Potential difference

It is known that one body can be heated more and the other less. The degree of heating of a 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 the body? This means telling him electric charge, i.e., add a certain number of electrons to it 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, moreover, a positively charged body has a positive potential, and a negatively charged body has a negative potential.

The difference in the levels of electric charges two bodies are called electric potential difference or simply potential difference.

It should be borne in mind that if two identical bodies are charged with the same charges, but one is larger than the other, then there will also be a potential difference between them.

In addition, a potential difference exists between two such bodies, one of which is charged and the other has no charge. So, for example, if any body isolated from the earth has a certain potential, then the potential difference between it and the earth (whose potential is considered to be 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 inevitably exists a potential difference between them.

Everyone knows electrification phenomenon combs when rubbing it against the hair is nothing more than the creation of a potential difference between the comb and human hair.

Indeed, when the comb rubs against the hair, part of the electrons passes to the comb, charging it negatively, while the hair, having lost some of the 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 an electrified comb is brought close to the ear. A characteristic crackle will indicate the current discharge.

Speaking above about the potential difference, we had in mind two charged bodies, however the potential difference can also 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, there will be a shortage of electrons at the other end of the wire, and then a potential difference will arise between the ends of the wire.

As soon as we stop the action of the external force, the electrons immediately, due to the attraction of opposite charges, will rush to the end of the wire, which is positively charged, i.e., to the place where they are lacking, and electrical equilibrium will again come in the wire.

Electromotive force and voltage

D To maintain an electric current in a conductor, some external source of energy is needed to maintain the potential difference at the ends of this conductor all the time.

These sources of energy are the so-called electric current sources having a certain electromotive force, which creates and maintains a potential difference at the ends of the conductor for a long time.

The electromotive force (abbreviated EMF) is denoted by the letter E. The unit of measure for EMF is the volt. In our country, the volt is abbreviated by the letter "B", and in the international designation - by the letter "V".

So, to get a continuous flow, you need an electromotive force, that is, you need a source of electric current.

The first such current source was the so-called "voltaic column", which consisted of a series of copper and zinc circles lined with leather soaked in acidified water. Thus, one of the ways to obtain an electromotive force is the chemical interaction of certain substances, as a result of which chemical energy is converted into electrical energy. 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 engineering and power industry.

Another main current source that has become widespread in all areas of electrical engineering and the electric power industry are generators.

Generators are installed at power stations and serve as the only source of current for supplying electricity to industrial enterprises, electric lighting of cities, electric railways, tram, metro, trolleybus, etc.

Both in chemical sources of electric current (cells and batteries) and in generators, the action of the 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 always experiences a shortage of electrons and, therefore, has a positive charge, the other pole experiences 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 supply electric current to various devices -. Current consumers are connected to the poles of the current source by means of conductors, forming a closed electrical circuit. The potential difference that is established between the poles of the current source with a closed electrical circuit, is called voltage and is denoted by the letter U.

The unit of voltage, like EMF, is the volt.

If, for example, it is necessary to write down that the voltage of the current source is 12 volts, then they write: U - 12 V.

A device called a voltmeter is used to measure or measure voltage.

To measure the EMF or voltage of a current source, you need 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, then the voltmeter will no longer show the EMF, but 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.

The potential difference between points 1 and 2 is the work done by the field forces when moving a unit positive charge along an arbitrary path from point 1 to point 2. For potential fields, this work does not depend on the shape of the path, but is determined only by the positions of the start and end points

the potential is defined up to an additive constant. The work of the forces of the electrostatic field when moving the charge q along an arbitrary path from the starting point 1 to the end point 2 is determined by the expression

The practical unit of potential is the volt. A volt is the potential difference between such points when, when moving one pendant of electricity from one point to another electric field does work in one joule.

1 and 2 are infinitely close points located on the x-axis, so that X2 - x1 = dx.

Work when moving a unit of charge from point 1 to point 2 will be Ex dx. The same work is equal to . Equating both expressions, we get

- scalar gradient

function gradient is a vector directed towards the maximum increase of this function, and its length is equal to the derivative of the function in the same direction. The geometric meaning of the gradient is equipotential surfaces (surfaces of equal potential), a surface on which the potential remains constant.

13 Potential charges

Potential of the field of a point charge q in a homogeneous dielectric.

- electrical displacement of a point charge in a homogeneous dielectric D - vector of electrical induction or electrical displacement

Zero should be taken as the integration constant, so that at , the potential vanishes, then

Field potential of a system of point charges in a homogeneous dielectric.

Using the principle of superposition, we get:

Potential of continuously distributed electric charges.

- elements of volume and charged surfaces centered at a point

If the dielectric is inhomogeneous, then integration should be extended to polarization charges as well. The inclusion of such

charge automatically takes into account the influence of the environment, and the value does not need to be entered

14 Electric field in matter

Electric field in matter. A substance introduced into an electric field can significantly change it. This is due to the fact that matter consists of charged particles. In the absence of an external field, the particles are distributed inside the substance in such a way that the electric field created by them, on average, over volumes that include a large number of atoms or molecules, is equal to zero. In the presence of an external field, the redistribution of charged particles occurs, and an intrinsic electric field arises in the substance. The total electric field is formed in accordance with the principle of superposition from the external field and the internal field created by the charged particles of matter. The substance is diverse in its electrical properties. The broadest classes of matter are conductors and dielectrics. A conductor is a body or material in which electric charges begin to move under the action of an arbitrarily small force. Therefore, these charges are called free. In metals, free charges are electrons, in solutions and melts of salts (acids and alkalis) - ions. A dielectric is a body or material in which, under the action of arbitrarily large forces, the charges are displaced only by a small distance, not exceeding the size of an atom, relative to its equilibrium position. Such charges are called bound. Free and bound charges. FREE CHARGES 1) excess electric. charges communicated to a conducting or non-conducting body and causing a violation of its electrical neutrality. 2) Electrical current carrier charges. 3) put. electric charges of atomic residues in metals. RELATED CHARGES the charges of the particles that make up the atoms and molecules of the dielectric, as well as the charges of the ions in the crystal. dielectrics with an ionic lattice.

Let we have an infinite uniform electric field. A charge + Q is placed at the point M. The charge + Q left to itself under the action of the electric forces of the field will move in the direction of the field for an infinitely long distance. This movement of the charge will consume energy electric field. The potential of a given point in the field is the work that an electric field expends when it moves a positive unit of charge from a given point in the field to a point at infinity. To move the charge + Q from an infinitely distant point back to point M, external forces must produce work A, going to overcome the electric forces of the field. Then for the potential of point M we get:

Thus, the absolute electrostatic unit of potential is three hundred times greater than the practical unit - the volt.

If a charge equal to 1 coulomb moves from a point at infinity to a point in the field, the potential of which is 1 volt, then work of 1 joule is done. If, however, 15 coulombs of electricity move to a point in a field with a potential of 10 V from an infinitely distant point, then work is done 10 -15 \u003d 150 joules.

Mathematically, this dependence is expressed by the formula:

To move from point A with a potential of 20V to point B with a potential of 15V 10 coulombs of electricity, the field must do work:

Studying the electric field, we note that in this field the potential difference between two points of the field is also called the voltage between them, measured in volts and denoted by the letter U.

The work of the electric field forces can be written as follows:

In order to move the charge q along the field lines from one point of a homogeneous field to another, located at a distance l, you need to do the work:

This is the simplest relationship between electric field strength and electric voltage for a uniform field.

The location of points with equal potential around the surface of a charged conductor depends on the shape of this surface. If you take for example, a charged metal ball, then points of equal potential in the electric field created by the ball will lie on the spherical surface surrounding the charged ball. The surface of equal potential, or, as it is also called, the equipotential surface, serves as a convenient graphical way to depict the field. In FIG. 13 shows a picture of the equipotential surfaces of a positively charged ball.

For a visual representation of how the potential difference changes in a given field, equipotential surfaces should be drawn so that the potential difference between points lying on two

The gray surfaces were the same, for example, equal to 1 in. We outline the initial, zero, equipotential surface with an arbitrary radius. The remaining surfaces 1, 2, 3, 4 are drawn so that the potential difference between the points lying on this surface and on neighboring surfaces is 1 volt. According to the definition of an equipotential surface, the potential difference between individual points lying on the same surface is zero; Therefore, the charge moves along the equipotential surface without the expenditure of work. It can be seen from this figure that as we approach the charged body, the equipotential surfaces are located closer to each other, since the potential of the field points increases, and the potential difference between adjacent surfaces, according to the accepted condition, remains the same. Conversely, as the distance from the charged body increases, the equipotential surfaces are located less frequently. Electrical lines of force are perpendicular to the equipotential surface at any point, since only under the condition that the force and displacement are perpendicular, the work of electric forces when the charge moves along the equipotential surface can be equal to zero. The surface of a charged conductor itself is an equipotential surface, i.e., all points on the surface of the conductor have the same potential. All points inside the conductor have the same potential.

If we take two conductors with different potentials and connect them with a metal wire, then, since there is a potential difference or voltage between the ends of the wire, an electric field will act along the wire. The free electrons of the wire under the action of the field will begin to move in the direction of increasing potential, i.e., they will begin to pass through the wire electricity. The movement of electrons will continue until the potentials of the conductors become equal, and the potential difference between them becomes zero.

If two vessels with different levels of water are connected from below by a tube, then water will flow through the tube. The movement of water will continue until the water levels in the vessels are at the same height, and the level difference becomes zero.

Since any charged conductor connected to the ground loses almost all of its charge, the ground potential is conditionally taken to be zero.

In order to give a deeper definition of the already familiar to us from the eighth grade physical quantity, recall the definition of the field point potential and how to calculate the work of the electric field.

Potential, as we remember, is the ratio of the potential energy of a charge placed at a certain point in the field to the value of this charge, or it is the work that the field will do if a single positive charge is placed at this point.

Here is the potential energy of the charge; - amount of charge. As we remember from mechanics to calculate the work done by the field on the charge: .

We now write out the potential energy using the definition of the potential: . And let's perform some algebraic transformations:

Thus, we get that .

For convenience, we introduce a special value denoting the difference under brackets: .

Definition: voltage (potential difference) - the ratio of the work performed by the field when transferring charge from the starting point to the final point, to the value of this charge.

Unit of measurement - V - volt:
.

Particular attention should be paid to the fact that, in contrast to the standard concept in physics of difference (the algebraic difference of a certain value at the final moment and the same value at the initial moment), to find the potential difference (voltage), one should subtract the final potential from the initial potential.

To obtain the formula for this connection, we, as in the previous lesson, for simplicity, will 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 tension vectors of all field points between the plates have one direction and one module. Now, if a positive charge is placed near the positive plate, then under the influence of the Coulomb force, it will naturally move towards the negative plate. Thus, the field will do some work on this charge. Let's write down the definition of mechanical work: . Here is the modulus of force; - movement module; - angle between force and displacement vectors.

In our case, the force and displacement vectors are co-directed (the positive charge is repelled from the positive and attracted to the negative), so the angle is zero, and the cosine is one:.

We write the force through tension, and the module of displacement is denoted as d - the distance between two points - the beginning and end of the movement: .

In the same time . By equating the right-hand sides of the equalities, we obtain the desired relationship:

It follows that tension can also be measured in .

Moving away from our model of a uniform field, special attention should be paid to the inhomogeneous field, which is created by a charged metal ball. From experiments, the fact is available that the potential of any point inside or on the surface of a ball (hollow or solid) does not change its value, namely:
.

Here is the electrostatic coefficient; - full charge of the ball; is the radius of the ball.

The same formula is also valid for calculating the field potential of a point charge at a distance from this charge.

Energy of interaction of two charges

How to determine the interaction energy of two charged bodies located at some distance from each other (see Fig. 2).

Rice. 2. Interaction of two bodies located at some 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 the external field, the formula for which we know: .

Now, knowing the nature of the external field (the field of a point charge), we know the formula for calculating the potential at a point at a certain distance from the field source:
.

Substitute the second expression into the first and get the final result:
.

If we had initially imagined that this charge 1 is in the external field of charge 2, then, of course, the result would not change.

In electrostatics, it is interesting to single out all points in space that have the same potential. Such points form certain surfaces, which are called equipotential.

Definition: equipotential surfaces - surfaces, each point of which has the same potential. If you draw such surfaces and draw the lines of force of the same electric field, you can see that the equipotential surfaces are always perpendicular to the lines of force, and, in addition, the lines of force are always directed in the direction of decreasing potential (see Fig. 3).

Rice. 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 work of the field to move the charge from one point of the equipotential surface to another is also zero.

In the next lesson, we will take a closer look at the field of two charged plates, namely: the capacitor device and its properties.

1) Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) M.: Mnemosyne. 2012

2) Gendenstein L.E., Dick Yu.I. Physics grade 10. M.: Ileksa. 2005

3) Kasyanov V.A. Physics grade 10. M.: Bustard. 2010

1) Website "Physicon" ()

Homework

1) Page 95: No. 732 - 736. Physics. Task book. 10-11 grades. Rymkevich A.P. M .: Bustard 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 charge of the body?

3) What kinetic energy received an electron by passing through an accelerating potential difference of 2 kV?

4) On what trajectory should the charge be moved in an electric field so that its work is minimal?

5) * Draw the equipotential surfaces of the field created by two opposite charges.

electrical voltage.
Potential difference. voltage.

Topic: what is electric voltage and potential difference.

Perhaps one of the most commonly used expressions among electricians is the concept of electrical voltage. It is also called the potential difference and not quite the right phrase, such as voltage, well, the meaning of the names is essentially the same. What does this concept really mean? Perhaps, to begin with, I will give a book formulation: electrical voltage - this is the ratio of the work of the electric field of charges during the transfer of a test charge from point 1 to point 2. well and in simple words speaking, it is explained thus.

Let me remind you that there are two types of charges, these are positive with a “+” sign and negative with a “-” sign. Most of us in childhood played with magnets, which were honestly obtained from another broken car with an electric motor, where they stood. So, when we tried to bring these same magnets closer to each other, in one case they were attracted, and if one of them was turned the other way around, they repelled accordingly.

This happened because any magnet has two poles, these are south and north. In the case when the poles are the same, then the magnets will repel, but when they are opposite, they will attract. The same thing happens with electric charges, and the force of interaction depends on the number and variety of these charged particles. Simply put, the more “plus” on one object, and on the other, respectively, “minus”, the stronger they will be attracted to each other. Or vice versa, repel with the same charge (+ and + or - and -).

Now imagine that we have two small iron balls. If you mentally look into them, you can see a huge number of small particles that are located at a small distance from each other and are incapable of free movement, these are the nuclei of our substance. Smaller particles, called electrons. They can break away from some nuclei and join others, thus traveling all over the iron ball. In the case when the number of electrons corresponds to the number of protons in the nucleus, the balls are electrically neutral.

But if you somehow take away a certain amount, such a ball will tend to attract this very missing amount of electrons to itself, thereby forming a positive field around itself with a “+” sign. The more electrons are missing, the stronger it will be. positive field. In the neighboring ball, we will do a turn and add extra electrons. As a result, we get an excess and, accordingly, the same electric field, but with a "-" sign.

As a result, we get two potentials, one of which is eager to receive electrons, and the second one will get rid of them. An excess of tightness arises in the ball, and these particles, around which there is a field, push and push each other out of the ball. And where there is a lack of them, accordingly, something like a vacuum occurs, which tries to draw these electrons. it good example potential difference and nothing more than the voltage between them. But, as soon as these iron balls are connected to each other, an exchange will take place and the tension will disappear, since neutrality is formed.

Roughly speaking, this force of the tendency of charged particles to move from more charged parts to less charged parts between two points will be the potential difference. Let's mentally imagine the wires that are connected to the battery from an ordinary flashlight. In the battery itself chemical reaction, which results in an excess of electrons ("-"), inside the battery they are pushed to the negative terminal. These electrons tend to return to their place, from where they were pushed out before.

They don’t succeed inside the battery, so it remains to wait for the moment when they will make a bridge in the form of an electrical conductor and along which they will quickly run to the positive terminal of the battery, where they are attracted. In the meantime, there is no bridge, then there will be a desire to cross in the form of this very electrical voltage or potential difference(voltage).

I will give some similar example on a different view. There is a regular faucet with water. The tap is closed and, therefore, water will not come out of it, but there is still water inside and moreover, it is there under some pressure, because of this pressure it tends to break out, but the closed tap prevents it. And as soon as you turn the faucet handle, the water will immediately run. So this pressure can be roughly compared with voltage, and water with charged particles. The flow of water itself will in this example act as an electric current in the wires themselves, and a closed faucet in the role electrical switch. I gave this example only for clarity, and it is not a complete analogy!

Oddly enough, but people who are not closely associated with the profession of an electrician quite often refer to electrical voltage as , expression is voltage and this is an incorrect formulation, since voltage, as we found out, is the potential difference of electric charges, and current is the flow of these charged particles itself. And it turns out that, pronouncing the voltage, as a result, a slight discrepancy in the concept itself.

Voltage, like all other quantities, has its own unit of measurement. It is measured in Volts. These are the same volts that are written on devices and power supplies. For example, in a regular home socket 220 V, or a battery you bought with a voltage of 1.5 V. In general, I think you understand in general terms, what is this most electrical voltage. In this article, I was based only on a simple understanding of this term and did not go into the depths of formulations and formulas, so as not to complicate understanding. In fact, this topic can be studied much more widely, but it already depends on you and your desire.