Let's hang a charged cartridge case on a thread and bring an electrified glass rod to it. Even in the absence of direct contact, the sleeve on the thread deviates from the vertical position, being attracted to the stick (Fig. 13).
Charged bodies, as we see, are able to interact with each other at a distance. How is the action transmitted from one of these bodies to another? Maybe it's all about the air between them? Let's find out this by experience.
Let's place a charged electroscope (with the glasses removed) under the bell of the air pump, and then pump out the air from under it. We will see that in airless space the leaves of the electroscope will still repel each other (Fig. 14). This means that air does not participate in the transmission of electrical interaction. Then by what means does the interaction of charged bodies take place? The answer to this question was given in their works by the English scientists M. Faraday (1791-1867) and J. Maxwell (1831-1879).
According to the teachings of Faraday and Maxwell, the space surrounding a charged body differs from the space around unelectrified bodies. There is an electric field around charged bodies. With the help of this field, electrical interaction is carried out.
Electric field is a special type of matter, different from matter and existing around any charged bodies.
It is impossible to see it or touch it. The existence of an electric field can be judged only by its actions.
Simple experiments allow us to establish basic properties of the electric field.
1. The electric field of a charged body acts with some force on any other charged body that finds itself in this field.
This is evidenced by all experiments on the interaction of charged bodies. So, for example, a charged sleeve that found itself in the electric field of an electrified stick (see Fig. 13) was subjected to the force of attraction towards it.
2. Near charged bodies, the field they create is stronger, and farther away it is weaker.
To verify this, let us again turn to the experiment with a charged cartridge case (see Fig. 13). Let's start bringing the stand with the cartridge case closer to the loaded stick. We will see that as the sleeve approaches the stick, the angle of deviation of the thread from the vertical will become larger and larger (Fig. 15). An increase in this angle indicates that the closer the sleeve is to the source of the electric field (an electrified rod), the greater the force this field acts on it. This means that near a charged body the field it creates is stronger than at a distance. 
It should be borne in mind that not only a charged stick acts on a charged sleeve with its electric field, but also the sleeve, in turn, acts on the stick with its electric field. It is in this mutual action on each other that the electrical interaction of charged bodies is manifested.
The electric field also manifests itself in experiments with dielectrics. When a dielectric is in an electric field, the positively charged parts of its molecules (atomic nuclei) are shifted in one direction under the influence of the field, and the negatively charged parts (electrons) are shifted in the other direction. This phenomenon is called dielectric polarization. It is polarization that explains the simplest experiments on the attraction of light pieces of paper by an electrified body. These pieces are generally neutral. However, in the electric field of an electrified body (for example, a glass rod), they become polarized. On the surface of the piece that is closer to the stick, a charge appears that is opposite in sign to the charge of the stick. Interaction with it leads to the attraction of pieces of paper to the electrified body.
The force with which an electric field acts on a charged body (or particle) is called electrical force:
F el - electric force.
Under the influence of this force, a particle caught in an electric field acquires acceleration a, which can be determined using Newton’s second law:
a = F el / m (6.1)
where m is the mass of a given particle.
Since the time of Faraday, it has been customary to use field lines to graphically represent the electric field.
These are lines indicating the direction of the force acting in this field on a positively charged particle placed in it. The field lines created by a positively charged body are shown in Figure 16, a. Figure 16, b shows the field lines created by a negatively charged body. 
A similar picture can be observed using a simple device called an electric plume. Having given it a charge, we will see how all its paper strips will disperse in different directions and will be located along the electric field lines (Fig. 17).
When a charged particle enters an electric field, its speed in this field can either increase or decrease. If the charge of a particle q>0, then when moving along the lines of force it will accelerate, and when moving in the opposite direction it will slow down. If the particle charge q< 0, то все будет наоборот ее скорость будет уменьшаться при движении в направлении силовых линий и увеличиваться при движении в противоположном направлении.
1. What is an electric field? 2. How does a field differ from matter? 3. List the main properties of the electric field. 4. What do electric field lines indicate? 5. How is the acceleration of a charged particle moving in an electric field found? 6. In what case does an electric field increase the speed of a particle and in what case does it decrease it? 7. Why are neutral pieces of paper attracted to an electrified body? 8. Explain why, after charging the electric sultan, its paper strips diverge in different directions.
Experimental task. Electricize the comb on your hair, then touch it to a small piece of cotton wool (fluff). What will happen to the cotton wool? Shake the fluff from the comb and, when it is in the air, make it float at the same height by placing an electrified comb from below at some distance. Why does the fluff stop falling? What will keep her in the air?
An electric field arises around a charge or charged body in space. In this field, any charge is affected by the electrostatic Coulomb force. A field is a form of matter that transmits force interactions between macroscopic bodies or particles that make up the substance. In an electrostatic field, the force interaction of charged bodies occurs. An electrostatic field is a stationary electric field and is a special case of an electric field created by stationary charges.
The electric field is characterized at each point in space by two characteristics: force - the vector of electrical intensity and energy - potential, which is a scalar quantity. The strength of a given point of the electric field is a vector physical quantity that is numerically equal and coincides in direction with the force acting from the field on a unit positive charge placed at the field point in question:
An electric field line is a line whose tangents at each point determine the directions of the intensity vectors of the corresponding points of the electric field. The number of field lines passing through a unit area normal to these lines is numerically equal to the magnitude of the electric field strength vector at the center of this area. The electrostatic field strength lines begin at a positive charge and go to infinity for the field created by this charge. For the field created by a negative charge, the lines of force come from infinity to the charge.
The electrostatic field potential at a given point is a scalar quantity that is numerically equal to the potential energy of a unit positive charge placed at a given field point:
The work that is done by the forces of the electrostatic field when moving a point electric charge is equal to the product of this charge and the potential difference between the starting and ending points of the path:
where and are the potentials of the initial and final points of the field when the charge moves.
The tension is related to the potential of the electrostatic field by the relation:
The potential gradient indicates the direction of the fastest change in potential when moving in a direction perpendicular to a surface of equal potential.
The field strength is numerically equal to the change in potential per unit length , measured in the direction perpendicular to the surface of equal potential, and directed in the direction of its decrease (minus sign):
The geometric location of electric field points whose potentials are the same is called an equipotential surface or a surface of equal potential. The intensity vector of each point of the electric field is normal to the equipotential surface drawn through this point. In Fig. 1 graphically shows the electric field formed by a positive point charge and a negatively charged plane R.
Solid lines are equipotential surfaces with potentials , , etc., dotted lines are field lines, their direction is shown by an arrow.
As you know, a characteristic feature of conductors is that they always contain a large number of mobile charge carriers, i.e. free electrons or ions.
Inside a conductor, these charge carriers, generally speaking, move chaotically. However, if there is an electric field in the conductor, then the chaotic movement of the carriers is superimposed by their ordered movement in the direction of the action of electric forces. This directed movement of mobile charge carriers in a conductor under the influence of a field always occurs in such a way that the field inside the conductor is weakened. Since the number of mobile charge carriers in a conductor is large (the metal contains about free electrons), their movement under the influence of the field occurs until the field inside the conductor disappears completely. Let's find out in more detail how this happens.
Let a metal conductor, consisting of two parts tightly pressed to each other, be placed in an external electric field E (Fig. 15.13). The free electrons in this conductor are acted upon by field forces directed to the left, i.e., opposite to the field strength vector. (Explain why.) As a result of the displacement of electrons under the influence of these forces, an excess of positive charges appears at the right end of the conductor, and an excess of electrons at the left end. Therefore, an internal field (field of displaced charges) arises between the ends of the conductor, which in Fig. 15.13 is shown with dotted lines. Inside
conductor, this field is directed towards the external one and each free electron remaining inside the conductor acts with a force directed to the right.
At first, the force is greater than the force and their resultant is directed to the left. Therefore, the electrons inside the conductor continue to shift to the left, and the internal field gradually increases. When quite a lot of free electrons accumulate at the left end of the conductor (they still constitute an insignificant fraction of their total number), the force will become equal to the force and their resultant will be equal to zero. After this, the free electrons remaining inside the conductor will move only chaotically. This means that the field strength inside the conductor is zero, i.e., that the field inside the conductor has disappeared.
So, when a conductor enters an electric field, it becomes electrified so that a positive charge appears at one end, and a negative charge of the same magnitude appears at the other. This electrification is called electrostatic induction or electrification by influence. Note that in this case only the conductor’s own charges are redistributed. Therefore, if such a conductor is removed from the field, its positive and negative charges will again be evenly distributed throughout the entire volume of the conductor and all its parts will become electrically neutral.
It is easy to verify that at the opposite ends of a conductor electrified by influence, there are indeed equal amounts of charges of opposite sign. Let's divide this conductor into two parts (Fig. 15.13) and then remove them from the field. By connecting each part of the conductor to a separate electroscope, we will make sure that they are charged. (Think about how you can show that these charges have opposite signs.) If we reconnect the two parts so that they form one conductor, we will find that the charges cancel out. This means that before the connection, the charges on both parts of the conductor were equal in magnitude and opposite in sign.
The time during which the conductor is electrified by the influence is so short that the balance of charges on the conductor occurs almost instantly. In this case, the tension, and therefore the potential difference inside the conductor, becomes zero everywhere. Then for any two points inside the conductor the relation is true
Consequently, when the charges on the conductor are in equilibrium, the potential of all its points is the same. This also applies to a conductor electrified by contact with a charged body. Let's take a conducting ball and place a charge at point M on its surface (Fig. 15.14). Then a field appears in the conductor for a short time, and an excess charge appears at point M. Under the influence of the forces of this field
the charge is evenly distributed over the entire surface of the ball, which leads to the disappearance of the field inside the conductor.
So, regardless of how the conductor is electrified, when the charges are in equilibrium, there is no field inside the conductor, and the potential of all points of the conductor is the same (both inside and on the surface of the conductor). At the same time, the field outside the electrified conductor, of course, exists, and its intensity lines are normal (perpendicular) to the surface of the conductor. This can be seen from the following reasoning. If the tension line were somewhere inclined to the surface of the conductor (Fig. 15.15), then the force acting on the charge at this point on the surface could be decomposed into components. Then, under the influence of a force directed along the surface, the charges would move along the surface of the conductor, which There should be no charge equilibrium. Consequently, when the charges on the conductor are in equilibrium, its surface is an equipotential surface.
If there is no field inside a charged conductor, then the volume density of charges in it (the amount of electricity per unit volume) must be zero everywhere.
Indeed, if there was a charge in any small volume of a conductor, then an electric field would exist around this volume.
In field theory it has been proven that at equilibrium, all the excess charge of an electrified conductor is located on its surface. This means that the entire interior of this conductor can be removed and nothing will change in the arrangement of charges on its surface. For example, if two solitary metal balls of equal size, one of which is solid and the other is hollow, are equally electrified, then the fields around the balls will be the same. M. Faraday was the first to prove this experimentally.
So, if a hollow conductor is placed in an electric field or electrified by contact with a charged body, then
When the charges are in equilibrium, the field inside the cavity will not exist. Electrostatic protection is based on this. If any device is placed in a metal case, then external electric fields will not penetrate inside the case, i.e., the operation and readings of such a device will not depend on the presence and changes of external electric fields.
Let us now find out how the charges are located on the outer surface of the conductor. Let's take a metal mesh on two insulating handles, to which paper leaves are glued (Fig. 15.16). If you charge the mesh and then stretch it (Fig. 15.16, a), the leaves on both sides of the mesh will separate. If you bend the mesh into a ring, then only the leaves on the outer side of the mesh are deflected (Fig. 15.16, b). By giving the mesh a different bend, you can make sure that the charges are located only on the convex side of the surface, and in those places where the surface is more curved (smaller radius of curvature), more charges accumulate.
So, the charge is distributed evenly only over the surface of a spherical conductor. With an arbitrary shape of the conductor, the surface charge density and, therefore, the field strength near the surface of the conductor is greater where the curvature of the surface is greater. The charge density is especially high on the protrusions and on the tips of the conductor (Fig. 15.17). This can be verified by touching various points of the electrified conductor with a probe and then touching the electroscope. An electrified conductor that has points or is equipped with a point quickly loses its charge. Therefore, the conductor on which the charge must be maintained for a long time should not have sharp points.
(Think about why the rod of an electroscope ends in a ball.)
The electric field is one of the theoretical concepts that explains the phenomena of interaction between charged bodies. The substance cannot be touched, but its existence can be proven, which was done in hundreds of natural experiments.
Interaction of charged bodies
We are accustomed to considering outdated theories a utopia, yet men of science are not at all stupid. Today, Franklin’s doctrine of electric fluid sounds funny; the prominent physicist Apinus devoted an entire treatise to it. Coulomb's law was discovered experimentally on the basis of torsion balances; Georg Ohm used similar methods to derive the well-known law. But what lies behind all this?
We must admit that the electric field is simply another theory, not inferior to the Franklin fluid. Today two facts are known about the substance:
The stated facts laid the basis for the modern understanding of interactions in nature and act as a support for the theory of short-range interaction. In addition to this, scientists have put forward other assumptions about the essence of the observed phenomenon. The theory of short-range action implies the instantaneous distribution of forces without the participation of the ether. Since phenomena are more difficult to sense than an electric field, many philosophers have dubbed such views idealistic. In our country, they were successfully criticized by the Soviet government, since, as is known, the Bolsheviks did not like God, and at every opportunity they pecked at the idea of the existence of something “depending on our ideas and actions” (at the same time studying Juna’s superpowers).
Franklin explained the positive and negative charges of bodies by excess and insufficiency of electrical fluid.
Electric field characteristics
The electric field is described by a vector quantity - intensity. An arrow whose direction coincides with the force acting at a point on a unit positive charge, the length of which is proportional to the magnitude of the force. Physicists find it convenient to use potential. The quantity is scalar; it is easier to imagine it using the example of temperature: at each point in space there is a certain value. Electric potential refers to the work done to move a unit charge from a point of zero potential to a given point.
A field described in the above manner is called irrotational. Sometimes called potential. The electric field potential function is continuous and varies smoothly over the extent of space. As a result, we select points of equal potential that fold the surfaces. For a unit charge, a sphere: further away the object, weaker the field (Coulomb’s law). Surfaces are called equipotential.
To understand Maxwell's equations, understand several characteristics of a vector field:
- The gradient of the electric potential is a vector whose direction coincides with the fastest growth of the field parameter. The faster the value changes, the greater the value. The gradient is directed from a smaller potential value to a larger one:
- The gradient is perpendicular to the equipotential surface.
- The greater the gradient, the closer the location of equipotential surfaces that differ from each other by a given value of the electric field potential.
- The potential gradient, taken with the opposite sign, is the electric field strength.
Electric potential. Gradient "climbing uphill"
- Divergence is a scalar quantity calculated for the electric field strength vector. It is analogous to a gradient (for vectors), shows the rate of change of a value. The need to introduce an additional characteristic: the vector field has no gradient. Therefore, the description requires a certain analogue - divergence. The parameter in mathematical notation is similar to the gradient, denoted by the Greek letter nabla, and is used for vector quantities.
- The rotor of the vector field is called a vortex. Physically, the value is zero when the parameter changes uniformly. If the rotor is nonzero, closed line bends occur. By definition, potential fields of point charges do not have a vortex. The lines of tension in this case are not necessarily straight. They simply change smoothly without forming vortices. A field with a non-zero rotor is often called solenoidal. The synonym is often used - vortex.
- The total flux of the vector is represented by the surface integral of the product of the electric field strength and the elementary area. The limit of magnitude when the body's capacitance tends to zero represents the divergence of the field. The concept of limit is studied in senior high school, the student can get some idea of the subject of discussion.
Maxwell's equations describe a time-varying electric field and show that in such cases a wave arises. It is generally accepted that one of the formulas indicates the absence of isolated magnetic charges (poles) in nature. Sometimes in the literature we come across a special operator - the Laplacian. Denoted as the square of the nabla, calculated for vector quantities, represented by the divergence of the field gradient.
Using these quantities, mathematicians and physicists calculate electric and magnetic fields. For example, it has been proven: only an irrotational field (point charges) can have a scalar potential. Other axioms have been invented. The vortex field of the rotor is devoid of divergence.
We can easily use such axioms as the basis for describing the processes occurring in real existing devices. Anti-gravity, perpetual motion would be a good help to the economy. If no one has succeeded in putting Einstein’s theory into practice, Nikola Tesla’s achievements are being studied by enthusiasts. There is no rotor or divergence.
A Brief History of the Development of the Electric Field
The formulation of the theory was followed by numerous works on the application of electric and electromagnetic fields in practice, the most famous of which in Russia is considered to be Popov’s experience in transmitting information through the air. A number of questions arose. Maxwell's harmonious theory is powerless to explain the phenomena observed during the passage of electromagnetic waves through ionized media. Planck hypothesized that radiant energy is emitted in measured portions, later called quanta. The diffraction of individual electrons, kindly demonstrated in English on YouTube, was discovered in 1949 by Soviet physicists. The particle simultaneously exhibited wave properties.
This tells us: the modern idea of a constant and variable electric field is far from perfect. Many people know Einstein, but are powerless to explain what the physicist discovered. The 1915 theory of relativity links electric, magnetic fields and gravity. True, no formulas were presented in the form of a law. Today it is known: there are particles that move faster than the propagation of light. Another stone in the garden.
Unit systems were constantly changing. The initially introduced GHS, based on the work of Gauss, is not convenient. The first letters indicate the basic units: centimeter, gram, second. Electromagnetic quantities were added to the GHS in 1874 by Maxwell and Thomson. The USSR began to use the ISS (meter, kilogram, second) in 1948. The introduction of the SI system (GOST 9867) in the 60s of the 20th century, where the electric field strength is measured in V/m, put an end to the battles.
Using an electric field
Electric charge accumulates in capacitors. Consequently, a field is formed between the plates. Since the capacitance directly depends on the magnitude of the voltage vector, in order to increase the parameter, the space is filled with a dielectric.
Indirectly, electric fields are used by picture tubes and Chizhevsky chandeliers; the grid potential controls the movement of electron tube beams. Despite the lack of a coherent theory, electric field effects underlie many images.