In order to give a deeper definition of a physical quantity already familiar to us in the eighth grade, let us recall the definition of the potential of a field point and how to calculate the work electric field.
The potential, as we remember, is the ratio of the potential energy of a charge placed at a certain point of the field to the magnitude of this charge, or is it the work that the field will do if you put a single positive charge at that point.
Here is the potential energy of the charge; - amount of charge. As we remember from the mechanics for calculating the field work performed on the charge:.
We now write out the potential energy using the definition of potential:. And perform some algebraic transformations:
Thus, we obtain that.
For convenience, we introduce a special value denoting the difference under the brackets: 
.
Definition: voltage (potential difference) - the ratio of the work performed by the field during charge transfer from the initial point to the final, to the magnitude of this charge.
Unit of measure - V - volt:
.
Special attention should be paid to the fact that, in contrast to the standard concept in physics of difference (an algebraic difference of a certain value at the final moment and the same value at the initial moment), to find the potential difference (voltage) it is necessary to take the final one from the initial potential.
To obtain the formula for this connection, we, as in the last lesson, for simplicity, use the case of a uniform field created by two oppositely charged plates (see Fig. 1).
Fig.1. An example of a uniform field
In this case, the strength vectors of all points of the field between the plates have one direction and one module. Now, if a positive charge is placed near the positive plate, then under the action of the Coulomb force, it naturally moves towards the negative plate. Thus, the field will do some work on this charge. We write the definition of mechanical work:. Here is the power module; - displacement module; - the angle between the force and displacement vectors.
In our case, the force and displacement vectors are co-directed (the positive charge is repelled from the positive and is attracted to the negative), so the angle is zero and the cosine is unity:.
Let us write the force through the intensity, and the displacement module is denoted as d - the distance between two points - the beginning and end of the movement:.
In the same time . Equating the right-hand sides of the equalities, we get the desired connection:
It follows that tension can also be measured in.
Moving away from our uniform field model, special attention should be given to a non-uniform field, which is created by a charged metal ball. From the experiments available is the fact that the potential of any point inside or on the surface of the ball (hollow or solid) does not change its value, namely:
.
Here is the electrostatic coefficient; - full charge of the ball; - radius of the ball.
The same formula is valid for calculating the field potential point charge away from that charge.
The interaction energy of the two charges
How to determine the interaction energy of two charged bodies located at some distance from each other (see Fig. 2).
Fig. 2. The interaction of two bodies located at a distance r
To do this, imagine the whole situation: as if body 2 is in the external field of body 1. Accordingly, now the interaction energy can be called the potential energy of charge 2 in an external field, the formula for which we know:.
Now, knowing the nature of the external field (point charge field), we know the formula for calculating the potential at a point at a certain distance from the field source:
.
Substitute the second expression in the first and get the final result:
.
If we initially imagined that this charge 1 is in the external field of charge 2, then, of course, the result would not have changed.
In electrostatics, it is interesting to select all points of space that have the same potential. Such points form certain surfaces, which are called equipotential.
Definition: equipotential surfaces are surfaces with each point having the same potential. If we draw such surfaces and draw the force lines of the same electric field, we can see that the equipotential surfaces are always perpendicular to the lines of force, and, moreover, the lines of force are always directed towards a decrease in potential (see. Fig. 3).
Fig. 3. Examples of equipotential surfaces
Another important fact about equipotential surfaces: based on the definition, the potential difference between any points on such a surface is zero (the potentials are equal), which means that the field work on moving the charge from one point of the equipotential surface to another is also zero.
In the next lesson, we will consider in more detail the field of two charged plates, namely, the device capacitor and its properties.
1) Tikhomirova S.A., Yavorsky B.M. Physics (basic level) M .: Mnemosyne. 2012
2) Gendenshtein L.E., Dick Yu.I. Physics 10 class. M .: Ileksa. 2005
3) Kasyanov V.A. Physics 10 class. M .: Drofa. 2010
1) Physicon website ()
Homework
1) p. 95: No. 732 - 736. Physics. Problem Book 10-11 classes. Rymkevich A.P. M .: Drofa 2013 ()
2) At a point with a potential of 300 V, a charged body has a potential energy of -0.6 μJ. What is the body charge?
3) What kind of kinetic energy did an electron get by passing an accelerating potential difference of 2 kV?
4) On what trajectory should the charge be moved in the electric field so that its work is minimal?
5) * Draw equipotential surfaces of the field created by two opposite charges.
Electrostatic field has energy. If an electric charge is in an electrostatic field, the field, acting on it with some force, will move it, doing work. Any work is connected with the change of some kind of energy. Work electrostatic field the movement of the charge is usually expressed in terms of a value called the potential difference.
where q is the amount of the charge to be moved,
j 1 and j 2 are the potentials of the starting and ending points of the path.
For brevity, we will denote further. V is the potential difference.
V = A / q. THE DIFFERENCE OF POTENTIALS BETWEEN THE ELECTROSTATIC FIELD POINTS IS THE WORK THAT THE ELECTRIC FORCES MAKE THROUGH THE MOVEMENT BETWEEN THEM CHARGING IN ONE PENDANT .
[V] = V. 1 volt is the potential difference between the points, moving between which the charge in 1 pendant, the electrostatic forces do the work in 1 joule.
The potential difference between the bodies is measured by an electrometer, for which one of the bodies is connected with conductors to the body of an electrometer, and the other with an arrow. In electrical circuits, the potential difference between the points of the circuit is measured with a voltmeter.
With distance from the charge, the electrostatic field weakens. Consequently, the energy characteristic of the field - the potential tends to zero. In physics, the potential of an infinitely distant point is taken as zero. In electrical engineering, they believe that the surface of the Earth has zero potential.
If the charge moves from this point to infinity, then
A = q (j - O) = qj =\u003e j = A / q, i.e. POTENTIAL OF A POINT IS A WORK THAT IS TO BE EXECUTED BY ELECTRIC FORCES BY MOVING A CHARGE IN ONE PENDANT FROM THIS POINT TO INFINITY .
Suppose that in a uniform electrostatic field with an intensity E the positive charge q moves along the direction of the intensity vector by a distance d. The field work on the movement of the charge can be found through the field strength and through the potential difference. Obviously, with any method of calculating the work, the same value is obtained.
A = Fd = Eqd = qV. =\u003e
This formula connects the power and energy characteristics of the field. In addition, it gives us a unit of tension.
[E] = V / m. 1 V / m is the intensity of such a uniform electrostatic field, the potential of which changes by 1 V when moving along the direction of the intensity vector by 1 m.
THE LAW OF OMA FOR THE CHAIN SECTION.
Increasing the potential difference at the ends of the conductor causes an increase in the current in it. Ohm experimentally proved that the current in a conductor is directly proportional to the potential difference across it.
When different consumers are switched on in the same electrical circuit, the current strength in them is different. It means that different consumers in different ways prevent the electric current from passing through them. PHYSICAL SIZE, THE CHARACTERISTIC ABILITY OF THE CONDUCTOR TO ENABLE THE ELECTRIC CURRENT TO PASSAGE THERE IS ELECTRICAL CURRENT, CALLED ELECTRIC RESISTANCE . The resistance of a given conductor is a constant value at a constant temperature. With increasing temperature, the resistance of metals increases, liquids - decreases. [R] = ohm. 1 Ohm is the resistance of such a conductor through which a current of 1 A flows with a potential difference at its ends 1B. The most commonly used metal conductors. Carriers in them are free electrons. When moving along a conductor, they interact with the positive ions of the crystal lattice, giving them some of their energy and losing speed. To obtain the desired resistance using the resistance store. Resistance shop is a set of wire spirals with known resistances that can be included in the circuit in the desired combination.
Ohm experimentally established that CURRENT POWER IN A UNIFORM CHAIN SECTION IS DIRECTLY PROPORTIONAL OF THE DIFFERENCE OF POTENTIALS AT THE END OF THIS SITE AND BACK PROPORTIONAL TO RESISTANCE OF THIS SITE.
A homogeneous section of the circuit is called the section where there are no current sources. This Ohm's law for a homogeneous section of the circuit - the basis of all electrical engineering calculations.
Including conductors of different lengths, different cross sections, made of different materials, it was found: THE RESISTANCE OF THE CONDUCTOR IS DIRECTLY PROPORTATIONAL TO THE LENGTH OF THE CONDUCTOR AND REVERSE PROPORTIONALLY THE AREA OF ITS TRANSVERSE SECTION. THE RESISTANCE OF CUBA WITH A FIN IN 1 METER MADE OF ANYTHING SUBSTANCE, IF THE CURRENT COMES TO A RENDERED ITS OPPOSITE FRONT, IS CALLED WITH SPECIFIC RESISTANCE OF THIS SUBSTANCE . [r] = Ohm m. A non-systemic unit of resistivity is often used - the resistance of a conductor with a cross-sectional area of 1 mm 2 and a length of 1 m. [r] = Ohm mm 2 / m.
The resistivity of a substance is a tabular value. Conductor resistance is proportional to its resistivity.
The action of the sliders and step resistors is based on the dependence of the conductor resistance on its length. Slider rheostat is a ceramic cylinder with nickel-nickel wound on it. The rheostat is connected to the circuit by means of a slider that includes a greater or lesser length of the winding in the circuit. The wire is covered with a layer of scale, insulating the coils from each other.
A) CONSISTENT AND PARALLEL CONNECTION OF CONSUMERS.
Often, several current consumers are included in the electrical circuit. This is due to the fact that it is not rational to have each consumer its own current source. There are two ways to turn on heat exchangers: serial and parallel, and their combinations in the form of a mixed compound.
a) Consistent connection of consumers.
With serial connection The consumers form a continuous chain in which consumers are connected one after another. With a serial connection there are no branches of connecting wires. Consider for simplicity a chain of two series-connected consumers. An electric charge that has passed through one of the consumers will pass through the second one, since in the conductor connecting consumers there can be no disappearance, occurrence and accumulation of charges. q = q 1 = q 2. Dividing the resulting equation by the time of current flow through the circuit, we obtain the connection between the current flowing through the entire connection and the currents flowing through its sections.
Obviously, the work of moving a single positive charge throughout the compound is composed of work to move this charge in all its parts. Those. V = V 1 + V 2 (2).
The total potential difference across the series-connected consumers is equal to the sum of the potential differences across the consumers.
We divide both sides of equation (2) by the current in the circuit, we get: U / I = V 1 / I + V 2 / I. Those. the resistance of the entire series-connected section is equal to the sum of the resistances of the heat emitters of its components.
B) Parallel connection of consumers.
This is the most common way to include consumers. With this connection, all consumers are switched on to two points common to all consumers.
With the passage of parallel connection, the electric charge going along the circuit is divided into several parts, going to individual consumers. According to the law of conservation of charge, q = q 1 + q 2. Dividing this equation by the time of the passage of a charge, we obtain the connection between common currentrunning along the circuit and currents going to individual consumers.
In accordance with the definition of the potential difference V = V 1 = V 2 (2).
According to Ohm’s law for a section of a circuit, we replace the forces of the currents in equation (1) by the ratio of the potential difference to the resistance. We obtain: V / R = V / R 1 + V / R 2. After reduction: 1 / R = 1 / R 1 + 1 / R 2,
those. the inverse of the resistance of a parallel connection is equal to the sum of the inverse of the resistances of its individual branches.
Potential difference
It is known that one body can be heated more, and another less. The degree of heating of the body is called its temperature. Similarly, one body can be electrified more than another. The degree of electrification of the body characterizes a quantity called the electric potential or simply the potential of the body.
What does it mean to electrify a body? It means to inform him electric charge, ie, add to it a certain number of electrons, if we charge the body negatively, or take them away from it, if we charge the body positively. In either case, the body will have a certain degree of electrification, i.e., one or another potential, and the body that is positively charged will have a positive potential, and the body that is negatively charged will have a negative potential.
Level difference electric charges two bodies called called electric potential difference or simply potential difference.
It should be borne in mind that if two identical bodies are charged with like charges, but one is larger than the other, then there will also be a potential difference between them.
In addition, the potential difference exists between two such bodies, one of which is charged, and the other has no charge. For example, if a body isolated from the earth has a certain potential, then the potential difference between it and the earth (the potential of which is considered to be equal to zero) is numerically equal to the potential of this body.
So, if two bodies are charged in such a way that their potentials are not the same, there is inevitably a potential difference between them.
Everyone knows the phenomenon of electrification combing her hair against hair is nothing but the creation of a potential difference between a comb and a person's hair.
Indeed, when rubbing a hairbrush into a hair, some electrons pass to the comb, charging it negatively, while the hair, having lost some electrons, is charged to the same extent as the comb, but positively. The potential difference created in this way can be reduced to zero by touching the comb to the hair. This reverse transition of electrons is easily detected by ear if the electrified comb is brought closer to the ear. A characteristic crackle will indicate a discharge occurring.
Speaking above about the potential difference, we had in mind two charged bodies, however the potential difference can be obtained between different parts (points) of the same body.
So, for example, consider what happens in if, under the action of some external force, we manage to move the free electrons in the wire to one end of it. Obviously, at the other end of the wire, there will be a lack of electrons, and then a potential difference will arise between the ends of the wire.
As soon as we stop the action of an external force, as electrons immediately, due to the attraction of opposite charges, will rush towards the end of the wire, which is positively charged, i.e., to the place where they are lacking, and electric equilibrium will come again.
Electromotive force and voltage
D to maintain an electrical current in a conductor, some kind of external energy source is needed, which all the time would support the potential difference at the ends of this conductor.
These energy sources are the so-called sources of electrical currentpossessing a certain electromotive force, which creates a long time and maintains the potential difference at the ends of the conductor.
Electromotive force (abbreviated as EMF) is denoted by the letter E. The unit of measurement of EMF is the volt. In our country, the volt is abbreviated to the letter "B", and in the international designation - the letter "V".
So, to get a continuous flow, an electromotive force is needed, i.e., a source of electrical current is needed.
The first such source of current was the so-called "voltaic pole", which consisted of a series of copper and zinc circles, laid with leather dipped in acidified water. Thus, one of the methods for obtaining an electromotive force is the chemical interaction of certain substances, as a result of which chemical energy is converted into electrical energy. The current sources in which an electromotive force is created in this way are called chemical current sources.
Currently, chemical current sources - galvanic cells and batteries - are widely used in electrical and power engineering.
Another major source of current, widely used in all areas of electrical engineering and electric power, are generators.
Generators are installed at electric stations and serve as the only source of current for supplying electricity to industrial enterprises, electric lighting of cities, electric railways, trams, subways, trolley buses, etc.
Like chemical sources of electric current (cells and batteries) and generators, the action of an electromotive force is exactly the same. It lies in the fact that the emf creates a potential difference at the terminals of the current source and maintains it for a long time.
These clamps are called current source poles. One pole of the current source is always experiencing a shortage of electrons and, therefore, has a positive charge, the other pole is experiencing an excess of electrons and, therefore, has a negative charge.
Accordingly, one pole of the current source is called positive (+), the other - negative (-).
Current sources are used to power electric shock various devices. Current consumers with the help of conductors are connected to the poles of the current source, forming a closed electrical circuit. The potential difference that is established between the poles of the current source when closed electrical circuit, is called voltage and is denoted by the letter U.
The unit of voltage measurement, as well as the EMF, is the volt.
If, for example, you need to write down that the voltage of the current source is 12 volts, then write: U - 12 V.
To measure or voltage is used a device called a voltmeter.
To measure the EMF or voltage of the current source, it is necessary to connect a voltmeter directly to its poles. In this case, if open, the voltmeter will show the emf of the current source. If you close the circuit, the voltmeter does not show the emf, and the voltage at the terminals of the current source.
The EMF developed by the current source is always greater than the voltage at its terminals.
Potential fields. It can be proved that the work of any electrostatic field when moving a charged body from one point to another does not depend on the shape of the trajectory, as well as the work of a uniform field. On a closed trajectory, the electrostatic field is always zero. Fields with this property are called potential. Potential character, in particular, has an electrostatic field of a point charge.
The work of a potential field can be expressed through a change in potential energy. The formula is valid for an arbitrary electrostatic field. But only in the case of a uniform field, the energy is expressed by the formula (8.19)
Potential. The potential charge energy in an electrostatic field is proportional to the charge. This is true both for a uniform field (see formula 8.19), a hook and for any other. Consequently, the ratio of potential energy to charge does not depend on the charge placed in the field.
This allows you to enter a new quantitative characteristic of the field - the potential. The potential of the electrostatic field is the ratio of the potential energy of a charge in a field to this charge.
According to this definition, the potential is equal to:
The field strength is a vector and represents power characteristic fields; it determines the force acting on the charge at a given point in the field. The potential is a scalar, it is an energy characteristic of the field; it determines the potential energy of a charge at a given point of the field.
If a negatively charged plate (Fig. 124) is taken as the zero level of potential energy, and therefore the potential, then according to formulas (8.19 and 8.20) the potential of a uniform field is equal to:
Potential difference. Like potential energy, the value of the potential at a given point depends on the choice of the zero level for the reference potential. Practical significance is not the potential at the point itself, but the change in potential, which does not depend on the choice of the zero potential reference level.
Thus, the potential difference (voltage) between two points is equal to the ratio of the field work on the charge transfer from the initial point to the final one to this charge.
Knowing the voltage in the lighting network, we thereby know the work that the electric field can do when moving a single charge from one outlet contact to another along any electrical circuit. We will deal with the concept of the potential difference throughout the course of physics.
The unit of potential difference. The unit of potential difference is set using formula (8.24). In the International System of Units, work is expressed in joules, and charge in pendants. Therefore, the potential difference between two points is equal to one, if, when a charge of 1 C moves from one point to another, the electric field performs work at 1 J. This unit is called a volt
1. What fields are called potential? 2. How is the change in potential energy associated with work? 3. What is the potential energy of a charged particle in a uniform electric field? 4. Give a definition of potential. What is the potential difference between two points of the field?
In many cases, in order to properly understand the essence of the issue concerning electrical engineering, it is necessary to know exactly what is the potential difference.
Determination of potential difference
The general concept is the electric voltage formed between two points, which is the work of the electric field that must be performed to move a positive unit charge from one point to another.
Thus, in a uniform and infinite electric field, a positive charge under the influence of this field will be moved to an infinite distance in the same direction as the electric field. The potential of a particular field point is the work produced by an electric field when a positive charge moves from this point to a point that is infinite. When the charge moves in the opposite direction, external forces perform work aimed at overcoming the electric field strength.
Potential difference in practice
The potential difference that exists at two different points of the field, has received the concept of voltage, measured in volts. In a uniform electric field, the dependence between electric voltage and the electric field intensity.
Points with the same potential, located around the charged surface of the conductor, are completely dependent on the shape of this surface. At the same time, the potential difference for individual points lying on the same surface is zero. Such a surface, where each point has the same potential, is called an equipotential surface.
When an approach to a charged body occurs, a rapid increase in potential occurs, and the arrangement of equipotential surfaces becomes closer relative to each other. When moving away from charged bodies, the arrangement of equipotential surfaces becomes more rare. Electrical location power lines always perpendicular with an equipotential surface at each point.
In a charged conductor, all points on its surface have the same potential. The same value exists in the inner points of the conductor.
Conductors having different potentials, interconnected by metal wire. A voltage or potential difference appears at its ends, therefore, an electric field is observed along the whole wire. Free electrons begin to move in the direction of increasing potential, which causes the appearance of an electric current.