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 which parts of the bodies these charges are located. If the dimensions of charged bodies are much smaller than the distance between them, then such bodies are called point bodies. The force of 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 Ch. Coulomb when he measured the repulsive force between small like-charged metal balls (see Fig. 34a). The installation of the Pendant 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 at the other a counterweight (4). The repulsive force between the stationary ball (5) and ball 3 led to the twisting of the thread through a certain angle, a, from which it was possible to determine the magnitude of this force. Bringing together and moving away 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 proceeded 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 come into contact, the electric charge will be equally distributed between them, and therefore only half of its initial charge will remain on ball 3. In this case, as experiments have shown, the repulsive force between balls 3 and 5 decreased by half, compared with the original. Changing the charges of the balls in this 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 that determines the modulus of the force F 12 acting between two fixed point bodies with charges q 1 and q 2 located at a distance r from each other:
where k is a proportionality factor, the value of which depends on the system of units used, and which is often, for reasons related to the history of the introduction of systems of units, replaced by (4pe0)-1 (see 34.1). e0 is called the electrical constant. The force vector F 12 is directed along the straight line connecting the bodies, so that oppositely charged bodies attract, and similarly charged bodies repel (Fig. 34b). This law (see 34.1) is called Coulomb's law, and the corresponding electric forces are called Coulomb. Coulomb's law, namely the dependence of the interaction force on the second power of the distance between charged bodies, is still subject to experimental verification. It has now been shown that the exponent in Coulomb's law can differ from two 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 in 1 s through the cross section of the conductor at a current strength of 1 ampere (A). In the SI system
k \u003d 9.109 N.m 2 / C 2, and e0 \u003d 8.8.10-12 C 2 / (N.m 2) (34.2)
The elementary electric charge, e, in SI is:
e \u003d 1.6.10 -19 C. (34.3)
In its form, Coulomb's law is very similar to the law of universal gravitation (11.1), if we replace masses with charges in the latter. However, despite the external similarity, the gravitational forces and the 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 that repels two electrons from each other is 1042 times greater than the force of their gravitational attraction.
Review questions:
What is a point charged body?
· Describe the experiments by which Coulomb established the law named after him?
Rice. 34. (a) - scheme of Coulomb's experimental setup for determining the repulsive forces between charges of the same name; (b) - to the determination of the magnitude and direction of the Coulomb forces when using formula (34.1).
§ 35. ELECTRIC FIELD. TENSION. THE PRINCIPLE OF SUPERPOSITION OF FIELDS.
Coulomb's law allows you to calculate the force of interaction between two charges, but does not explain how one charge acts on another. After what time, for example, will one of the charges “feel” that the other charge has begun to approach or move away from it? Are the charges connected in any way? 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, the charge q1 generates an electric field around itself, and another charge q2, being in this field, experiences the action of the 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 will 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 charges is consistent with the short-range theory. 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 a given electric field, it is sufficient to measure the force acting on a point charge in different regions of this field. Experiments and Coulomb's law (34.1) show that the force acting on the 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 magnitude of this charge q no longer depends on q and is a characteristic of the electric field, called its strength, 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 of the field on a positive charge. It follows from Coulomb's law (34.1) that the modulus of strength 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 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 strength E at any point of this field is equal to the sum of the strengths 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 you to determine the strength of the field created by several charges (Fig. 35b).
To show how the field strength changes in its various areas, lines of force are drawn - continuous lines, the tangents to which at each point coincide with the strength vectors (Fig. 35c). Field lines cannot intersect with each other, because. at each point, the field strength vector has a well-defined direction. They begin and end on charged bodies, near which the tension modulus and the density of field lines increase. The density of field lines is proportional to the modulus of the electric field strength.
Review questions:
· What is an electric field and how is it related to the theory of short-range action?
· Give the definition of electric field strength.
· Formulate the principle of superposition of fields.
What do the field lines correspond to, and what are their properties?
Rice. 35. (a) - intensity vectors at various points of the electric field of positive (top) and negative (bottom) charge; intensity vectors (b) and the same vectors together with lines of force (c) of the electric field of two point charges of different signs.
§ 36. CONDUCTORS AND DIELECTRIC IN AN ELECTROSTATIC FIELD.
The electric field, according to elementary physical concepts, is nothing but a special type of material medium that arises around charged bodies and affects the organization of interaction between such bodies at a certain finite speed and in a strictly limited space.
It has long been proven that an electric field can arise both in motionless and in motion bodies. The main indication of the presence 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 trial charge, directly to the quantitative expression of this charge.
The fact that the charge is trial means that it does not take any part in the creation of this field, and its value is so small that it does not lead to any distortion of the original data. The field strength is measured in V / m, which is conditionally equal to N / C.
The famous English researcher M. Faraday introduced the method of graphic representation of the electric field into scientific circulation. In his opinion, this special kind of matter in the drawing should be depicted in the form of continuous lines. They subsequently began to be called "lines of electric field intensity", and their direction, based on the basic physical laws, coincides with the direction of tension.
Field lines are necessary to show such qualitative characteristics of tension as density or density. In this case, the density of tension lines depends on their number per unit area. The created picture of field lines allows you to determine the quantitative expression of the field strength in its individual sections, as well as find out how it changes.
The electric field of dielectrics has rather curious properties. 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. First of all, all gases, ceramics, porcelain, distilled water, mica, etc. should be attributed to such substances.
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 limits of their molecules. The directionality of the displacement implies that positively charged ones are displaced along the direction of the electric field, and negatively charged ones are displaced 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 one. This internal field noticeably weakens the external one, therefore, the intensity of the latter decreases.
The 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, using the drawing of force lines of tension, one can get an idea of \u200b\u200bits density and direction in space.
Details Category: Electricity and magnetism Posted on 06/05/2015 20:46 Views: 13114Variable electric and magnetic fields under certain conditions can give rise to each other. They form an electromagnetic field, which is not their totality at all. This is a single whole in which these two fields cannot exist without each other.
From the history
The experiment of the Danish scientist Hans Christian Oersted, carried out in 1821, showed that an 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 the phenomenon of electromagnetic induction in 1831. He is also the author of the term "electromagnetic field".
In those days, Newton's concept of long-range action was accepted in physics. It was believed that all bodies act on each other through the void at an infinitely high speed (almost instantly) and at any distance. It was assumed that electric charges interact in a similar way. Faraday, on the other hand, believed that emptiness does not exist in nature, and the interaction occurs at a finite speed through a certain material medium. This medium for electric charges is electromagnetic field. And it propagates at a speed equal to the speed of light.
Maxwell's 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 can already exist independently of such sources, causing the appearance of each other. I.e, electric and magnetic fields are components of a single electromagnetic field. And every 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 vortex. His lines of force are closed.
This theory is phenomenological. This means that it is based on assumptions and observations, and does not consider the cause that causes the occurrence of electric and magnetic fields.
Properties of the electromagnetic field
The electromagnetic field is a combination of electric and magnetic fields, therefore, at each point in its space, it is described by two main quantities: the strength of the electric field E and magnetic field induction AT .
Since the electromagnetic field is a process of transforming an electric field into a magnetic field, and then a magnetic field into an electric one, 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-rays and gamma radiation.
The intensity and induction vectors of the electromagnetic field are mutually perpendicular, and the plane in which they lie is perpendicular to the direction of wave propagation.
In the theory of long-range action, the propagation velocity of electromagnetic waves was considered to be infinitely large. However, Maxwell proved that this was not the case. In a substance, 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 short-range theory.
Maxwell's theory was experimentally confirmed in 1888 by the German physicist Heinrich Rudolf Hertz. He proved that electromagnetic waves exist. Moreover, he measured the speed of propagation of electromagnetic waves in vacuum, which turned out to be equal to the speed of light.
In integral form, this law looks like this:
Gauss' law for a magnetic field
The flux of magnetic induction through a closed surface is zero.
The physical meaning of this law is that there are no magnetic charges in nature. 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.
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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.
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E is the electric field strength;
H is the magnetic field strength;
AT- magnetic induction. This is a vector quantity showing how strong the 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 is the Nabla operator. The action of this operator on a specific field is called the rotor of this field.
Δ x E = rot E
ρ - density of external electric charge;
j- current density - a value showing the strength of the current flowing through a unit area;
with is the speed of light in vacuum.
The science that studies the electromagnetic field is called electrodynamics. She considers its interaction with bodies that have an electric charge. Such an interaction is called electromagnetic. Classical electrodynamics describes only the continuous properties of an electromagnetic field using Maxwell's equations. Modern quantum electrodynamics considers that the electromagnetic field also has discrete (discontinuous) properties. And such an electromagnetic interaction occurs with the help of indivisible particles-quanta that do not have mass and charge. The quantum of the electromagnetic field is called photon .
The electromagnetic field around us
An electromagnetic field is formed around any conductor with alternating current. The sources of electromagnetic fields are power lines, electric motors, transformers, urban electric transport, railway transport, electrical and electronic household appliances - televisions, computers, refrigerators, irons, vacuum cleaners, cordless telephones, mobile phones, electric shavers - in a word, everything related to consumption or transmission of electricity. Powerful sources of electromagnetic fields are television transmitters, antennas of cellular telephone stations, radar stations, microwave ovens, etc. And since there are quite a lot of such devices around us, electromagnetic fields surround us everywhere. These fields affect the environment and humans. It cannot be said that this influence is always negative. Electric and magnetic fields have existed around a person for a long time, but the power of their radiation a few decades ago was hundreds of times lower than today.
To a certain level, electromagnetic radiation can be safe for humans. So, in medicine, with the help of low-intensity electromagnetic radiation, tissues heal, eliminate inflammatory processes, and have an analgesic effect. UHF devices relieve spasms of the smooth muscles of the intestines and stomach, improve metabolic processes in the cells of the body, reducing the tone of capillaries, and lower blood pressure.
But strong electromagnetic fields cause malfunctions in the work of the cardiovascular, immune, endocrine and nervous systems of a person, can cause insomnia, headaches, and stress. The danger is that their impact is almost imperceptible to humans, and violations occur gradually.
How can we protect ourselves from the electromagnetic radiation around us? It is impossible to do this completely, so you need to try to minimize its impact. First of all, you need to arrange household appliances in such a way that they are away from those places where we are most often. For example, do not 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 device plugged in. But the electromagnetic field disappears only when the device is disconnected from the mains.
Human health is also affected by natural electromagnetic fields - cosmic radiation, the Earth's magnetic field.
We always receive signals about distant events using an intermediate medium. For example, telephone communication is carried out using electric wires, speech is transmitted over a distance using sound waves propagating in the air.
(Sound cannot travel 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 a material environment.
The most important sign that an intermediate medium is involved in signal transmission is the finite speed of signal propagation from the source to the observer, which depends on the properties of the medium. For example, sound travels in air at a speed of about 330 m/s.
If there were phenomena in nature in which the speed of propagation of signals was infinitely large, i.e., the signal would be instantly transmitted from one body to another at any distance between them, then this would mean that the bodies can act on each other at a distance and in the absence of matter between them. Such an action of bodies on each other in physics is called long-range action. When bodies act on each other with the help of matter located between them, their interaction is called short-range action. Consequently, with short-range action, the body directly affects the material environment, and this environment already affects another body.
To transfer the influence of one body to another through an intermediate medium, some time is required, since any processes in the material medium are transmitted from point to point with a finite and well-defined speed. The mathematical substantiation of the theory of short-range action was given by the outstanding English scientist D. Maxwell (1831-1879). Since instantaneously propagating signals do not exist in nature, in the future we will adhere to the short-range theory.
In some cases, the propagation of signals occurs with the help of a substance, for example, the propagation of sound in air. In other cases, the substance does not directly participate in the transmission of signals, for example, light from the Sun reaches the Earth through airless space. Therefore, matter exists not only in the form of matter.
In cases where the impact of bodies on each other can occur through an airless space, the material medium that transmits this impact is called a field. Thus, matter exists in the form of matter and in the form? fields. Depending on the kind of forces acting between the bodies, the fields can be of various types. The field that transmits the influence of one body to another in accordance with the law of universal gravitation is called the gravitational field. The field that transmits the effect of one fixed electric charge on another fixed 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 high but finite speed, which is approximately 300,000 km/s (§ 27.7). This is
proves that the electric field is the same physical reality as the substance. The study of the properties of the field made it possible to transfer energy over a distance using the field and use it for the needs of mankind. An example is the action of radio communication, television, lasers, etc. However, many properties of the field are poorly understood 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 trial charge into the point of space that interests us. If there is a field at this point, then an electric force will act on it.
When the field is examined with a test charge, it is believed that its presence does not distort the field under study. This means that the value of the test charge must be very small compared to the charges that create the field. We agreed to use a positive charge as a test charge.
It follows from Coulomb's law that the absolute value of the force of interaction between electric charges decreases with increasing distance between them, but never completely disappears. This means that, theoretically, the electric charge field extends to infinity. However, in practice, we believe that the field exists only where an appreciable 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 on the test charge at any point in space no longer practically acts, we say that the field has disappeared, although in reality it has moved to other points in space.
The action of some charged bodies on other charged bodies is carried out without their direct contact, by means of an electric field.
The electric field is material. It exists independently of us and our knowledge of it.
The electric field is created by electric charges and is detected using electric charges by the action of a certain force on them.
The electric field propagates with a finite speed of 300,000 km/s in a vacuum.
Since one of the main properties of the electric field is its action on charged particles with a certain force, then to introduce the quantitative characteristics of the field, it is necessary to place a small body with a charge q (test charge) at the point in space under study. A force will act on this body from the side of the field
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If you change the value of the test charge, for example, twice, the force acting on it will also change twice.
When the value of the test charge changes n times, the force acting on the charge also changes n times.
The ratio of the force acting on a test charge placed at a given point of the field to the magnitude of this charge is a constant value and does not depend either on this force, or on the magnitude of the charge, or on whether there is any charge. This ratio is denoted by a letter and is taken as the power characteristic of the electric field. The corresponding physical quantity is called electric field strength .
The intensity shows what force acts from the electric field on a unit charge placed at a given point in the field.
To find the unit of tension, it is necessary to substitute the units of force - 1 N and charge - 1 C into the defining equation of tension. We get: [ E ] \u003d 1 N / 1 Cl \u003d 1 N / Cl.
For clarity, electric fields in the drawings are depicted using lines of force.
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An electric field can do work to move a charge from one point to another. Hence, a charge placed at a given point in the field has a potential energy reserve.
The energy characteristics of the field can be introduced similarly to the introduction of the force characteristic.
When the value of the test charge changes, not only the force acting on it changes, but also the potential energy of this charge. The ratio of the energy of the test charge located at a given point of the field to the magnitude of this charge is a constant value and does not depend on either energy or charge.
To obtain a unit of potential, it is necessary to substitute the units of energy - 1 J and charge - 1 C into the defining equation of the potential. We get: [φ] = 1 J / 1 C = 1 V.
This unit has its own name 1 volt.
The field potential of a point charge is directly proportional to the magnitude of the charge that creates the field and inversely proportional to the distance from the charge to a given point of the field:
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Electric fields in the drawings can also be depicted using surfaces of equal potential, called equipotential surfaces .
When an electric charge moves from a point with one potential to a point with another potential, work is done.
A physical quantity equal to the ratio of work to move a charge from one point of the field to another, to the value of this charge, is called electric voltage :
The voltage shows what the work done by the electric field is when moving a charge of 1 C from one point of the field to another.
The unit of voltage, as well as potential, is 1 V.
The voltage between two field points located at a distance d from each other is related to the field strength: 
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In a uniform electric field, the work of moving a charge from one point of the field to another does not depend on the shape of the trajectory and is determined only by the magnitude of the charge and the potential difference of the field points.
