Electric field – FIZI4KA

Unified State Exam 2022 in Physics ›

Electrodynamics is a branch of physics that studies the properties and interactions of electric charges carried out through an electromagnetic field.

Electrostatics is the branch of electrodynamics that examines the properties and interactions of stationary electrically charged bodies or particles.

Electromagnetic interaction is the interaction between electrically charged particles or macrobodies.

A point charge is a charged body whose size is small compared to the distance at which its action is assessed.

Electrification of bodies

Electrification is the process of imparting an electric charge to the body, i.e., violating its electrical neutrality. The process of electrification is the transfer of electrons or ions from one body to another. As a result of electrification, the body gains the opportunity to participate in electromagnetic interaction.

Methods of electrification:

friction, for example, electrification of an ebonite stick when rubbing against fur. When two bodies come into close contact, some electrons transfer from one body to another; As a result, a deficiency of electrons is created on the surface of one of the bodies and the body receives a positive charge, while the other has an excess, and the body becomes negatively charged. The charges of the bodies are the same;
through influence (electrostatic induction) - the body remains electrically neutral, the electric charges inside it are redistributed so that different parts of the body acquire charges of different signs;
When a charged and uncharged body comes into contact, the charge is distributed between these bodies in proportion to their sizes. If the sizes of the bodies are the same, then the charge is distributed equally between them;
upon impact;
under the influence of radiation - under the influence of light, electrons can escape from the surface of the conductor, and the conductor acquires a positive charge.

Properties of electrostatic field lines

Two properties of field lines created by stationary charges can be distinguished:

Lines of force have a beginning and an end - they begin on positive charges and end on negative charges.
The field strength is greater in the area in which the lines are denser.

Rice. 15. Two properties of electric field lines created by stationary charges

Note: There is also a vortex electric field. This field is not associated with stationary charges. Its lines are closed on themselves. The picture of such a field is something similar to a vortex, hence its name. More details about the vortex electric field are written in the article devoted to electromagnetic waves.

The field is stronger where its lines are located closer to one another, as well as where the vector E is longer.

Where do the single charge lines end?

Electrostatic field lines starting on a positive charge must end on some negative charge.

If there is no second charge located nearby a charge that has the opposite sign, then the field lines of such a lonely charge go to infinity.

There, far away, at infinity, there will always be a charge with the opposite sign, on which the lines of the single charge in question will end.

Rice. 16. If the charge is unit and there are no other charges of the opposite sign nearby, then its lines of force go to infinity and end there at the opposite charge

Interaction of charges. Two types of charges

Electric charge is a scalar physical quantity that characterizes the ability of a body to participate in electromagnetic interactions.

Designation – \( q \), SI unit of measurement – pendant (C).

There are two types of electrical charges: positive and negative. The electron has the smallest negative charge (–1.6·10-19 C), the smallest positive charge (1.6·10-19 C) has the proton. The minimum charge that can be imparted to a body is equal to the charge of an electron (elementary charge). If a body has excess (extra) electrons, then the body is negatively charged, if the body has a lack of electrons, then the body is positively charged.

The amount of charge on the body will be equal to

where \( N \) is the number of excess or missing electrons; \( e \) - elementary charge equal to 1.6·10-19 C.

Important! A particle may have no charge, but charge does not exist without a particle.

Electric charges interact:

charges of the same sign repel:

charges of opposite signs attract:

The device for detecting electric charge is called an electroscope. The main part of the device is a metal rod on which two sheets of metal foil are attached, placed in a glass vessel. When a charged body comes into contact with the electroscope rod, the charges are distributed between the sheets of foil. Since the charge of the leaves is of the same sign, they repel each other.

An electrometer can also be used to measure charges. Its main parts are a metal rod and an arrow, which can rotate around a horizontal axis. The rod with the arrow is fixed in a plastic sleeve and placed in a metal case covered with glass covers. When a charged body comes into contact with a rod, the rod and the arrow receive electric charges of the same sign. The arrow rotates at a certain angle.

The interaction of charges is transmitted without the participation of matter

Charges will attract and repel not only in air, but even in airless space. This can be easily verified by placing a charged electroscope under the bell and pumping out the air from under the bell. Strips of paper that have the same charges will still continue to repel each other, regardless of whether they are in air or in airless space.

Rice. 2. To transmit the mutual action of charges, a substance is not needed, since this interaction is not transmitted through a substance

This means that the transfer of charge interactions does not occur through matter.

Scientists from England - Michael Faraday and James Maxwell - have been studying electric charges for a long time. They found that charges are surrounded by a special type of matter, which they called an electric field.

Any charge is surrounded by an electric field - a special type of matter.

Law of conservation of electric charge

A system is called closed (electrically isolated) if there is no exchange of charges with the environment.

In any closed (electrically isolated) system, the sum of electric charges remains constant regardless of any interactions within it.

The total electric charge \( (q) \) of the system is equal to the algebraic sum of its positive and negative charges \( (q_1, q_2 … q_N) \):

Important! In nature, charges of the same sign do not arise or disappear: positive and negative charges can mutually neutralize each other if they are equal in magnitude.

Why are charges called sources of electric fields?

The electrostatic field has its own electrical sources.

We know that electrostatic field lines have a beginning and an end. They start on positive charges and end on negative charges.

Therefore, positive charges are called field sources, and negative charges are called field sinks.

Rice. 17. Electric charges are called sources of electrostatic field

Coulomb's law

Coulomb's law was discovered experimentally: in experiments using torsion balances, the interaction forces of charged balls were measured.

Coulomb's law is formulated as follows: the force of interaction \( F \) of two point stationary electric charges in a vacuum is directly proportional to their modules \( q_1 \) and \( q_2 \) and inversely proportional to the square of the distance between them \( r \ ):

where \( k=\frac{1}{4\pi\varepsilon_0}=9\cdot10^9 \) (N m2)/Cl2 – proportionality coefficient, \( \varepsilon_0=8.85\cdot10^{- 12} \) C2/(N m2) – electrical constant.

The coefficient \( k \) is numerically equal to the force with which two point charges of 1 C each interact in a vacuum at a distance of 1 m.

The Coulomb force is directed along the straight line connecting the interacting charges. Charges interact with each other with forces equal in magnitude and opposite in direction.

The value of the Coulomb force depends on the environment in which they are located. In this case, the formula of the law is:

where \( \varepsilon \) is the dielectric constant of the medium.

Coulomb's law applies to interactions

stationary point charges;
uniformly charged spherical bodies.

In this case, \( r \) is the distance between the centers of the spherical surfaces.

Important! If the charged body is extended, then it is necessary to split it into point charges, calculate the forces of their pairwise interaction and find the resultant of these forces (superposition principle).

How to depict the electric field of a unit charge

Let a stationary positive point charge create an electric field in the space surrounding it. Let's draw several vectors of the strength of this field.

The red dot in the figure indicates the charge. And the points where the test charge was placed and the field was measured are indicated in black.

Rice. 12. You can depict the field of a stationary charge by placing tension vectors in space

Based on the length of the vectors, we can conclude that the closer the test charge is located to the charged body, the stronger the field affects it. By increasing the distance between the charged body and the test charge, we note that the effect of the field will decrease.

Fields whose effects will differ at different points in space are called inhomogeneous. This means that the electric field around point charges is nonuniform.

We represent a non-uniform electric field with lines of force

As you can see, we can depict the field using tension vectors drawn at various points. However, there is a more convenient way.

Taking a closer look at the figure, you can see that the voltage vectors surrounding the charge are located on some straight lines. These straight lines are indicated by dotted lines in the figure. They are called electric field lines, or tension lines.

Note: It is more convenient to depict the electrostatic field not using vectors, but using tension lines.

If there is only one charge, and there are no other charges nearby, then its field is depicted by lines radiating in all directions.

Rice. 13. A set of field lines of a single point charge, this is a non-uniform field

Lines of positive charges are directed away from them, and lines of negative charges are directed towards these charges, just like voltage vectors.

We remember that the voltage vector describes the force with which the field created by a charge can act on other charges. Therefore, tension lines are also often called field lines.

What does the field of two interacting charges look like?

Let us now consider the field of interacting charges - positive and negative.

Rice. 14. Inhomogeneous field of two point interacting charges

As you can see, the lines of interacting charges are bent and their configuration is distorted.

We know that the field of one point charge is inhomogeneous. The field of two interacting charges is also non-uniform.

Now let’s make a generalization; in the figure, a non-uniform field is depicted:

either straight lines radiating in all directions from a single charge, or
curved lines for interacting charges.

As you move away from the charges, the distance between the lines will increase. The further the lines are located from one another in a certain region of space, the weaker the field in this region.

The effect of an electric field on electric charges

An electric field is a special form of matter that exists around electrically charged bodies.

The concept of an electric field was first introduced by Faraday. He explained the interaction of charges as follows: each charge creates an electric field around itself, which acts with some force on the other charge.

The properties of the electric field are that it:

financially;
created by charge;
detected by the effect on the charge;
continuously distributed in space;
weakens with increasing distance from the charge.

The action of a charged body on surrounding bodies manifests itself in the form of forces of attraction and repulsion, tending to rotate and move these bodies in relation to the charged body.

The force with which the electric field acts on the charge can be calculated using the formula:

where \( \vec{E} \) is the electric field strength, \( q \) is the charge.

Solving problems about point charges and systems that can be reduced to them is based on the application of the laws of mechanics, taking into account Coulomb's law and the consequences arising from it.

Algorithm for solving problems about point charges and systems that can be reduced to them:

make a drawing; indicate the forces acting on a point charge placed in an electric field;
write down the equilibrium condition for the charge or the basic equation of the dynamics of a material point;
express the forces of electrical interaction through charges and fields and substitute these expressions into the original equation;
if during the interaction of charged bodies a redistribution of charges occurs between them, add the equation of the law of conservation of charges to the compiled equation;
write down all auxiliary conditions mathematically;
solve the resulting system of equations for an unknown quantity;
check the solution

Theories of long-range and short-range action

Physicists have put forward various theories trying to explain the interaction of charges. The two most widely used are the theories of short-range and long-range action.

Long range

The theory of long-range action states that one charge acts directly on another charge. That is, to transfer the action of one charge to another, intermediaries are not needed.

In addition, interaction occurs instantly at any distance. This means that if you remove one of the interacting charges, its effect on the remaining charge will stop instantly.

Proximity

In contrast to this theory, Michael Faraday proposed his theory of short-range action.

This theory states that charges cannot directly act on each other. That is, in order to transmit its effect, the charge needs some help. And each charge creates this assistant in the space around itself. Faraday called it the electric field.

Other charges will be affected not by the charge itself, but by the field created by this charge. Such a field does not propagate in space instantly, but at a finite speed.

Note: As it turned out later, this is a very high speed - three hundred thousand kilometers per second. It is called the speed of light.

Therefore, if one of the interacting charges is quickly removed, then the second charge will learn about its disappearance not instantly, but after some, albeit short, time.

It turns out that the interaction of charges does not occur directly, but in the form of a chain. Each charge creates a field around itself, and it is the field that acts on another charge placed in it.

And the force acting on a charge located at any point in space depends on the characteristics of the field at this point.

Rice. 3. The main differences between the theory of long-range action and the theory of short-range action

Currently, the generally accepted theory explaining the interaction of charges is Faraday's theory of short-range interaction. Since this theory was completely confirmed experimentally.

Note: In addition to electric fields, there are also magnetic fields. Unlike an electrostatic field, a magnetic field does not have its own magnetic sources. It occurs in the space around moving charges. That is, a magnetic field is a field of electric charges in motion.

James Clerk Maxwell showed in the mid-19th century that electric and magnetic fields are coupled and that this electromagnetic field propagates through space at a very high but finite speed.

Field and matter are two types of matter

The world around us is material. This means that matter is something that really exists, regardless of whether we observe it or not.

It can manifest itself in the form of two parts - matter and field. We are surrounded by matter, and atoms and molecules are the smallest units of matter.

A field is another type of matter. The field is not a substance, however, it really exists.

Rice. 4. Matter consists of two parts - field and substance

Electric field strength

Electric field strength \( \vec{E} \) is a vector physical quantity equal to the ratio of the force \( F \) acting on a test point charge to the magnitude of this charge \( q \):

Designation – \( \vec{E} \), unit of measurement in SI – N/C or V/m.

The field strength of a point charge in vacuum is calculated by the formula:

where \( k=\frac{1}{4\pi\varepsilon_0}=9\cdot10^9 \) (N m2)/C2, \( q_0 \) – charge creating the field, \( r \) – the distance from the charge creating the field to this point.

The field strength of a point charge in a medium is calculated by the formula:

where \( \varepsilon \) is the dielectric constant of the medium.

Important! The electric field strength does not depend on the magnitude of the test charge; it is determined by the magnitude of the charge creating the field.

The direction of the voltage vector at a given point coincides with the direction of the force with which the field acts on a positive test charge placed at this point.

The electric field intensity line is a line whose tangent at each point is directed along the intensity vector \( \vec{E} \).

Electrostatic field strength lines begin at positive electric charges and end at negative electric charges, or go to infinity from a positive charge and come from infinity to a negative charge.

The distribution of tension lines around positive and negative point charges is shown in the figure.

By determining the direction of the vector \( \vec{E} \) at various points in space, one can imagine a picture of the distribution of electric field strength lines.

A field in which the intensity is the same in magnitude and direction at any point is called a uniform electric field. The electric field between two oppositely charged metal plates can be considered homogeneous. Tension lines in a uniform electric field are parallel to each other.

Definition

The electric field is inextricably linked with the magnetic field, and arises as a result of its change. These two types of matter are components of electromagnetic fields that fill the space around charged particles or charged bodies.

Thus, this term means a special type of matter that has its own energy, which is an integral component of the vector electromagnetic field. The electric field has no boundaries, but its force influence tends to zero as we move away from the source - a charged body or point charges [].

An important property of the field form of matter is the ability of the electric field to maintain the ordered movement of charge carriers.

Rice. 1. Definition of the concept of “electric field”

The energy of the electric field is subject to the conservation law. It can be converted into other types or used to perform work.

The strength characteristic of fields is their intensity - a vector quantity, the numerical value of which is defined as the ratio of the force acting on a test positive charge to the magnitude of this charge.

Characteristic physical properties:

reacts to the presence of charged particles;
interacts with magnetic fields;
is the driving force for the movement of charges - both positive ions and negative charges in metal conductors;
can be determined only by the results of observing the manifestation of an action.

It always surrounds stationary static (not changing over time) charges, which is why it is called electrostatic. Experiments confirm that the same forces act in an electrostatic field as in an electric one.

The electrostatic interaction of the field on charged bodies can be observed when an electrified ebonite stick is brought to small objects. Depending on the polarity of the electrified particles, they will either be attracted or repelled from the stick.

Strong electrostatic fields are formed near powerful electrical discharges. On the surface of a conductor caught in the discharge zone, a redistribution of charges occurs.

Due to the distribution of charges, the conductor becomes charged, which is a sign of the influence of the electric field.

Electrostatic field potential

An electric field with intensity \( \vec{E} \) does work when moving a charge \( q \). The work \( A \) of the electrostatic field is calculated by the formula:

where \( d \) is the distance over which the charge moves, \( \alpha \) is the angle between the vectors of the electric field strength and the charge movement.

Important! This formula is applicable to finding work only in a uniform electrostatic field.

The work of electrostatic field forces when moving a charge from one point in the field to another does not depend on the shape of the trajectory, but is determined only by the initial and final position of the charge.

potential if the work done by forces to move a charge along a closed path is zero.

Important! The work done by the electrostatic field forces when moving a charge along any closed trajectory is zero. The electrostatic field is potential.

The work of the electrostatic field to move a charge is equal to the change in potential energy, taken with the opposite sign. In electrodynamics, energy is usually denoted by the letter \( W \), since the letter \( E \) denotes field strength:

The potential energy of a charge \( q \) placed in an electrostatic field is proportional to the magnitude of this charge. The potential energy of interaction of charges is calculated relative to the zero level (similar to the potential energy of the gravity field). The choice of the zero level of potential energy is determined based on considerations of convenience when solving the problem.

Where is vector E directed?

Let us once again pay attention to the formula:

\[\large \vec{E} = \frac {\vec{F}}{q} \]

Charge q is a scalar quantity. And the force F is vector.

Let's use the mathematical properties of vectors: dividing the vector F by the scalar q, we get a new vector E:

its length is different from the vector F.
the directions of the vectors F and E coincide (or the vectors F and E are directed in opposite directions).

Rice. 8. The direction of vector E is selected from positive charges and towards negative charges

Vector E is co-directed with the vector of force acting on a test charge placed in the field. For a positive charge, its vector E is directed away from that charge. And for a negative charge, its vector E is directed towards this charge.

Note: Unidirectional or oppositely directed, that is, parallel vectors are called collinear. They may have different lengths.

Electric field potential. Potential difference

Potential is a scalar physical quantity equal to the ratio of the potential energy of an electric charge in an electrostatic field to the value of this charge.

The designation is \( \varphi \), the SI unit is volt (V).

Potential \(\varphi\) is an energy characteristic of the electrostatic field.

The potential difference is numerically equal to the work done by the electric force when moving a unit positive charge between two points of the field:

Designation – \( \Delta\varphi \), SI unit of measurement is volt (V).

Sometimes the potential difference is denoted by the letter \(U\) and is called voltage .

Important! Potential difference \(\Delta\varphi=\varphi_1-\varphi_2\), not potential change \(\Delta\varphi=\varphi_2-\varphi_1\). Then the work of the electrostatic field is:

Important! This formula allows you to calculate the work of electrostatic forces in any field.

In electrostatics, potential is often calculated relative to a point at infinity. In this case, the field potential at a given point is equal to the work done by electric forces when removing a unit positive charge from a given point to infinity.

The field potential of a point charge \( q \) at a point distant from it at a distance \( r \) is calculated by the formula:

To visually represent the electric field, equipotential surfaces are used.

Important! Inside a conducting ball, the potential of all points inside the ball is equal to the potential of the ball’s surface and is calculated using the formula for the potential of a point charge (\( r =R \), where \( R \) is the radius of the ball). The field strength inside the ball is zero.

An equipotential surface, or surface of equal potential, is a surface at all points of which the potential has the same value.

Properties of equipotential surfaces

The tension vector is perpendicular to the equipotential surfaces and directed in the direction of decreasing potential.
The work done to move a charge along an equipotential surface is zero.

In the case of a uniform field, equipotential surfaces are a system of parallel planes. For a point charge, the equipotential surfaces are concentric circles.

Potential difference and tension are related by the formula:

From the principle of superposition of fields follows the principle of superposition of potentials:

The potential of the resulting field is equal to the sum of the potentials of the fields of individual charges.

Important! Potentials are added algebraically, and tensions are added according to the rule of vector addition.

The solution of problems about point charges and systems that can be reduced to them is based on the application of conservation laws, the theorem on the change in the kinetic energy of a charge, taking into account the work of electrostatic forces.

Algorithm for solving such problems:

establish the nature and features of electrostatic interactions of system objects;
introduce the characteristics (force and energy) of these interactions, make a drawing;
write down the laws of conservation and motion for objects;
express the energy of electrostatic interaction through charges, potentials, tensions;
create a system of equations and solve it relative to the desired value;
check the solution.

Characteristics

The main characteristics are:

potential;
tension;
voltage.

Potential

The term means the ratio of the potential energy W possessed by the test charge q′ at a given point to its value. Expression φ =W/q′. is called the electric field potential at that point.

In other words: the amount of accumulated energy that can potentially be spent on doing work aimed at moving a unit charge to infinity, or to another point with conditionally zero energy, is called the potential of the electric field in question at a given point.

The field energy is taken into account in relation to a given point. It is also called the potential at a given point. The total potential of the system is equal to the sum of the potentials of the individual charges. This is one of the most important characteristics of the field. The potential can be compared to the energy of a compressed spring, which, when released, is capable of performing a certain amount of work.

The unit of measurement for potential is 1 volt. When a point moves infinitely away from an electrified body, the potential at this point decreases to 0: φ∞=0 .

Field strength

It is reliably known that the electric field of a single charge q acts with a certain force F on a point test charge, regardless of the distance at which it is located. The force acting on an isolated positive test charge is called tension and is symbolized by E.

Tension is a vector quantity. The magnitude of the tension vector: E=F/q′ .

Electric field strength lines (known as field lines) are tangent lines, which at the points of contact coincide with the orientation of the strength vectors. The density of the field lines determines the magnitude of the tension.

Rice. 5. Electric field of positive and negative voltage vector

The tension around a point charge Q at a distance r from it is determined by Coulomb’s law: E = 14πε0⋅Qr2 . Such fields are called Coulomb fields.

The intensity vectors of a positive point charge are directed away from it, and of a negative one – towards the center (toward the charge). The directions of the Coulomb field vectors can be seen in Fig. 6.

Rice. 6. Direction of lines of tension of positive and negative charges

For Coulomb fields, the principle of superposition is valid. The essence of the principle is as follows: the tension vector of several charges can be represented as a geometric sum of the tensions created by each individual charge included in this system.

For the general case of charge distribution we have:

The tension lines are shown schematically in Figure 7. The picture shows lines characteristic of the fields:

electrostatic;
dipole;
systems and charges of the same name;
homogeneous field.

Rice. 7. Lines of intensity of various fields

Voltage

Since electric field forces are capable of doing work to move elementary charge carriers, the presence of a field is a condition for the existence of electric current. Electrons and other elementary charges always move from a point of higher potential to a point of lower potential. In this case, part of the energy is spent on moving work.

To maintain a constant current (ordered movement of elementary charge carriers), it is necessary to maintain a potential difference at the ends of the conductor, which is also called voltage. The greater this difference, the more actively the work is performed, the more powerful the current in this area. The functions of maintaining the potential difference are assigned to current sources.

Conductors in an electric field

Conductors are substances in which the ordered movement of electrical charges can occur, i.e., electric current can flow.

Conductors are metals, aqueous solutions of salts, acids, and ionized gases. Conductors contain free electrical charges. In metals, the valence electrons of atoms interacting with each other become free.

If a metal conductor is placed in an electric field, then under its action the free electrons of the conductor will begin to move in the direction opposite to the direction of the field strength. As a result, an excess negative charge will appear on one surface of the conductor, and an excess positive charge on the opposite surface.

These charges create an internal electric field inside the conductor, the intensity vector of which is directed opposite to the external field intensity vector. Under the influence of an external electrostatic field, conduction electrons in a metal conductor are redistributed so that the resulting field strength at any point inside the conductor is zero. Electric charges are located on the surface of the conductor.

Important! If there is a cavity inside the conductor, then the voltage in it will be zero regardless of what field is present outside the conductor and how charged the conductor is. The internal cavity in the conductor is shielded (protected) from external electrostatic fields. Electrostatic protection is based on this.

The phenomenon of charge redistribution in an external electrostatic field is called electrostatic induction .

Charges separated by an electrostatic field cancel each other out if the conductor is removed from the field. If such a conductor is cut without taking it out of the field, then its parts will have charges of different signs.

Important! At all points on the surface of the conductor, the voltage vector is directed perpendicular to its surface. The surface of the conductor is equipotential (the potentials of all points on the surface of the conductor are equal).

How to detect an electric field

We do not feel the electric field because we do not have sense organs capable of detecting it.

But by using something that is sensitive to the electric field, you can verify that there is a field surrounding the charges.

Any electric charge can be used as a sensitive element. Because any charge is surrounded by its own electric field and, thanks to it, can feel similar fields created by other charges. Physicists call such a charge, used to detect the field, a test charge.

Rice. 5. Description of the concept of a test point charge

Notes:

Some living things can sense electric fields, such as some species of fish.
An electric field can be detected by its effect on charges, as well as using various instruments.
The field of a charge acts with some force on another charge located nearby. That is, charges act on each other due to their electric fields.

We can detect an electric field due to its effect on other charges. Electric force is the force with which the field acts on the test charge introduced into it.

Note: Do not confuse test and elementary charge.

Dielectrics in an electric field

Dielectrics are substances that do not conduct electric current. Dielectrics are glass, porcelain, rubber, distilled water, and gases.

There are no free charges in dielectrics; all charges are bound. In a dielectric molecule, the total negative charge of the electrons is equal to the positive charge of the nucleus. There are polar and non-polar dielectrics.

In molecules of polar dielectrics, nuclei and electrons are located so that the centers of mass of positive and negative charges do not coincide and are at some distance from each other. That is, molecules represent dipoles regardless of the presence of an external electric field. In the absence of an external electric field, due to the thermal motion of molecules, the dipoles are located randomly, so the total field strength of all dielectric dipoles is zero.

If, in the absence of an external electric field, the centers of mass of positive and negative charges in a dielectric molecule coincide, then it is called non-polar. An example of such a dielectric is the hydrogen molecule. If such a dielectric is placed in an external electric field, then the directions of the force vectors acting on positive and negative charges will be opposite. As a result, the molecule is deformed and turns into a dipole. When a dielectric is introduced into an electric field, its polarization occurs.

Polarization of a dielectric is the process of displacement in opposite directions of unlike bound charges that make up the atoms and molecules of a substance in an electric field.

If the dielectric is non-polar, then a displacement of positive and negative charges occurs in its molecules. Surface bound charges will appear on the surface of the dielectric. These charges are called bound because they cannot move freely separately from each other.

Inside the dielectric, the total charge is zero, and on the surfaces the charges are not compensated and create a field inside the dielectric, the intensity vector of which is directed opposite to the external field strength vector. This means that inside the dielectric the field has a lower intensity than in a vacuum.

A physical quantity equal to the ratio of the modulus of the electric field strength in a vacuum to the modulus of the electric field strength in a homogeneous dielectric is called dielectric constant of a substance :

In a polar dielectric, in an external electric field, the dipoles rotate and they line up along the tension lines.

If a dielectric introduced into an electric field is cut, then its parts will be electrically neutral.

Classification

Electric fields are of two types: homogeneous and inhomogeneous.

Uniform electric field

The state of the field is determined by the spatial location of the tension lines. If the intensity vectors are identical in magnitude and they are co-directed at all points in space, then the electric field is uniform. In it, the lines of tension are located parallel.

An example is the electric field formed by opposite charges on a section of flat metal plates (see Fig. 2).

Rice. 2. Example of homogeneity

Non-uniform electric field

More often there are fields whose strengths differ at different points. Their tension lines have a complex configuration. The simplest example of inhomogeneity is an electric dipole, that is, a system of two opposite charges influencing each other (see Fig. 3). Despite the fact that the electric dipole intensity vectors form beautiful lines, but since they are not equal, such a field is inhomogeneous. Vortex fields have a more complex configuration (Figure 4). Their heterogeneity is obvious.

Rice. 3. Electric dipole

Rice. 4. Vortex fields

Electrical capacity. Capacitor

Electric capacitance (electric capacity) is a scalar physical quantity that characterizes the ability of an isolated conductor to hold an electric charge.

The designation is \( C \), the SI unit is farad (F).

A solitary conductor is a conductor that is distant from other conductors and charged bodies.

Farad is the electrical capacity of such an isolated conductor, the potential of which changes by 1 V when a charge of 1 C is imparted to it:

Formula for calculating electrical capacity:

where \( q \) is the charge of the conductor, \( \varphi \) is its potential.

Electrical capacity depends on its linear dimensions and geometric shape. Electrical capacity does not depend on the material of the conductor and its state of aggregation. The electrical capacity of a conductor is directly proportional to the dielectric constant of the medium in which it is located.

A capacitor is a system of two conductors separated by a dielectric layer, the thickness of which is small compared to the size of the conductors.

The conductors are called capacitor plates. The charges of the capacitor plates are equal in magnitude and opposite in sign of charge. The electric field is concentrated between the plates of the capacitor. Capacitors are used to store electrical charges.

The electrical capacity of the capacitor is calculated by the formula:

where \( q \) is the charge modulus of one of the plates, \( U \) is the potential difference between the plates.

The electrical capacity of a capacitor depends on the linear dimensions and geometric shape and the distance between the conductors. The electrical capacity of a capacitor is directly proportional to the dielectric constant of the substance between the conductors.

A flat capacitor consists of two parallel plates of area \( S \) located at a distance \( d \) from each other.

Electrical capacity of a flat capacitor:

where \( \varepsilon \) is the dielectric constant of the substance between the plates, \( \varepsilon_0 \) is the electrical constant.

On the electrical diagram the capacitor is designated:

Types of capacitors:

by type of dielectric - air, paper, etc.;
shape – flat, cylindrical, spherical;
by electrical capacity - constant and variable capacity.

Capacitors can be connected to each other.

Parallel connection of capacitors

In a parallel connection, capacitors are connected by similarly charged plates. The capacitor voltages are:

Total capacity:

Series connection of capacitors

When capacitors are connected in series, their oppositely charged plates are connected.

The charges of the capacitors with this connection are equal:

Total voltage:

The reciprocal of the total capacity:

With this connection, the total capacitance is always less than the capacitances of the individual capacitors.

Important! If a capacitor is connected to a current source, then the potential difference between its plates does not change when the electrical capacitance changes and is equal to the source voltage. If a capacitor is charged to a certain potential difference and is disconnected from the current source, then its charge does not change when the electrical capacitance changes.

Application of capacitors Capacitors are used in electronic devices as charge storage devices to smooth out ripples in AC rectifiers.

A Brief History of the Study of the Electric Field

It is believed that the engineer and physicist Charles Coulomb became the first researcher of the interaction of static charges. It was he who deduced the principle of their interaction. The foundation of Coulomb's research was Isaac Newton's theory of gravitational interaction.

Hans Oersted became the scientist who discovered the magnetic properties of electric current and field, and thanks to James Maxwell, we know that an electric field cannot exist without a magnetic field, which induces it. Maxwell also approved the concept of short-range electromagnetic interactions.

I advise you to read about the properties of the magnetic field.

Hans Oersted and James Maxwell
However, the electric field became the object of human research long before recent centuries. Thales of Miletus in the 7th century BC explored the nature of static electricity.

At the end of the 19th century, Joseph Thomson discovered the electron, a “living” example of the carrier of electricity. Years later, Ernst Rutherford proved the place in the structure of atoms where electrons are located.

Electric field energy of a capacitor

The energy of a charged capacitor is equal to the work of external forces that must be expended to charge the capacitor.

The electrical energy of a capacitor is concentrated in the space between the plates of the capacitor, that is, in the electric field, therefore it is called electric field energy . Formulas for calculating the electric field energy:

Since the electric field strength is directly proportional to the voltage, the energy of the electric field of the capacitor is proportional to the square of the strength.

Electric field energy density:

where \( V \) is the volume of space between the plates of the capacitor.

The energy density does not depend on the parameters of the capacitor, but is determined only by the electric field strength.

How to use a known intensity to calculate the force with which the field acts on a charge

If the field strength is known, then the force that acts on a charge placed in this field can be calculated using the formula:

\[\large \boxed{ \vec{E} \cdot q = \vec{F} } \]

\(\large q \left( \text{Cl}\right) \) – a charge, positive or negative, placed at a selected point in space in which an electric field exists;

The formula is written in vector form. This means that it allows you to find both characteristics of the force acting on the charge - the direction of the force vector and its magnitude.

By multiplying the charge by the intensity at a selected point in the field, you can calculate the force acting on the charge from the field.

Rice. 11. The directions of the force and tension vectors coincide for a positive charge and are directed in the opposite direction for a negative charge

Since tension is included in the formula for calculating force, it is called the force characteristic of the electric field.

Knowing the force, we can use Newton's second law to calculate the acceleration of the charge. And using kinematics formulas for uniformly alternating motion, knowing the acceleration, you can determine the movement of the charge or the trajectory of its movement.

Basic formulas of the section “Electric field”

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Electric field

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Lecture on the topic “Basic properties and characteristics of the electric field”

Electrical engineering and electronics – 2

Assignment for students using distance learning technologies and e-learning

date 03.12

Group A-19

Academic discipline OP.03 Electrical engineering and electronics

Lesson topic Basic properties and characteristics of the electric field

Lecture form

Lesson plan

1. Introduction. Characteristics of the academic discipline “Electrical and Electronics Engineering”, its place and role in the professional training of specialists. The main stages of development of the domestic electric power industry

2 Basic properties and characteristics of the electric field

Exercise

— Give a lecture

LECTURE

INTRODUCTION

Characteristics of the academic discipline “Electrical and Electronics Engineering”, its place and role in the professional training of specialists

The existence of human society requires constant expenditure of energy. The level of energy production and consumption largely characterizes the level of productive forces of society.

Electrical energy is a secondary form of energy that does not exist in ready-made form in nature. More than 100 years ago, electrical engineering was just in its infancy. It is impossible to imagine the life of modern society without the use of electrical energy.

The discipline “Electrical Engineering and Electronics” is the basis for studying professional module topics related to electrical devices, electronic devices, and electrical machines.

Electrical engineering

– a branch of science and technology related to the production, transformation and use of electrical energy in practical human activities, covering issues of the use of electromagnetic phenomena in various industries and in everyday life.

Electronics

– a branch of science and technology associated with the creation and description of the physical principles of operation of new electronic instruments and devices or electronic circuits based on them.

Electrical energy has become widespread in modern industry and transport due to its advantages over other types of energy:

- any type of energy can be easily converted into electricity;

- Electrical energy can be transmitted over any distance. This makes it possible to build power plants in places where there are natural energy resources, and transfer it to places where sources of industrial raw materials are located, but there is no local energy base;

— the ability to convert electrical energy into other types of energy;

— the processes of receiving, transmitting and consuming electricity are easy to automate;

— the possibility of transforming electrical energy;

- processes that use electrical energy allow simple control (pressing a switch button, etc.).

The only drawback of electrical energy is the inability to store it in large quantities and maintain these reserves for a long time.

The main stages of development of the domestic electric power industry

People have been familiar with electrical phenomena for a long time, but their practical use began only at the end of the 19th century, after the creation of classical electrodynamics by J. C. Maxwell. The invention of radio by A. S. Popov and G. Marconi is one of the most important applications of the principles of the new theory. For the first time in human history, scientific research preceded technical applications. If the steam engine was built long before the creation of the theory of heat (thermodynamics), then it was possible to construct an electric motor or implement radio communication only after the discovery and study of the laws of electrodynamics.

Then the first electric bells, electric irons, etc. appeared in Europe. In Russia, the electrical industry and the electrification of transport began after the October Revolution, and the construction of power plants began. Hydroelectric power stations Bratsk, Sayano-Shushenskaya, Krasnoyarsk are the largest in the world. The first nuclear power plant was built in 1954 in the city of Obninsk near Moscow.

In 1926, the first section of the Baku-Surakhani railway was electrified.

M.V. is considered the founder of electrical engineering in Russia. Lomonosov. He created the first laboratory for the study of electrical phenomena and predicted the possibility of transmitting electrical energy over a distance. Russian scientists and engineers have made many discoveries. P.N. Yablochkov created an alternating current generator and transformer; M.O. Dolivo-Dobrovolsky developed a three-phase current system; A.S. Popov carried out the first radio transmission of waves over a distance; A.N. Lodygin invented the first electric light bulb, etc. In the process of studying electrical engineering, we will become acquainted with the work of these scientists and many others.

An important role in the discovery of the laws and phenomena of electrical engineering belongs to foreign scientists: A. Ampere, C. Coulomb, G. Ohm, N. Tesla, G. Kirchhoff, etc., whose names are the basic laws of electrical engineering and the units of measurement of the main electrical quantities.

Topic 1.1 Electric field

1 Basic properties and characteristics of the electric field

The theory that explains the electrical properties of bodies by the presence of electrons in them and their movement is called the electron theory

As you know, all substances, both simple and complex, consist of molecules, and molecules of atoms. The structure of an atom is very complex, but in a simplified way it can be represented as a nucleus surrounded by a shell. The shell is formed from tiny particles – electrons – constantly moving at a very high speed. The number of electrons in a neutral atom is exactly equal to the number of protons in the nucleus of the atom. The number of electrons in the atoms of different substances is not the same. For example, a hydrogen atom has one electron, and a sodium atom has 11 electrons rotating in three orbits.

Figure 1 – Atom model

The nucleus and electrons have energy. The nucleus has positive energy, electrons have negative energy. If the energy of the nucleus and electrons in an atom is the same, then such an atom is neutral

But if the atom loses one or more electrons, then the positive energy prevails and the atom becomes a positive ion

If an atom accepts one or more electrons, it becomes a negative ion

.
The process of converting atoms into ions is called ionization
.

If positive or negative energy predominates in the volume of a body, then the body is said to be charged. The amount of electricity contained in a charged body is called charge

. The amount of charge is denoted in the SI system - Q, q, and the unit of measurement is C (Coulomb). At the end of the 19th century, an electron was discovered - a carrier of a negative electric charge; at the beginning of the 20th century - a proton, which has the same positive charge. The electron charge is equal to e=16·10-20 C. If 6.29·1018 e passed through the wire, then they say that an amount of electricity of 1 C passed through the wire.

an electric field around any charged body

.
It is impossible to see the electric field, but its presence can be judged by the mechanical forces experienced by stationary charged bodies introduced into this field.
In the figures, the electric field is represented by electric lines of force that start at a positive charge and end at a negative charge (Figure 2).

Figure 2 – Image of the electric field

Opposite charges located at a short distance from each other are attracted to each other. Charges of the same name, due to the opposite direction of the electric field lines, repel.

One of the basic laws of electrostatics, which determines the magnitude and direction of the interaction force between two stationary point electric charges. Installed by S. O. Kulon in 1785.

In his experiments, Coulomb measured the forces of attraction and repulsion of charged balls using torsion balances, and measured the interaction between balls whose dimensions were much smaller than the distance between them. Such charged bodies, the dimensions of which can be neglected in the conditions of this problem, are usually called point charges

Based on numerous experiments, Coulomb established the following law:

The force of interaction between two stationary charged bodies is proportional to the product of the magnitudes of the charges, inversely proportional to the square of the distance between them and depends on the medium

where Q1, Q2 are the magnitude of the charges, C; r

– distance between charge centers, m;
ε а
– absolute dielectric constant of the medium.

k=9∙109 N m2 / Cl2

The force F is directed along a straight line connecting the interacting charges, i.e.

is central. This force is called the Coulomb force. Coulomb forces can be either attractive or repulsive forces. If F<0 for unlike charges, then an attractive force acts between the charges; if F>0 for like charges, then a repulsive force acts between the charges. In practice, Coulomb's law is well satisfied if the sizes of charged bodies are much smaller than the distance between them.

Different substances have different absolute dielectric constants. It is determined by the product of the relative dielectric constant and the dielectric constant of vacuum.