How to prove that the electric field is material. Electric field. The electromagnetic field around us

An electric field exists around each charge based on the theory of short-range action. An electric field is a material object, constantly exists in space and is able to act on other charges. An electric field propagates in space at the speed of light. A physical quantity equal to the ratio of the force with which an electric field acts on a test charge (a positive small point charge that does not affect the field configuration) to the value of this charge is called the electric field strength. Using Coulomb's law it is possible to obtain a formula for the field strength created by a charge q  on distance r  from charge   . The field strength does not depend on the charge on which it acts. Lines of tension begin on positive charges and end on negative ones, or go to infinity. An electric field, the intensity of which is the same for all at any point in space, is called a homogeneous electric field. The field between two parallel oppositely charged metal plates can be considered approximately homogeneous. With uniform charge distribution q  on the surface of the square S  surface charge density is equal to. For an infinite plane with a surface charge density s, the field strength is the same at all points in space and equal   .Potential difference.

When a charge moves an electric field a distance, the perfect work is   . As in the case of the work of gravity, the work of the Coulomb force does not depend on the trajectory of the charge. When the direction of the displacement vector changes by 180 0, the work of the field forces changes its sign to the opposite. Thus, the work of the forces of the electrostatic field when the charge moves along a closed loop is zero. A field whose work of forces along a closed path is equal to zero is called a potential field.

Just like a body mass m  in a gravitational field has potential energy proportional to body mass, an electric charge in an electrostatic field has potential energy W pproportional to the charge. The work of the forces of the electrostatic field is equal to the change in the potential energy of the charge, taken with the opposite sign. At one point of the electrostatic field, different charges can have different potential energy. But the ratio of potential energy to charge for a given point is a constant value. This physical quantity is called the electric field potential, whence the potential energy of the charge is equal to the product of the potential at a given point by the charge. Potential is a scalar quantity, the potential of several fields is equal to the sum of the potentials of these fields. A measure of energy change in the interaction of bodies is work. When the charge moves, the work of the forces of the electrostatic field is equal to the change in energy with the opposite sign, therefore. Because Since the work depends on the potential difference and does not depend on the trajectory between them, the potential difference can be considered the energy characteristic of the electrostatic field. If the potential at an infinite distance from the charge is taken equal to zero, then at a distance r  from charge it is determined by the formula

We always receive signals about distant events using an intermediate medium .. For example, telephone communication is carried out using electric wires, voice transmission over a distance is carried out using sound waves propagating in the air

(sound cannot propagate in airless space). Since the appearance of a signal is always a material phenomenon, its propagation associated with the transfer of energy from point to point in space can occur only in the material environment.

The most important sign that an intermediate medium is involved in signal transmission is the final speed of the signal from the source to the observer, which depends on the properties of the medium. For example, sound in the air travels at a speed of about 330 m / s.

If there existed phenomena in nature in which the speed of signal propagation was infinitely large, i.e., the signal would be instantly transmitted from one body to another at any distance between them, this would mean that bodies can act on each other at a distance and in the absence of matter between them. Such an effect of bodies on one another in physics is called long-range action. When the bodies act on each other with the help of matter located between them, their interaction is called short-range interaction. Consequently, with short-range action, the body directly affects the material environment, and this medium already acts on another body.

It takes some time to transfer the influence of one body to another through an intermediate medium, since any processes in the material medium are transferred from point to point with a finite and well-defined speed. The mathematical justification of the theory of short range was given by the outstanding English scientist D. Maxwell (1831-1879). Since signals propagating instantly do not exist in nature, in the future we will adhere to the theory of short range.

In some cases, the propagation of signals occurs using a substance, for example, the propagation of sound in air. In other cases, the substance does not directly participate in signal transmission, for example, light from the Sun reaches the Earth through airless space. Consequently, matter exists not only in the form of matter.

In those cases when the influence of bodies on each other can occur through airless space, the material medium transmitting this effect is called a field. Thus, matter exists in the form of matter and in the form of? fields. Depending on the kind of forces acting between the bodies, the fields can be of various kinds. The field transmitting the effect of one body on another in accordance with the law of universal gravitation is called the gravitational field. A field transmitting the effect of one motionless electric charge on another motionless charge in accordance with Coulomb's law is called an electrostatic or electric field.

Experience has shown that electrical signals propagate in airless space at a very large but finite speed, which is approximately 300,000 km / s (§ 27.7). it

proves that the electric field is the same physical reality as the substance. Studying the properties of the field made it possible to transfer energy to a distance using the field and use it for the needs of mankind. An example is the effect of radio communications, television, lasers, etc. However, many field properties are poorly studied or not yet known. The study of the physical properties of the field and the interaction between the field and matter is one of the most important scientific problems of modern physics.

Any electric charge creates an electric field in space, with the help of which it interacts with other charges. The electric field acts only on electric charges. Therefore, there is only one way to detect such a field: to introduce a test charge into the point of space that interests us. If there is a field at this point, then an electric force will act.

When the field is examined with a test charge, it is believed that it does not distort the field under study by its presence. This means that the value of the test charge must be very small in comparison with the charges that create the field. As a test charge agreed to use a positive charge.

It follows from Coulomb's law that the absolute value of the interaction force of electric charges decreases with increasing distance between them, but never disappears at all. This means that theoretically the field of electric charge extends to infinity. However, in practice, we believe that the field is present only where a noticeable force acts on the test charge.

We also note that when the charge moves, its field also moves with it. When the charge is removed so much that the electric force practically does not affect the test charge at any point in space, we say that the field has disappeared, although in reality it has moved to other points in space.

  Details Category: Electricity and magnetism Posted on 06/05/2015 20:46 Views: 13114

Under certain conditions, alternating electric and magnetic fields can give rise to each other. They form an electromagnetic field, which is not at all their totality. This is a whole in which these two fields cannot exist without each other.

From the history

The experience of Danish scientist Hans Christian Oersted, conducted in 1821, showed that electric current generates a magnetic field. In turn, a changing magnetic field is capable of generating an electric current. This was proved by the English physicist Michael Faraday, who discovered in 1831 the phenomenon of electromagnetic induction. He is the author of the term "electromagnetic field".

In those days, the concept of Newton's long-range action was adopted in physics. It was believed that all bodies act on each other through the void with infinitely high speed (almost instantly) and at any distance. It was assumed that electric charges interact in a similar way. Faraday believed that emptiness does not exist in nature, and interaction occurs at a finite speed through a certain material environment. This medium for electric charges is electromagnetic field. And it spreads at a speed equal to the speed of light.

Maxwell theory

Combining the results of previous studies, english physicist James Clerk Maxwell  in 1864 created electromagnetic field theory. According to it, a changing magnetic field generates a changing electric field, and an alternating electric field generates an alternating magnetic field. Of course, at first one of the fields is created by a source of charges or currents. But in the future, these fields may already exist independently of such sources, causing each other to appear. I.e, electric and magnetic fields are components of a single electromagnetic field. And any change in one of them causes the appearance of another. This hypothesis forms the basis of Maxwell's theory. The electric field generated by the magnetic field is a vortex. His lines of force are closed.

This theory is phenomenological. This means that it was created on the basis of assumptions and observations, and does not consider the cause of the occurrence of electric and magnetic fields.

Electromagnetic field properties

An electromagnetic field is a combination of electric and magnetic fields; therefore, at each point of its space it is described by two main quantities: electric field strength E and magnetic field induction AT .

Since the electromagnetic field is the process of converting an electric field into a magnetic field, and then a magnetic field into an electric field, its state is constantly changing. Spreading in space and time, it forms electromagnetic waves. Depending on the frequency and length, these waves are divided into radio waves, terahertz radiation, infrared radiation, visible light, ultraviolet radiation, x-ray and gamma radiation.

The vectors of the intensity and induction of the electromagnetic field are mutually perpendicular, and the plane in which they lie is perpendicular to the direction of wave propagation.

In long-range theory, the propagation velocity of electromagnetic waves was considered infinite large. However, Maxwell proved that this is not so. In matter, electromagnetic waves propagate at a finite speed, which depends on the dielectric and magnetic permeability of the substance. Therefore, Maxwell's theory is called the theory of short-range.

Experimentally, Maxwell's theory was confirmed in 1888 by the German physicist Heinrich Rudolph Hertz. He proved that electromagnetic waves exist. Moreover, he measured the speed of propagation of electromagnetic waves in a vacuum, which turned out to be equal to the speed of light.

In integral form, this law looks like this:

Gauss law for magnetic field

Magnetic flux through a closed surface is zero.

The physical meaning of this law is that in nature there are no magnetic charges. The poles of a magnet cannot be separated. The lines of force of the magnetic field are closed.

Faraday's law of induction

A change in magnetic induction causes the appearance of a vortex electric field.

,

Magnetic Field Circulation Theorem

This theorem describes the sources of the magnetic field, as well as the fields themselves created by them.

Electric current and change in electric induction generate a vortex magnetic field.

,

,

E  - electric field strength;

N  - magnetic field strength;

AT   - magnetic induction. This is a vector quantity showing the force with which a magnetic field acts on a charge of q moving at a speed v;

D   - electrical induction, or electrical displacement. It is a vector quantity equal to the sum of the intensity vector and the polarization vector. Polarization is caused by the displacement of electric charges under the action of an external electric field relative to their position when such a field is absent.

Δ    - operator Nabla. The action of this operator on a specific field is called the rotor of this field.

Δ x E \u003d rot E

ρ    - the density of the external electric charge;

j   - current density - a value showing the strength of the current flowing through a unit area;

with   - the speed of light in vacuum.

The study of the electromagnetic field is a science called electrodynamics. She considers its interaction with bodies having an electric charge. This interaction is called electromagnetic. Classical electrodynamics describes only the continuous properties of the electromagnetic field using Maxwell's equations. Modern quantum electrodynamics believes that the electromagnetic field also has discrete (discontinuous) properties. And such an electromagnetic interaction occurs with the help of indivisible quantum particles that have no mass and charge. The quantum of the electromagnetic field is called photon .

The electromagnetic field around us

An electromagnetic field forms around any alternating current conductor. Sources of electromagnetic fields are power lines, electric motors, transformers, urban electric vehicles, railway transport, electric and electronic appliances - televisions, computers, refrigerators, irons, vacuum cleaners, cordless phones, mobile phones, electric shavers - in short, everything related to consumption or electric power transmission. Powerful sources of electromagnetic fields - television transmitters, antennas of cellular telephone communication stations, radar stations, microwave ovens, etc. And since there are a lot of such devices around us, electromagnetic fields surround us everywhere. These fields affect the environment and humans. This is not to say that this influence is always negative. Electric and magnetic fields existed around a person for a long time, but the power of their radiation a few decades ago was hundreds of times lower than the current one.

To a certain level, electromagnetic radiation can be safe for humans. So, in medicine, with the help of low-intensity electromagnetic radiation heal tissues, eliminate inflammatory processes, and have an analgesic effect. UHF devices relieve spasms of smooth muscles of the intestines and stomach, improve metabolic processes in the cells of the body, lowering the tone of capillaries, and lowering blood pressure.

But strong electromagnetic fields cause malfunctions of the cardiovascular, immune, endocrine and nervous systems of a person, can cause insomnia, headaches, stress. The danger is that their effect is almost invisible to humans, and violations occur gradually.

How to protect yourself from electromagnetic radiation surrounding us? It is completely impossible to do this, so you need to try to minimize its impact. First of all, you need to arrange household appliances so that they are away from those places where we are most often. For example, you don’t need to sit too close to the TV. After all, the farther the distance from the source of the electromagnetic field, the weaker it becomes. Very often we leave the appliance plugged in. But the electromagnetic field disappears only when the device is disconnected from the electrical network.

Natural human electromagnetic fields — cosmic radiation, Earth’s magnetic field — also affect human health.

The electric field, according to elementary physical concepts, is nothing more than a special kind of material medium that arises around charged bodies and affects the organization of interaction between such bodies with a certain finite speed and in a strictly limited space.

It has long been proven that an electric field can occur both in motionless and in motion bodies. The main sign of this is its effect on

One of the main quantitative is the concept of "field strength". In numerical terms, this term means the ratio of the force that acts on the test charge directly to the quantitative expression of this charge.

The fact that the charge is test means that it itself does not take any part in creating this field, and its value is so small that it does not lead to any distortion of the initial data. The field strength is measured in V / m, which is conditionally equal to N / C.

The famous English researcher M. Faraday introduced the scientific method of graphic representation of the electric field. In his opinion, this particular type of matter in the drawing should be depicted as continuous lines. They subsequently became known as the “lines of electric field strength,” and their direction, based on basic physical laws, coincides with the direction of tension.

Lines of force are needed to show quality characteristics of tension such as density or density. The density of the tension lines depends on their number per unit surface. The created picture of the lines of force allows us to determine the quantitative expression of the field strength in its individual sections, as well as to find out how it changes.

Quite curious properties are possessed by the electric field of dielectrics. As you know, dielectrics are substances in which there are practically no free charged particles, therefore, as a result, they are not able to conduct. These substances include primarily all gases, ceramics, porcelain, distilled water, mica, etc.

In order to determine the field strength in a dielectric, an electric field should be passed through it. Under its action, the bound charges in the dielectric begin to shift, but they are not able to leave the boundaries of their molecules. The bias direction implies that positively charged ones move along the direction of the electric field, and negatively charged ones - against. As a result of these manipulations, a new electric field arises inside the dielectric, the direction of which is directly opposite to the external. This internal field noticeably weakens the external, therefore, the intensity of the latter decreases.

Field strength is its most important quantitative characteristic, which is directly proportional to the force with which this special type of matter acts on an external electric charge. Despite the fact that it is impossible to see this value, with the help of the drawing of the force lines of tension, one can get an idea of \u200b\u200bits density and directivity in space.

According to Coulomb's law, the force of interaction between two motionless charged point bodies is proportional to the product of their charges and inversely proportional to the square of the distance between them.

The electric force of interaction between charged bodies depends on the magnitude of their charges, the size of the bodies, the distance between them, and also on what parts of the bodies these charges are located. If the size of the charged bodies is much less than the distance between them, then such bodies are called point. The strength of the interaction between point charged bodies depends only on the magnitude of their charges and the distance between them.

The law describing the interaction of two point charged bodies was established by the French physicist S. Coulomb when he measured the repulsive force between small like-charged metal balls (see Fig. 34a). The Coulomb installation consisted of a thin elastic silver thread (1) and a light glass rod (2) suspended on it, at one end of which a charged metal ball (3) was fixed, and on the other a counterweight (4). The repulsive force between the stationary ball (5) and ball 3 led to the twisting of the thread at a certain angle, a, from which it was possible to determine the magnitude of this force. By bringing together equally charged balls 3 and 5, Coulomb found that the repulsive force between them is inversely proportional to the square of the distance between them.

To establish how the force of interaction between the balls depends on the magnitude of their charges, Coulomb acted as follows. First, he measured the force acting between equally charged balls 3 and 5, and then touched one of the charged balls (3) with another, uncharged ball of the same size (6). Coulomb rightly believed that when identical metal balls touched, the electric charge would be evenly distributed between them, and therefore only half of its initial charge would remain on ball 3. In this case, as experiments showed, the repulsive force between balls 3 and 5 was halved, compared with the original. By changing the charges of the balls in a similar way, Coulomb found that they interact with a force proportional to the product of their charges.

As a result of numerous experiments, Coulomb formulated a law defining the modulus of force F 12 acting between two stationary point bodies with charges q 1 and q 2 located at a distance r from each other:

where k is the proportionality coefficient, the value of which depends on the system of units used, and which is often replaced by (4pe0) -1 for reasons related to the history of the introduction of system of units (see 34.1). e0 is called the electric constant. The force vector F 12 is directed along the straight line connecting the bodies, so that oppositely charged bodies are attracted, and the same charged bodies repel each other (Fig. 34b). This law (see 34.1) is called the Coulomb law, and the corresponding electric forces are called Coulomb forces. Coulomb's law, namely the dependence of the interaction force on the second degree of the distance between charged bodies, is still undergoing experimental verification. It has now been shown that the exponent in the Coulomb law can differ from a deuce by no more than 6.10-16.

In the SI system, the unit of electric charge is the pendant (C). A charge of 1 C is equal to the charge passing through the cross section of the conductor for 1 s at a current strength of 1 ampere (A). In the SI system

k \u003d 9.109 N.m 2 / Cl 2, and e0 \u003d 8.8.10-12 Cl 2 /(N.m 2) (34.2)

The elemental electric charge, e, in SI is:

e \u003d 1.6.10 -19 Cl. (34.3)

In its appearance, the Coulomb law is very similar to the law of universal gravitation (11.1), if the mass is replaced by charges in the latter. However, despite the external similarity, gravitational forces and Coulomb forces differ from each other in that

1. gravitational forces always attract bodies, and Coulomb forces can both attract and repel bodies,

2. Coulomb forces are much stronger than gravitational ones, for example, the Coulomb force repelling two electrons from each other is 1042 times greater than the force of their gravitational attraction.

Questions to repeat:

What is a point charged body?

· Describe the experiences with which Coulomb established the law named after him?

Fig. 34. (a) - diagram of the experimental setup of Coulomb to determine the repulsive forces between the same charges; (b) - to determine the magnitude and direction of action of the Coulomb forces when using the formula (34.1).

§ 35. ELECTRIC FIELD. TENSION. PRINCIPLE OF SUPERPOSITION OF FIELDS.

Coulomb's law allows you to calculate the strength of the interaction between two charges, but does not explain how one charge acts on the other. After what time, for example, does one of the charges “feel” that the other charge has begun to approach or move away from it? Are the charges connected with each other? To answer these questions, the great English physicists M. Faraday and J. Maxwell introduced the concept of an electric field - a material object that exists around electric charges. Thus, charge q1 generates an electric field around itself, and another charge q2, once in this field, experiences the action of charge q1 according to Coulomb's law (34.1). Moreover, if the position of the charge q1 has changed, then the change in its electric field will occur gradually, and not instantly, so that at a distance L from q1 the field changes occur after a time interval L / c, where c is the speed of light, 3.108 m / s . The delay in changes in the electric field proves that the interaction between the charges is consistent with the theory of short range. This theory explains any interaction between bodies, even distant from each other, by the existence of any material objects or processes between them. The material object that interacts between charged bodies is their electric field.

To characterize this electric field, it is enough to measure the force acting on a point charge in various regions of this field. The experiments and Coulomb's law (34.1) show that the force acting on a charge from the field is proportional to the magnitude of this charge. Therefore, the ratio of the force F acting on the charge at a given point of the field to the value of this charge q no longer depends on q and is a characteristic of the electric field, called its intensity, E:

The electric field strength, as follows from (35.1), is a vector whose direction coincides with the direction of the force acting at a given point in the field on a positive charge. It follows from Coulomb's law (34.1) that the modulus of the intensity E of the field of a point charge q depends on the distance r to it as follows:

The intensity vectors at various points of the electric field of the positive and negative charges are shown in Fig. 35a.

If the electric field is formed by several charges (q 1, q 2, q 3, etc.), then, as experience shows, the intensity E at any point in this field is equal to the sum of the intensities E 1, E 2, E 3, etc. . electric fields created by charges q 1, q 2, q 3, etc., respectively:

This is the principle of superposition (or superposition) of fields, which allows one to determine the field strength created by several charges (Fig. 35b).

To show how the field strength varies in its various areas, draw lines of force — continuous lines whose tangents at each point coincide with the intensity vectors (Fig. 35c). The lines of force cannot intersect each other, because at each point, the field strength vector has a definite direction. They begin and end on charged bodies, near which the modulus of tension and density of field lines increases. The density of the lines of force is proportional to the modulus of the electric field.

Questions to repeat:

· What is an electric field and how is it related to short-range theory?

· Give a definition of electric field strength.

· State the principle of field superposition.

· What do field lines of force correspond to and what are their properties?

Fig. 35. (a) - intensity vectors at various points of the electric field of a positive (top) and negative (bottom) charge; intensity vectors (b) and the same vectors together with field lines (c) of the electric field of two point charges of different signs.

§ 36. CONDUCTORS AND DIELECTRICS IN AN ELECTROSTATIC FIELD.