists of an electronic gun, focusing and deflecting systems, accelerating the anodes and a screen with a proposed layer of phosphor. In color kinescopes (Calt), the number of elements creating electronic rays is tripled by the number of displayed colors - red, green and blue. Screens of colored kinescopes have slotted or point masks that prevent other color from entering other color to a specific phosphor.

The luminophore coating is a mosaic of three layers of phosphors with different color glow. Mosaic elements can be located in the same plane or in the vertices of the triangle of the display.

The electron cannon consists of a cathode, control electrode (modulator), an accelerating electrode, and one or more anodes. In the presence of two or more anodes, the first anode is called the focusing electrode.

The cathode of the kinescopes is made in the form of a hollow of the sleeve, on the outer side of the bottom of which an oxide layer of alkaline earth metal oxides is applied, providing sufficient thermoemission of electrons when heated to a temperature of about 800 ° C due to the heater electrically isolated from the cathode.

The modulator is a cylindrical glass with a bottom covering a cathode. In the center of the bottom of the glass there is a calibrated hole of about 0.01 mm, called a carrier diaphragm, through which an electron beam passes.

Since the modulator is at a short distance from the cathode, its purpose and action is similar to the purpose and the action of the control grid in the electron lamp.

The accelerating electrode and the anodes are hollow cylinders, the last anode is also made in the form of a sleeve with a calibrated hole at the bottom, which is called the output diaphragm. This system of electrodes is designed to impart electrons the necessary speed and forming the stains of small sizes on the Kinescope screen, representing an electrostatic lens. Its parameters depend on the geometry of these electrodes and the surface densities of the charge on them, which are created by feeding on them the corresponding stresses relative to the cathode.

One of the recently widely used electronic devices was the oscillographic electron beam tube (OELT), designed to visualize electrical signals due to their electronic beam on the luminescent monochrome screen. The main difference between the oscillographic tube from the kinescope is the principle of building a deflecting system. It is applied to the OELT electrostatic system Deviations because it provides greater speed.

The oscillographic ELT is a vacuumed glass flask, inside of which there is an electron gun generating a narrow beam of electrons using a system of electrodes deflecting the electronic beam and accelerating it, and the fluorescent screen, which is glowing with accelerated electrons when bombarded.

The deflecting system consists of two pairs of plates arranged horizontally and vertically. The horizontal plates - otherwise the plates of vertical deviation - the test voltage is applied. On vertical plates - otherwise the plate of horizontal deviations - the saw-shaped voltage from the expandment generator is supplied. Under the action of stresses on the plates, the redistribution of charges on them occurs and due to the resulting total electric field (recall the principle of superposition of fields!) Flying electrons deviate from their initial trajectory proportional to the applied voltages. The electronic beam draws on the tube screen the form of the signal under study. Due to the voltage sawturity on the vertical plates, the electronic beam, in the absence of a signal on the horizontal plates, moves around the screen from left to right, while drawing a horizontal line.

If you have two different signals on vertical and horizontal deflecting plates, then the screen can be observed with the so-called figures of Lisp.

Since both pairs of plates form flat capacitors, the charges of which focus on the plates, the surface density of the charge is used to calculate the design of the electron beam tube, characterizing the sensitivity of the deviation of electrons to the acting voltage.

Electrolytic capacitor and ionistor

Surface charge calculations must also be performed when developing capacitors. In modern electrical engineering, radio engineering and electronics, the capacitors of various types used to separate the circuits of constant and alternating current And for accumulation electrical Energy.

The accumulative function of the condenser directly depends on the value of its container. A typical capacitor is a plate of conductor, called condenser plates (as a rule, various metals are used by their material) separated by a dielectric layer. The dielectric in capacitors serve solid, liquid or gaseous substances having a high dielectric constant. In the simplest case, the dielectric is the usual air.

We can say that cumulative capacity The capacitor for electrical energy is directly proportional to the surface density of charges on its plates or plates, and is inversely proportional to the distance between its plates.

Thus, two ways to increase the energy accumulated energy condenser are available - an increase in the area of \u200b\u200bplates and a reduction in the gap between them.

In electrolytic capacitors of a large capacity as a dielectric, a thin oxide film applied to the metal of one of the electrodes - anode - an electrolyte is used by another electrode. The main feature of electrolytic capacitors is that they, compared to other types of capacitors, have a large capacity with sufficiently small dimensions, in addition, they are polar electrical drives, that is, they should be included in the electrical circuit with polarity compliance. The capacity of electrolytic capacitors can reach about tens of thousands of microfrades; For comparison: the container of the metal ball with a radius equal to the radius of the Earth is only 700 microfrades.

Accordingly, the surface density of the charge of such capacitors under stress can reach considerable values.

Another way to increase the capacitor capacity is to increase the surface density of the charge due to the developed surface of the electrodes, which is achieved by the use of materials with increased porosity and using the properties of the double electric layer.

The technical implementation of this principle is the ionistor (other titles supercapacitor or ultra-confacitor), which is a condenser, "plates" which serves as a double electric layer on the boundary of the section of the electrode and electrolyte. Functionally, the ionistor is a hybrid of a capacitor and a chemical current source.

The double interfacial electrical layer is a layer of ions formed on the surface of the particles as a result of adsorption of ions from a solution or orientation of polar molecules at the phase boundary. Ions directly related to the surface are called potential determining. The charge of this layer is compensated by the charge of the second layer of ions called by the counterions.

Since the thickness of the double electrical layer, that is, the distance between the "plates" of the capacitor is extremely small (the size of the ion), the energy stored by the ionistor higher compared to the usual electrolytic capacitors of the same size. In addition, the use of a double electric layer instead of a conventional dielectric makes it much to increase the efficient surface area of \u200b\u200bthe electrode.

While typical ionistors on the density of the energy of the energy is inferior to electrochemical batteries, but the promising development of supercapacitors with nanotechnology has already been equal to them on this indicator and even exceed them.

For example, aerogel supercapacitors of the development of the company Ness Cap., Ltd with electrodes from foamed carbon have a volumetric capacity, in 2000 times the superior volumetric capacity of the electrolytic capacitor is the same size, and the specific power exceeds the specific power of electrochemical batteries 10 times.

To other valuable qualities of the supercapacitor, as electrical energy accumulation devices include small internal resistance and a very small leakage current. In addition, the supercapacitor has a small charge time, allows high discharge currents and a practically unlimited number of charge-discharge cycles.

Supercapacitors are used for long-term storage of electrical energy and with high current loads. For example, when recycling the braking energy by racing cars of formula 1, followed by recuperation of energy accumulated in the ionistors. For racing machines, where every gram is important and each cubic centimeter of volume, supercapacitors with a density of stable energy reaching 4000 W / kg are an excellent alternative to lithium-ion batteries. Ionistors also became familiar in passenger cars, where they are used to power the equipment during the starter operation and to smooth the voltage jumps during peak loads.

Experiment. Determination of the surface density of the boost of the coaxial cable

As an example, consider the calculation of the surface density of the charge on the coaxial cable fever.

To calculate the surface density of charge accumulated by the fever of the coaxial cable, considering the fact that the central lived together with the lamp form a cylindrical capacitor, we use the dependence of the capacitor charge from the applied voltage:

Q \u003d C u where q is a charge in the coulons, C - the container in the Farades, U is voltage voltage.

Take a segment of the radio frequency coaxial cable of a small diameter (with its capacity above its capacity and it is easier to measure) Leng to 10 meters.

Multimeter Measure Cable Cable Cable Cable capacity, micrometer - Diameter of length d

SC \u003d 500 PF; d \u003d 5 mm \u003d 0.005 m

Let's give a 10 volt calibrated voltage to the cable from the power supply, connecting the overall and the central cable core to the source terminals.

According to the above formula, we calculate the charge accumulated on the overall:

Q \u003d ck uk \u003d 500 10 \u003d 5000 PPC \u003d 5 ND

Considering the laptop of the cable segment with a solid conductor, we will find its area calculated according to the well-known formula of the cylinder area:

S \u003d π D L \u003d 3,14 0.005 10 \u003d 0.157 m²

and calculate the exemplary surface density of the charge of the cable of the cable:

σ \u003d q / s \u003d 5 / 0,157 \u003d 31.85 nkl / m²

Naturally, with an increase in the voltage applied to the overall and the central dwelling of the coaxial cable, the charge density increases and is growing and the surface density of charge.

On the principle of superposition of fields Magnetic induction in an arbitrary point of the magnetic field of the conductor with current equal

where - the magnetic induction of the field created by the element of the conductor length.

Integration is performed along the entire length of the conductor L..

2.3.1. Magnetic field of rectilinear current

Calculate the induction of the magnetic field INpoint BUT (Fig. 2.2) at a distance R 0 from the rectilinear conductor with a current:

;

;

. (2.4)

Express variables and . From fig. 2.2 It can be seen that. Differentiating this expression, we get:

.

From fig. 2.2 also follows that

Substituting the values \u200b\u200bof I. r. In equation (2.4), we have:

. (2.5)

For an infinitely long rectilinear conductor ( 1 \u003d 0,  2 \u003d ), equation (2.5) takes the form:

. (2.6)

9, Maxwell equations - system of equations in differential or integral form describing electromagnetic field and his connection with electric charges and tokami in vacuum and solid media. Together with the expression for lorentz's forcesdefining the measure of the electromagnetic field on charged particles, form a complete system of equations classic electrodynamics, Sometimes the Maxwell - Lorentz equations. Equations formulated James Clerk Maxwell based on the experimental results accumulated by the middle of the XIX century, played a key role in the development of the ideas of theoretical physics and had a strong, often decisive, influence not only on all areas of physics directly related to electromagnetism, but also for many subsequent fundamental theories, the subject of which did not boost to electromagnetism (one of the brightest examples here can serve special theory of relativity).

10, Electric charge (number of electricity) - this is physical scalar valuedefining the ability tel Be a source electromagnetic fields and take part in electromagnetic interaction. For the first time, the electric charge was introduced in culon law in 1785.

Charge measurement unit International Unit (SI) - pendant - Electric charge passing through a cross-section of the conductor at a current of 1 BUTduring the time from. One pendant is very large. If two charge carriers ( q. 1 = q. 2 \u003d 1 CL) located in vacuum at a distance of 1 m, then they would interact with strength9 · 10 9 H., that is, with the force with which the gravity of the Earth would attract the object with a lot of about 1 million tons.

Electric charge closed system persists 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 in any processes occurring in this system.

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 saving charge - One of the fundamental laws of physics. The law of saving charge was first experimentally confirmed in 1843. Great English scientist Michael Faraday and is considered to be one of the fundamental laws of preservation in physics (like laws of preservation of impulse and energy). An increasingly sensitive experimental checks of the law of preservation of charge, ongoing and today, have not yet revealed deviations from this law.

Point charge. The law of Kulon is the main law of electrostatics.

Point charge - this is electric chargeWhen the body size on which this charge is concentrated, much less than the distance between charged bodies.

The interaction of two relatives spot charges determines the main law of electrostatics - the law of Kulon.. This law was experimentally installed in 1785 French physicist Charles Apusten Coulomb (1736 - 1806). The wording of the Culon law is as follows:

The power of interaction Two point fixed charged bodies in a vacuum directly proportional to the product of charge modules and inversely proportional to the square of the distance between them.

This power of interaction is called coulomb force, I. formula of the law of Kulon It will be as follows: F \u003d k · (| q 1 | · | Q. 2 |) / R 2 where | Q1 |, | Q2 | - charge modules, R - distances between charges, k - proportionality coefficient.

The coefficient k in si is customary to record in the form: k \u003d 1 / (4πε 0 ε) where ε 0 \u003d 8.85 * 10 -12 kl / n * m 2 - electrical constant, ε - the dielectric constant medium.

For vacuum ε \u003d 1, k \u003d 9 * 10 9N * M / CL 2.

The strength of the interaction of fixed point charges in vacuum: F \u003d · [(| Q 1 | · | Q. 2 |) / R 2 ]

If two point charges are placed in the dielectric and the distance from these charges to the dielectric boundaries, much larger than the distance between charges, the strength of the interaction between them is: F \u003d · [(| Q 1 | · | Q. 2 |) / R 2 ] \u003d k · (1 / π) · [(| q 1 | · | Q. 2 |) / R 2 ]

Electric field strength. The principle of superposition for tensions. Field of an infinite uniformly charged thread.

Electric field strength. The power characteristic of the electric field is the electric field voltage vector E. equal to the ratio of the vector of the force acting at this point point on a test positive charge, to the magnitude of this charge:

The tension in the SI units is expressed in Newton to the pendant (N / CL).

The principle of superposition of the tensions of electrostatic fields. Of the principle of the superposition of fields, it follows that the force acting on the test charge from other charges is equal to the geometric sum of all the forces acting on the charge separately. But if so, then the tensions of electric fields, equal to the relationship of the forces to the magnitude of the test charge, are folded like the forces.

Thus, for electric fields fair superposition principle In the following wording: the tension of the resulting electric field is a geometric (vector) sum of the intensities of fields created by individual charges:

E. = E. 1 + E. 2 + E. 3 + … (5.3)

The use of the principle of superposition for tensions makes it possible to significantly facilitate the solution of many tasks of electrostatics.

Electric dipole. Dipole field.

Electric dipole. - a system of two equal in magnitude, but opposite to the sign of point electrical charges located at some distance from each other.

Distance between charges is calledshoulder dipole.

The main characteristic of the dipole is the vector value called electric moment dipole (P).

Electric field dipole

The dipole is the source of the electric field, the power lines and the equipotential surfaces of which are depicted in Fig. 13.1.

Fig.13.1.Dipol and It electric field

The central equipotential surface is a plane passing perpendicular to the shoulder of the dipole through its middle. All its points have zero potential (φ \u003d 0). She divides the electric field of the dipole into two halves, points of which have respectively positive (φ \u003e 0) and negative (φ < 0) потенциалы.

The absolute value of the potential depends on the dipole moment P, the dielectric permeability of the medium ε and on the position of this point of the field relative to the dipole. Let the dipole be in a non-conductive infinite environment and some point and removed from its center to the distance R \u003e\u003e λ (Fig. 13.2). Denote by α the angle between the vector r and the direction for this point. Then the potential created by the dipole at point A is determined by the following formula:

Fig.13.2.The potential of the electric field created by the dipolemb

Linear, surface and volumetric charge density.

volumetric density charge (R),

surface density charge (s) and linear density charge (t).

For a linear object (for example, in the case of a charge-bearing), the concept is introduced linear density charge τ (Fig.10.1, B),

where dQ.- charge coming per unit length dL.

If the object is two-dimensional (for example, in the case of a charged conductor) administered surface density charge(Fig.10.1, b)

, (10.1.2)

where dQ. - charge located on the surface element dS.

For three-dimensional objects introduced volumetric density charge(Fig.10.1, a)

, (10.1.3)

where dQ. - Charge of a small element of the charged body volume dV.

The electrostatic field can be clearly depicted using power lines (voltage lines). Power lines Correct the curves to which at each point coincide with the tension vector E..

Power lines are a conditional concept and really do not exist. Power lines of single negative and single positive charges are radial straight, emerging from a positive charge or going to a negative charge.

If the density and direction of power lines throughout the field of field are persisted unchanged, such an electrostatic field is considered uniform (\u003d Const). For example, a charge, distributed evenly on an infinite plane, creates a homogeneous electric field, whose power lines are depicted with equifiable from each other with parallel straight lines.

In order for the power lines to characterize not only the direction of the field, but also the value of its tension, the number of lines must be numerically equal to the field strengthE..

The number of power lines penetrating the elementary platform dS, perpendicular to them determines the stream of the tension of the electrostatic field:

where is the projection of the vector E. On the direction of Normal n. To the site ds.

Accordingly flow vector E. Through an arbitrary closed surface S.

On different sections of the surface S. Not only the magnitude, but also the flow sign can change:

3) when it means that the lines slide along the surface, without crossing it.

Cool law:

where F. - power of electrostatic interaction between two charged bodies;

q. 1 , Q. 2 – electric charges bodies;

ε - relative, dielectric permeability of the medium;

ε 0 \u003d 8.85 · 10 -12 F / M - electrical constant;

r.- Distance between two charged bodies.

Linear charge density:

where D. q -elementary coming on the length d length l.

Surface charge density:

where D. q -elementary coming on the surface D s.

Volume of charge density:

where D. q -elementary, in volume D V.

Electric field strength:

where F. – power acting for charge q..

Gauss Theorem:

where E. - Tension electrostatic field;

d. S. – vector , the module of which is equal to the surface of the surface, and the direction coincides with the direction of normal to the site;

q.- Algebraic amount of prisoners inside the surface D S.charges.

Tension vector circulation theorem:

The potential of the electrostatic field:

where W. P - Potential Energy Point Charge q..

Potential point charge:

Point charge field intensity:

.

The intensity of the field created by an infinite straight uniformly charged line or infinitely long cylinder:

where τ - linear density charge;

r.- distance from the thread or axis of the cylinder to the point, the field strength in which is determined.

The field strength created by an endless uniform charged plane:

where σ is the surface density of the charge.

Communication capacity with tension in the general case:

E \u003d -gradφ. = .

Connection capacity with tension in case uniform field:

E.= ,

where d.- distance between points with potentials φ 1 and φ 2.

Communication capacity with tension in the case of a field with central or axial symmetry:

Work of the Field forces to move the charge Q from the point of the field with the potential φ 1.to point with potential φ 2:

A \u003d Q (φ 1 - φ 2).

Conductor electrical capacity:

where q. - charge of the conductor;

φ is the potential of the conductor, provided that in infinity, the potential of the conductor is taken equal to zero.

Capacitor electrical condition:

where q. - the charge of the condenser;

U. - The potential difference between the plates of the capacitor.

Flat condenser electrical capacity:

where ε is the dielectric permeability of the dielectric located between the plates;

d.- distance between the plates;

S. - Total plates area.

Capacitor battery power capacity:

b) with parallel connection:

Energy of a charged condenser:

,

where q.- the charge of the condenser;

U. - the difference of potentials between the plates;

C. - Electrical capacity of the capacitor.

Force direct current:

where D. q.- charge, proceeding through the cross section of the conductor during the time D t..

Current density:

where I.- Current power in the conductor;

S. - Explorer area.

Ohm's law for a plot of a chain not containing EDC:

where I.- current strength on the site;

U.

R. - resistance of the site.

Ohm's law for a plot of a chain containing EMF:

where I.- current strength on the site;

U. - voltage at the ends of the site;

R. - full resistance of the site;

ε – EMF source.

Ohm law for closed (full) chain:

where I.- Current power in the chain;

R. - external chain resistance;

r.- internal source resistance;

ε – EMF source.

Kirchhoff laws:

2. ,

where is the algebraic amount of current forces converging in the node;

- Algebraic amount of stress drops in the circuit;

- Algebraic amount of EDC in the circuit.

Explorer resistance:

where R. - resistance of the conductor;

ρ is the resistivity of the conductor;

l. - the length of the conductor;

S.

Conductance of the conductor:

where G. - conductivity of the conductor;

γ - the specific conductivity of the conductor;

l. - the length of the conductor;

S. - Cross-section area of \u200b\u200bthe conductor.

Resistance system of conductors:

a) with a sequential connection:

a) with a parallel connection:

Current operation:

,

where A. - current operation;

U. - voltage;

I. - current strength;

R.- resistance;

t. - time.

Current power:

.

Joule Law - Lenza

where Q. - The amount of heat distinguished.

Ohm's law in differential form:

j.=γ E. ,

where j. - current density;

γ - specific conductivity;

E.- Electric field strength.

Communication of magnetic induction with magnetic field strength:

B.=μμ 0 H. ,

where B. - vector magnetic induction;

μ-magnetic permeability;

H. - magnetic field strength.

Bio Law - Savara - Laplace:

,

where D. B. - induction of the magnetic field created by the conductor at some point;

μ - magnetic permeability;

μ 0 \u003d 4π · 10 -7 Gn / m - magnetic constant;

I. - Current power in the conductor;

d. l. - element of the conductor;

r. - radius vector spent from the element D l. explorer to a point in which the induction of the magnetic field is determined.

Law full current For magnetic field (vector circulation theorem B.):

,

where n. - the number of conductors with currents covered by the contour L. arbitrary shape.

Magnetic induction in the center of the circular current:

where R. - Radius of a circular turn.

Magnetic induction on the axis of the circular current:

,

where h. - the distance from the center of the turn to the point in which the magnetic induction is determined.

Live current field induction:

where R. 0 - distance from the axis of the wire to the point in which the magnetic induction is determined.

Magnetic induction of solenoid field:

B \u003d.μμ 0 ni

where N. - The ratio of the number of turns of the solenoid to its length.

Ampere power:

d. F. \u003d I,

where D. F. – amper power;

I. - Current power in the conductor;

d. l. - the length of the conductor;

B.- induction of the magnetic field.

Lorentz power:

F.=q. E. +q.[v B. ],

where F. - Lorentz power;

q. - particle charge;

E. - electric field strength;

v. - particle speed;

B. - induction of the magnetic field.

Magnetic flow:

a) in the case of a homogeneous magnetic field and a flat surface:

Φ \u003d b n s,

where Φ -Magnetic stream;

B N.- projection of the magnetic induction vector on the vector of normal;

S. - contour area;

b) in the case of an inhomogeneous magnetic field and arbitrary projection:

Flow (full stream) for toroid and solenoid:

where Ψ - full stream;

N is the number of turns;

Φ - magnetic flux, permeating one round.

Inductance contour:

Solenoid inductance:

L \u003d.μμ 0 N. 2 V,

where L. - inductance of the solenoid;

μ - magnetic permeability;

μ 0 - magnetic constant;

n.- the ratio of the number of turns to its length;

V. - Solenoid volume.

Faraday electromagnetic induction law:

where ε. I. – EMF induction;

– change full stream per unit time.

Work on the movement of a closed contour in a magnetic field:

A \u003d I.Δ Φ,

where A. - work on the movement of the contour;

I.- Current power in the circuit;

Δ Φ – Change the magnetic flux that flows out the contour.

EMF self-induction:

Magnetic field energy:

Volume of magnetic field energy density:

,

where ω is the bulk density of the magnetic field energy;

B.- induction of the magnetic field;

H. - magnetic field strength;

μ - magnetic permeability;

μ 0 - Magnetic constant.

3.2. Concepts and definitions

? List the electrical charge properties.

1. There are charges of two types - positive and negative.

2. The charges of the same name are repelled, the variepetes are attracted.

3. Projections have the property of discreteness - all in the smallest elementary.

4. The charge is invariant, its value does not depend on the reference system.

5. The charge is additive - the charge of the tel system is equal to the sum of the charges of all bodies of the system.

6. Full electrical charge of a closed system there is a permanent value

7. Fixed charge - the source of the electric field, moving charge - the source of the magnetic field.

? Word the law of Coulomb.

The strength of the interaction of two point fixed charges is proportional to the product of charge values \u200b\u200band inversely proportional to the square square between them. The force along the line connecting the charges is directed.

? What is an electric field? Electric field strength? Word the principle of the superposition of the electric field strength.

The electric field is a type of matter associated with electrical charges and transmitting the action of some charges to others. Tension - power characteristic field equal powerPerforming on a single positive charge placed at this field. The principle of superposition is the field strength created by the dot charge system is equal to the vector sum of the field intensity of each charge.

? What is called power lines of the electrostatic field strength? List the properties of power lines.

The line tangent at each point of which coincides with the direction of the field strength vector is called power. Properties of power lines - begin on positive, ends on negative charges, do not interrupt, do not intersect with each other.

? Give the definition of an electric dipole. Dipole field.

The system of two equal in the module opposite to the sign of point electrical charges, the distance between which is not enough compared to the distance to the points, where the action of these charges is observed. The tension will be the direction opposite to the vector of the electric moment of the dipole (which, in turn, directed from negative charge to positive).

? What is the potential of the electrostatic field? Word the principle of superposition of the potential.

Scalar valuenumerically equal to attitude potential energy Electric charge placed at this field point to the magnitude of this charge. The principle of superposition - the potential of the dot charges system at some point of space is equal to the algebraic amount of potentials that would create separately these charges in the same point of space.

? What is the connection between tensions and potential?

E.=- (E. - The variability of the field at this point point, j - the potential at this point.)

? Determine the concept of "the stream of the vector of electric field strength". Formulate electrostatic theorem Gaussa.

For arbitrary closed surface stream of tension vector E. electric field F E.\u003d. Gauss Theorem:

\u003d (here Q I. - charges covered by a closed surface). Fair for the closed surface of any form.

? What substances are called conductors? How are chargers and an electrostatic field in conductor? What is electrostatic induction?

Conductors - Activities in which, under the action of an electric field, ordered free charges can move. Under the action of the external field, the charges are redistributed, creating its own field equal to the module external and directed oppositely. Therefore, the resulting tension inside the conductor is equal to 0.

Electrostatic induction - The type of electrification, in which under the action of the external electric field, the redistribution of charges between parts of this body occurs.

? What is the electrical capacity of a secluded conductor, a condenser. How to determine the container of a flat condestator, the capacitors batteries connected in series, in parallel? Unit of measuring electrical capacity.

Secluded conductor: where FROM -capacity, q.- Charge, J - potential. Unit of measurement - Farad [F]. (1 f - conductor capacity, in which the potential increases by 1 V when the charge conductor is reported 1 CL).

Capacity of a flat capacitor. Serial connection: . Parallel connection: With general \u003d with 1 + S. 2 + ... + with N.

? What substances are called dielectrics? What types of dielectrics do you know? What is polarization of dielectrics?

Dielectrics - substances in which under normal conditions there are no free electrical charges. There are polar dielectrics, non-polar, ferroelectrics. Polarization is called the process of orientation of dipoles under the influence of an external electric field.

? What is vector electric displacement? Formulate the postulate Maxwell.

Vector of electrical displacement D. It characterizes the electrostatic field created by free charges (i.e. in vacuum), but with this distribution in space, which is available in the presence of a dielectric. Postulate Maxwell :. Physical meaning - Expresses the law of creating electric fields by the action of charges in arbitrary environments. ? Determine the concept of "electric current". Types of currents. Electric current characteristics. What condition is necessary for its occurrence and existence?

Current is an ordered movement of charged particles. Types of conductivity current, ordered movement of free charges in the conductor, convection - arises when moving in the space of a charged macroscopic body. For the occurrence and existence of the current, it is necessary to have charged particles capable of moving ordered, and the presence of an electric field whose energy is consumed, would be spent on this ordered movement.

? Bring and explain the continuity equation. Word the condition of the stationarity of the current in the integral and differential forms.

Continuity equation. Expresses in differential form the law of saving charge. Stationar condition (constancy) current in integral form: and Differential -.

? Write down Ohm's law in integral and differential forms.

Integral form - ( I. -current, U.- voltage, R.-resistance). Differential shape - ( j. Current determination, G-specific electrical conductivity, E. - field strength in the explorer).

? What is third-party strength? EMF?

Third-party forces share charges for positive and negative. Eds- The ratio of work on the movement of the charge along the entire closed chain to its magnitude

? How is the operation and power of the current?

When moving charge q. by electrical chainat the ends of which acts voltage U., electric field Work is performed, current power (T-time)

? Word Kirchhoff rules for branched chains. What conservation laws are laid in Kirchhoff rules? How many independent equations should be based on the first and second laws of Kirchhoff?

1. Algebraic amount of currents converging in the node is 0.

2. In any arbitrarily selected closed circuit, the algebraic amount of stress drops is equal to the algebraic amount of EMFs encountered in this circuit. The first Rule of Kirchhoff follows from the law of conservation of an electric charge. The number of equations in the amount should be equal to the number of desired values \u200b\u200b(in the system of equations should include all resistance and emfs).

? Electric current in gas. Ionization and recombination processes. The concept of plasma.

Electric current in gases - directional motion of free electrons and ions. Under normal conditions, the gases are dielectrics, the conductor becomes after ionization. Ionization is the process of ion formation by separating electrons from gas molecules. Owning due to the effects of an external ionizer - strong heating, x-ray or ultraviolet irradiation, bombing by electrons. Recombination - process, reverse ionization. Plasma - represents completely or partially ionized gas, in which the concentrations of positive and negative charges are equal.

? Electric current in vacuum. Thermoelectronic emission.

Current carriers in vacuum - electrons that have passed due to emissions from the surface of the electrodes. Thermoelectronic emission is the emission of electrons with heated metals.

? What do you know about the phenomenon of superconductivity?

A phenomenon in which the resistance of some pure metals (tin, lead, aluminum) drops to zero at temperatures close to absolute zero.

? What do you know about electrical resistance conductors? What is the specific resistance, dependence on temperature, specific electrical conductivity? What do you know about the sequential and parallel connection of the conductors. What is shunt, additional resistance?

Resistance - the value, directly proportional to the length of the conductor l. and back proportional area S. Cross section of the conductor: (R-specific resistance). Performance, reverse resistance. Resist (resistance of the conductor with a length of 1 m cross section 1 m 2). The resistivity depends on the temperature, here a is the temperature coefficient, R. and R. 0, R and R 0 derail and specific resistances for t. and 0 0 C. Parallel - , consistent R \u003d R. 1 +R. 2 +…+R N.. The shunt-resistor connected parallel to the electro-measuring device for the lead part of the electric current to expand the measurement limits.

? A magnetic field. What sources can create a magnetic field?

The magnetic field is a special kind of matter through which the moving electrical charges interact. The reason for the existence of a permanent magnetic field fixed conductor with constant electric shock, or permanent magnets.

? Word Ampere Law. How do the conductors interact for which the current flows in one (opposite) direction?

The power of the ampere is applied to the conductor with the current.

B - magnetic induction, I-current in Explorer, D l. - Conduct site, A-angle between magnetic induction and conductor site. In one direction, they are engaged in the opposite - repel.

? Give the definition of the ampere power. How to determine its direction?

This is the force acting on the conductor with a current placed in a magnetic field. The direction is determined as: the palm of the left hand is in such a way that the magnetic induction lines consisted in it, and the four elongated fingers were targeted in the conductor. An outlined thumb show the direction of the amper power.

? Explain the movement of charged particles in a magnetic field. What is Lorentz power? How is its direction?

The moving charged particle creates its own magnetic field. If it is placed in an external magnetic field, then the interaction of the fields will appear in the occurrence of force acting on a particle from the external field - the forces of Lorentz. Direction - by the rule of the left hand. For positive charge- Vector B. Included in the palm of the left hand, four fingers are directed along the movement of a positive charge (velocity vector), the bent thumb shows the direction of Lorentz's power. On the negative charge The same force acts in the opposite direction.

(q.-charge, v.-speed, B.- induction, a- angle between the direction of speed and magnetic induction).

? Frame with current in a homogeneous magnetic field. How is the magnetic moment determined?

The magnetic field has an orienting action on a frame, turning it in a certain way. The torque is determined by the formula: M. =p. M.x. B. where p. M. - vector magnetic moment frame with current equal IS. n. (Current on the surface area of \u200b\u200bthe contour, per unit normal to the contour), B. Magnetic induction substator, quantitative characteristic of the magnetic field.

? What is a magnetic induction vector? How to determine his direction? How do you graphically portray a magnetic field?

The vector of magnetic induction is the power characteristic of the magnetic field. The magnetic field is clearly depicted using power lines. At every point of the field tangent force line Coincides with the direction of the magnetic induction vector.

? Word and explain the law of Bio - Savara - Laplace.

Bio-Savara law - Laplace allows you to calculate for conductor with current I. Magnetic Induction field D B. created in an arbitrary point of the field D l. Explorer: (here m 0 emagnetic constant, M-magnetic permeability of the medium). The direction of the induction vector is determined by the rule of the right screw, if the propulsive movement of the screw corresponds to the current direction in the element.

? Word the superposition principle for the magnetic field.

Superposition principle - the magnetic induction of the resulting field created by several currents or moving charges is equal to the vector amount of magnetic induction of foldable fields created by each current or moving charge separately:

? Explain the main characteristics of the magnetic field: magnetic flow, circulation of the magnetic field, magnetic induction.

Magnetic flow F.through any surface S. Call the value equal to the product of the magnetic induction vector module into the area S. and cosine angle A between vectors B. and n. (external norm to the surface). Circulating vector B. According to a given closed loop, the integral of the species is called where D l. - vector of elementary contour length. Vector circulation theorem B. : Circulation vector B. according to an arbitrary closed contour, it is equal to the product of the magnetic constant on the algebraic amount of currents covered by this circuit. The vector of magnetic induction is the power characteristic of the magnetic field. The magnetic field is clearly depicted using power lines. At each point of the field, the tangent of the power line coincides with the direction of the magnetic induction vector.

? Write down and comment on the solenoidal conditions of the magnetic field of integral and differential forms.

Vector fields in which there are no sources and drains are called solenoidal. The condition of the solenoidal of the magnetic field in the integral form: and the differential form:

? Magnetics. Types of magnetics. FeroMagnetics and their properties. What is hysteresis?

The substance is a magnetic, if it is capable of the magnetic field under the action of a magnetic field (magnetized). The substances magnetized in an external magnetic field against the direction of the field are called diamagnets. The vigorous in the external magnetic field in the direction of the field - paramagnets. These two classes are called low-magnetic substances. Silent substances magnetized even in the absence of an external magnetic field, called ferromagnets . Magnetic hysteresis - the difference in the magnetization values \u200b\u200bof the ferromagnetsis at the same tension of the magnetizing field depending on the value of pre-magnetization. This graphic dependence is called hysteresis loop.

?

Scrolling changes vectors IN and N. On the border due to the magnetization jump due to the difference in magnetic permeabilities of media.

? What is electromagnetic induction? Word and explain the main law of electromagnetic induction (Faraday law). Formulate Lenza rule.

The phenomenon of the occurrence of the electromotive force (EMF induction) in the conductor in a variable magnetic field or moving in a constant in a constant magnetic field is called electromagnetic induction. Faraday Law: What would have not been the reason for changing the magnetic induction flow covered by a closed conductive circuit that occurs in the EDC circuit

The minus sign is determined by the Lenz rule - the induction current in the circuit always has such a direction that the magnetic field created by it prevents the change in the magnetic flux by which caused this induction current.

? What is the phenomenon of self-induction? What is inductance, units of measurement? Currents when closing and opening the electrical circuit.

The occurrence of induction EMF in a conductive circuit under the action of its own magnetic field when it occurs, resulting in a change in the current power conductor. Inductance is a proportionality coefficient, depending on the shape and size of the conductor or contour, [GN]. In accordance with the rule of Lenz, self-induction is preventing the increase in current strength when the current force is turned on and descending when the chain is turned off. Therefore, the value of current force cannot change instantly (mechanical analog is inertness).

? The phenomenon of mutual induction. The coefficient of mutual induction.

If two fixed circuits are located close to each other, then when changing the current strength in one contour, EMF occurs in another circuit. This phenomenon is called mutual induction. Proportionality coefficients L.

The general patterns of electromagnetic fields are described by Maxwell equations. In relativistic electrodynamics, it was found that the relativistic invariance of these equations takes place only under the condition of the relativity of electrical and magnetic fields, i.e. With the dependence of the characteristics of these fields from the selection of inertial reference systems. In the mobile system, the electric field is the same as in the stationary, but in the movable system there is a magnetic field, which in the fixed system is not.

Wipers and waves