Potential difference
electric electric (voltage) between two points is equal to the work of the electric field to move a unit positive charge from one point of the field to another.
Electromotive force (EMF) is a physical quantity that characterizes the work of external (non-potential) forces in direct or alternating current sources. In a closed conducting circuit, the EMF is equal to the work of these forces to move a single positive charge along the circuit.
EMF can be expressed in terms of the electric field strength of external forces (Eex). In a closed loop (L), then the EMF will be equal to: , where dl is the element of the loop length. EMF, like voltage, is measured in volts.
Electric voltage is a physical quantity numerically equal to the ratio of the work done when transferring a charge between two points of the electric field and the magnitude of this charge.
Electrical resistance is a physical quantity that characterizes the properties of a conductor to prevent the passage of electric current and is equal to the ratio of the voltage at the ends of the conductor to the strength of the current flowing through it. Resistance for alternating current circuits and for alternating electromagnetic fields is described by the concepts of impedance and characteristic impedance. Resistance (resistor) is also called a radio component designed to introduce active resistance into electrical circuits.
Resistance (often denoted by the letter R or r) is considered, within certain limits, to be a constant value for a given conductor; it can be calculated as where
R - resistance;
U is the electrical potential difference at the ends of the conductor;
I is the current strength flowing between the ends of the conductor under the influence of a potential difference.
The resistance R of a homogeneous conductor of constant cross-section depends on the properties of the material of the conductor, its length and cross-section as follows:
where ρ is the resistivity of the conductor substance, L is the length of the conductor, and S is the cross-sectional area. The reciprocal of resistivity is called conductivity. This quantity is related to temperature by the Nernst-Einstein formula: where
T - conductor temperature;
D is the diffusion coefficient of charge carriers;
Z is the number of electrical charges of the carrier;
e - elementary electric charge;
C - Charge carrier concentration;
kB is Boltzmann's constant.
Therefore, the resistance of the conductor is related to temperature as follows:
Superconductivity is the property of some materials to have strictly zero electrical resistance when they reach a temperature below a certain value (critical temperature).
47.Branched chains. Kirchhoff's rules and their physical content.
The simplest branched chain. It has three branches and two nodes. Each branch has its own current flowing. A branch can be defined as a section of a circuit formed by elements connected in series (through which the same current flows) and contained between two nodes. In turn, a node is a point in a chain at which at least three branches converge. If there is a dot at the intersection of two lines on the electrical diagram (Figure 2), then at this place there is an electrical connection between the two lines, otherwise there is not. A node at which two branches converge, one of which is a continuation of the other, is called a removable or degenerate node
Kirchhoff's laws (or Kirchhoff's rules) are relationships that hold between currents and voltages in sections of any electrical circuit. Kirchhoff's rules allow you to calculate any electrical circuits of direct and quasi-stationary current. They are of particular importance in electrical engineering because of their versatility, as they are suitable for solving many problems in the theory of electrical circuits. Application of Kirchhoff's rules to a linear circuit allows us to obtain a system of linear equations for currents, and accordingly, find the value of the currents on all branches of the circuit. Formulated by Gustav Kirchhoff in 1845.
Kirchhoff's first law (Kirchhoff's Law of Currents, ZTK) states that the algebraic sum of currents in any node of any circuit is equal to zero (the values of the flowing currents are taken with the opposite sign):
In other words, as much current flows into a node, as much flows out of it. This law follows from the law of conservation of charge. If a circuit contains p nodes, then it is described by p − 1 current equations. This law can also be applied to other physical phenomena (for example, water pipes), where there is a law of conservation of quantity and the flow of this quantity.
Kirchhoff's second law (Kirchhoff's Stress Law, ZNK) states that the algebraic sum of the voltage drops along any closed circuit circuit is equal to the algebraic sum of the emf acting along the same circuit. If there is no EMF in the circuit, then the total voltage drop is zero:
for constant voltages
for alternating voltages
In other words, when going around the circuit along the circuit, the potential, changing, returns to its original value. If a circuit contains branches, of which the branches contain current sources in quantity, then it is described by voltage equations. A special case of the second rule for a circuit consisting of one circuit is Ohm's law for this circuit.
Kirchhoff's laws are valid for linear and nonlinear circuits for any type of change in currents and voltages over time.
For example, for the circuit shown in the figure, in accordance with the first law, the following relationships are satisfied:
Note that for each node the positive direction must be chosen, for example here, currents flowing into a node are considered positive and currents flowing out are considered negative.
In accordance with the second law, the following relations are valid:
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3.3. Potential. Potential difference.
The force with which a system of charges acts on some charge not included in the system is equal to the vector sum of the forces with which each of the charges in the system acts on the charge separately (superposition principle).
Here, each term does not depend on the shape of the path and, therefore, does not depend on the shape of the path and the sum.
So the electrostatic field is potential.
The work done by the electrostatic field forces can be expressed through the decrease
potential energy – the difference between two state functions: | |||||||||
A12= Ep1– Ep2 | |||||||||
Then expression (3.2.2) can be rewritten as: | |||||||||
Comparing formulas (3.2.2) and (3.2.3) we obtain an expression for the potential |
|||||||||
energy of charge q" in the field of charge q: | |||||||||
Potential energy is determined up to the integration constant. The value of the constant in the expression Epot. are chosen in such a way that when the charge is removed to infinity (i.e. at r = ∞), the potential energy is reversed
Different test charges q",q"",... will have different energies En", En"", and so on at the same point in the field. However, the ratio En/q"pr will be the same for all charges. Therefore, a scalar quantity was introduced, which is
From this expression it follows that the potential is numerically equal to the potential energy possessed by a unit positive charge at a given point in the field.
Substituting the value of potential energy (3.2.3) into (3.3.1.), we obtain for
Potential, like potential energy, is determined accurate to the integration constant. We agreed to assume that the potential of a point removed to infinity is zero. Therefore, when they say “the potential of such and such a point”, they mean the potential difference between this point and a point removed to infinity. Another definition of potential:
φ = Aq∞ or A∞ = qφ,
those. potential is numerically equal to the work that field forces do on a unit positive charge as it moves away from a given point to infinity
dA = Fl dl = El qdl
(on the contrary, the same work must be done to move a unit positive charge from infinity to a given point in the field.
If the field is created by a system of charges, then, using the principle of superposition, we obtain:
those. The field potential created by a system of charges is equal to the algebraic sum of the potentials created by each of the charges separately. But the tensions, as you remember, add up when fields are superimposed – vectorially.
Let us return to the work of the electrostatic field forces on the charge q". Let us express the work
where U is the potential difference or also called voltage. By the way, a good analogy:
A12 = mgh2 −mgh3 = m(gh2 − gh3)
gh – has the meaning of the gravitational field potential, and m – charge.
So potential is a scalar quantity, so use and calculate φ
simpler than E. Instruments for measuring potential differences are widespread. The formula A∞=qφ can be used to establish units of potential: unit φ is taken to be the potential at a point in the field to which to move from ∞ a unit positive charge it is necessary to do work equal to one.
So in SI – unit of potential 1V = 1J/1C, in SGSE 1 unit of pot. = 300V.
In physics, a unit of energy and work called eV is often used - this is the work done by field forces on a charge equal to the charge of an electron when it passes through a potential difference of 1V, that is:
1eV =1.6 10−19 C V =1.6 10−19 J
3.4. The relationship between tension and potential.
So the electrostatic field can be described either using a vector
quantities E, or using a scalar quantity φ. It is obvious that there must be a certain connection between these quantities. Let's find her:
Let us depict the movement of charge q along an arbitrary path.
The work done by the forces of the electrostatic field on an infinitesimal segment dl can be found as follows:
El – projection of E onto drl; dl – arbitrary direction of charge movement.
On the other hand, as we have shown, this work, if done by an electrostatic field, is equal to the decrease in the potential energy of a charge moved at a distance dl.
dA = −qdφ; El qdl= −qdφ | ||||
This is where the dimension of the field strength V/m comes from.
To orient dl – (direction of movement) in space, you need to know the projections E on the coordinate axes:
where i,j,k are unit vectors of the axes.
By the definition of gradient, the sum of the first derivatives of any function with respect to coordinates is the gradient of this function, that is:
gradφ = ∂∂φx ri + ∂∂φy rj + ∂∂φz kr
functions. The minus sign indicates that E is directed towards decreasing the electric field potential.
3.5. Field lines and equipotential surfaces.
As you and I already know, the direction of the field line (tension line) in
each point coincides with the direction E. It follows that the tension E
equal to the potential difference per unit length of the field line.
It is along the field line that the maximum change in potential occurs.
Therefore, it is always possible to determine E between two points by measuring U between them, and the closer the points are, the more accurately. In a uniform electric field, the forces
lines are straight. Therefore, here the definition of E is most simple:
When moving along this surface by dl, the potential will not change: dφ = 0. Therefore, the projection of the vector E onto dl is equal to 0, that is, El = 0. Hence
it follows that E at each point is directed along the normal to the equipotential surface.
You can draw as many equipotential surfaces as you like. By
The density of equipotential surfaces can be judged by the value of E, this will be provided that the potential difference between two adjacent equipotential surfaces is equal to a constant value. In one of the laboratory works, we will model the electric field and find equipotential surfaces and field lines from electrodes of various shapes - you will very clearly see how equipotential surfaces can be located.
The formula E = −gradφ expresses the relationship between potential and intensity and allows one to find the field strength at each point using known values of φ. You can also solve
the inverse problem, i.e. Using the known values of E at each point of the field, find the difference φ between two arbitrary points of the field. To do this, we take advantage of the fact that the work done by field forces on a charge q when moving it from point 1 to point 2 can be calculated as:
On the other hand, the work can be represented as:
A12= q(φ1−φ2)
φ1−φ2= ∫Edl | ||
The integral can be taken along any line connecting point 1 and point 2, because the work of field forces does not depend on the path. To go around a closed loop φ1 = φ2 we get:
those. we arrived at the well-known theorem about the circulation of the tension vector.
Consequently, the circulation of the electrostatic field strength vector along any closed loop is zero. A force field that has this
property is called potential. From the circulation of the vector E to zero,
it follows that the lines E of the electrostatic field cannot be closed: they begin on positive charges and end on negative charges or go to infinity.
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potential difference in electrical engineering and physics
The concept of “potential” is widely used in physics to characterize various fields and forces. The most famous applications are:
- Electromagnetic – characteristic of the electromagnetic field;
- Gravitational – characteristic of gravitational fields;
- Mechanical – determination of forces;
- Thermodynamic – a measure of the internal energy of bodies of a thermodynamic system;
- Chemical;
- Electrode.
Potential difference
In turn, electromagnetic is divided into two concepts:
- Electrostatic (scalar), as a characteristic of the electric field;
- Vector characterizing the magnetic field.
The strength of a changing electric field is found through the electric potential, while a static field is characterized by electrostatic.
Potential difference
Potential difference, or voltage, is one of the basic concepts of electrical engineering. It can be defined as the work done by the electric field to transfer charge between two points. Then, to the question of what potential is, we can answer that this is the work of transferring a unit charge from a given point to infinity.
As in the case of gravitational forces, a charge, like a body with potential energy, has a certain electric potential when introduced into an electric field. The higher the electric field strength and the larger the charge, the higher its electric potential.
To determine the voltage there is a formula:
which relates the work A does to move charge q from one point to another.
After carrying out the transformation, we get:
That is, the higher the voltage, the more work the electric field (electricity) must do to transfer charges.
This definition allows you to understand the essence of the power of the power source. The higher its voltage, the potential difference between the terminals, the more work it can provide.
Potential difference is measured in volts. To measure voltage, measuring instruments called voltmeters have been created. They are based on the principles of electrodynamics. The current passing through the wire frame of the voltmeter creates an electromagnetic field under the influence of the measured voltage. The frame is located between the poles of the magnets.
The interaction of the fields of the frame and the magnet causes the latter to deviate by a certain angle. A larger potential difference creates a larger current, resulting in a larger deflection angle. The scale of the device is proportional to the angle of frame deflection, that is, the potential difference and is graduated in volts.
Voltmeter
In the hands of a modern electrician there are not only dial gauges, but also digital measuring instruments that not only measure the electrical potential at a certain point in the circuit, but also other quantities that characterize the electrical circuit. Voltages at points are measured in relation to others, which are conventionally assigned a value of zero. Then the measured value between the zero and potential terminals will give the desired voltage.
The above refers to voltage as the potential difference between two charges. In electrical engineering, this difference is measured in a section of a circuit when current flows through it. In the case of alternating current, that is, changing amplitude and polarity over time, the voltage in the circuit changes according to the same law. This is only true if there are active resistances in the circuit. Reactive elements in an alternating current circuit cause a phase shift relative to the flowing current.
Potentiometers
The voltage of power sources, especially autonomous ones, such as batteries, chemical sources, solar and thermal batteries, is constant and cannot be adjusted. To obtain smaller values, in the simplest case, potentiometric voltage dividers using a three-terminal variable resistor (potentiometer) are used. How does a potentiometer work? A variable resistor is a resistive element with two terminals along which a contact slider with a third terminal can move.
Potentiometer-rheostat
The variable resistor can be switched on in two ways:
- Rheostat;
- Potentiometer.
In the first case, the variable resistor has two terminals: one is the main one, the other is from the slider. By moving the slider along the resistor body, the resistance is changed. By connecting a rheostat in an electric current circuit in series with a voltage source, you can regulate the current in the circuit.
Rheostat switching
Turning on with a potentiometer requires the use of all three pins. The main pins are connected in parallel with the power supply, and the reduced voltage is removed from the slider and one of the pins.
The principle of operation of the potentiometer is as follows. A current passes through a resistor connected to the power source, which creates a voltage drop between the slider and the outer terminals. The lower the resistance between the slider and the terminal, the lower the voltage. This circuit has a drawback: it heavily loads the power source, since correct and accurate adjustment requires that the resistance of the variable resistor be several times less than the load resistance.
Potentiometric switching
Note! The name “potentiometer” in this case is not entirely correct, since the name implies that it is a device for measuring, but since its operating principle is similar to a modern variable resistor, this name is firmly attached to it, especially among amateurs.
Many concepts in physics are similar and can serve as examples for each other. This is also true for such a concept as potential, which can be either a mechanical quantity or an electrical quantity. The potential itself cannot be measured, so we are talking about the difference when one of the two charges is taken as a reference point - zero or grounding, as is customary in electrical engineering.
Video
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POTENTIAL. POTENTIAL DIFFERENCE.
⇐ PreviousPage 4 of 6Next ⇒An electrostatic field has energy. If there is an electric charge in an electrostatic field, then the field, acting on it with some force, will move it, doing work. Any work involves a change in some type of energy. The work of an electrostatic field to move a charge is usually expressed through a quantity called potential difference.
where q is the amount of charge being moved,
j1 and j2 are the potentials of the starting and ending points of the path.
For brevity, in what follows we will denote . V - potential difference.
V = A/q. THE POTENTIAL DIFFERENCE BETWEEN THE POINTS OF AN ELECTROSTATIC FIELD IS THE WORK THAT ELECTRIC FORCES DO WHEN THE CHARGE OF ONE COULUM MOVES BETWEEN THEM.
[V] = V. 1 volt is the potential difference between points, when moving a charge of 1 coulomb between them, electrostatic forces do 1 joule of work.
The potential difference between bodies is measured with an electrometer, for which one of the bodies is connected by conductors to the body of the electrometer, and the other to the arrow. In electrical circuits, the potential difference between points in 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, also tends to zero. In physics, the potential of a point at infinity is taken to be zero. In electrical engineering, it is believed that the surface of the Earth has zero potential.
If a charge moves from a given point to infinity, then
A = q(j - O) = qj => j= A/q, i.e. POTENTIAL OF A POINT IS THE WORK THAT MUST BE DONE BY ELECTRIC FORCES, MOVING A CHARGE OF ONE COULDOMS FROM A GIVEN POINT TO INFINITY.
Let a positive charge q move along the direction of the intensity vector to a distance d in a uniform electrostatic field with intensity E. The work done by the field to move a charge can be found both through the field strength and through the potential difference. It is obvious that with any method of calculating the work, the same value is obtained.
A = Fd = Eqd = qV. =>
This formula connects the force 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.
OHM'S LAW FOR A CIRCUIT SECTION.
An increase in the potential difference at the ends of the conductor causes an increase in the current strength in it. Ohm experimentally proved that the current strength in a conductor is directly proportional to the potential difference across it.
When different consumers are connected to the same electrical circuit, the current strength in them is different. This means that different consumers hinder the passage of electric current through them in different ways. A PHYSICAL QUANTITY CHARACTERIZING THE ABILITY OF A CONDUCTOR TO PREVENT THE PASSAGE OF ELECTRIC CURRENT THROUGH IT IS CALLED ELECTRICAL RESISTANCE. The resistance of a given conductor is a constant value at a constant temperature. As the temperature rises, the resistance of metals increases, and that of liquids decreases. [R] = Ohm. 1 Ohm is the resistance of a conductor through which a current of 1 A flows with a potential difference of 1 V at its ends. Metal conductors are most often used. The current carriers in them are free electrons. When moving along a conductor, they interact with positive ions of the crystal lattice, giving them part of their energy and losing speed. To obtain the required resistance, use a resistance magazine. A resistance store is a set of wire spirals with known resistances that can be included in a circuit in the desired combination.
Ohm experimentally established that the CURRENT STRENGTH IN A HOMOGENEOUS SECTION OF A CIRCUIT IS DIRECTLY PROPORTIONAL TO THE POTENTIAL DIFFERENCE AT THE ENDS OF THIS SECTION AND INVERSE PROPORTIONAL TO THE RESISTANCE OF THIS SECTION.
A homogeneous section of a circuit is a section in which there are no current sources. This is Ohm's law for a homogeneous section of a circuit - the basis of all electrical calculations.
Including conductors of different lengths, different cross-sections, made of different materials, it was established: THE RESISTANCE OF A CONDUCTOR IS DIRECTLY PROPORTIONAL TO THE LENGTH OF THE CONDUCTOR AND INVERSE PROPORTIONAL TO THE AREA OF ITS CROSS SECTION. THE RESISTANCE OF A CUBE WITH AN EDGE OF 1 METER, MADE FROM SOME SUBSTANCE, IF THE CURRENT GOES PERPENDICULAR TO ITS OPPOSITE FACES, IS CALLED THE SPECIFIC RESISTANCE OF THIS SUBSTANCE. [r] = Ohm m. A non-system unit of resistivity is often used - the resistance of a conductor with a cross-sectional area of 1 mm2 and a length of 1 m. [r] = Ohm mm2/m.
The specific resistance of a substance is a tabular value. The resistance of a conductor is proportional to its resistivity.
The action of slider and step rheostats is based on the dependence of the conductor resistance on its length. The slider rheostat is a ceramic cylinder with nickel wire wound around it. The rheostat is connected to the circuit using a slider, which includes a larger or smaller winding length in the circuit. The wire is covered with a layer of scale, which insulates the turns from each other.
A) SERIES AND PARALLEL CONNECTION OF CONSUMERS.
Often several current consumers are included in an electrical circuit. This is due to the fact that it is not rational for each consumer to have their own current source. There are two ways to connect consumers: serial and parallel, and their combinations in the form of a mixed connection.
a) Serial connection of consumers.
With a series connection, consumers form a continuous chain in which consumers are connected one after another. With a series connection, there are no branches of connecting wires. For simplicity, let us consider a circuit of two series-connected consumers. An electric charge that passes through one of the consumers will also pass through the second one, because in the conductor connecting consumers there cannot be the disappearance, emergence or accumulation of charges. q=q1=q2. Dividing the resulting equation by the time the current passes through the circuit, we obtain a relationship between the current flowing throughout the entire connection and the currents flowing through its sections.
Obviously, the work to move a single positive charge throughout the compound consists of the work to move this charge across all its sections. Those. V=V1+V2 (2).
The total potential difference across series-connected consumers is equal to the sum of the potential differences across consumers.
Let's divide both sides of equation (2) by the current in the circuit, we get: U/I=V1/I+V2/I. Those. The resistance of the entire series-connected section is equal to the sum of the resistances of the voltages of its components.
B) Parallel connection of consumers.
This is the most common way to enable consumers. With this connection, all consumers are connected to two points common to all consumers.
When passing through a parallel connection, the electric charge flowing through the circuit is divided into several parts, going to individual consumers. According to the law of conservation of charge q=q1+q2. Dividing this equation by the charge passage time, we obtain a relationship between the total current flowing through the circuit and the currents flowing through individual consumers.
In accordance with the definition of potential difference V=V1=V2 (2).
According to Ohm's law for a section of the circuit, we replace the current strengths in equation (1) with the ratio of the potential difference to the resistance. We get: V/R=V/R1+V/R2. After reduction: 1/R=1/R1+1/R2,
those. the reciprocal of the resistance of a parallel connection is equal to the sum of the reciprocals of the resistances of its individual branches.
The potential difference between points 1 and 2 is the work done by 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 starting and ending points
the potential is determined up to an additive constant. The work done by the electrostatic field forces when moving a charge q along an arbitrary path from the starting point 1 to the ending 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 coulomb of electricity from one point to another, the electric field does one joule of work.
1 and 2 are infinitely close points located on the x axis, so X2 - x1 = dx.
The work done when moving a unit of charge from point 1 to point 2 will be Ex dx. The same work is equal. Equating both expressions, we get 
- scalar gradient
Gradient function 
there 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 a gradient is equipotential surfaces (surfaces of equal potential) - a surface on which the potential remains constant.
13 Charge potential
Field potential 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
We should take zero as the integration constant so that when 
the potential goes to zero, then 
Field potential of a system of point charges in a homogeneous dielectric.
Using the superposition principle we get:
Potential of continuously distributed electrical charges.
-
elements of volume and charged surfaces with centers at a point
If the dielectric is inhomogeneous, then the integration must be extended to polarization charges. Inclusion of such
charges 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, particles are distributed inside a substance in such a way that the electric field they create, on average over volumes that include a large number of atoms or molecules, is zero. In the presence of an external field, a redistribution of charged particles occurs, and its own electric field arises in the substance. The total electric field is composed in accordance with the principle of superposition from the external field and the internal field created by charged particles of matter. The substance is diverse in its electrical properties. The broadest classes of substances are conductors and dielectrics. A conductor is a body or material in which electrical charges begin to move under the influence 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 influence of arbitrarily large forces, charges are displaced only by a small distance, not exceeding the size of an atom, relative to their equilibrium position. Such charges are called bound. Free and bound charges. FREE CHARGES 1) excess electric. charges imparted to a conducting or non-conducting body and causing a violation of its electrical neutrality. 2) Electric. current carrier charges. 3) put. electric charges of atomic residues in metals. ASSOCIATED CHARGES Electric. charges of particles that make up the atoms and molecules of the dielectric, as well as charges of ions in the crystalline. dielectrics with an ionic lattice.
Potential fields. It can be proven 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, just like the work of a uniform field. On a closed trajectory, the work of the electrostatic field is always zero. Fields with this property are called potential. In particular, the electrostatic field of a point charge has a potential character.
The work of a potential field can be expressed in terms of 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 energy of a charge in an electrostatic field is proportional to the charge. This is true both for a homogeneous field (see formula 8.19) and for any other. Therefore, the ratio of potential energy to charge does not depend on the charge placed in the field.
This allows us to introduce a new quantitative characteristic of the field - potential. The electrostatic field potential is the ratio of the potential energy of a charge in the field to this charge.
According to this definition, the potential is equal to:
The field strength is a vector and represents the strength characteristic of the field; it determines the force acting on the charge at a given point in the field. Potential is a scalar, it is an energy characteristic of the field; it determines the potential energy of the charge at a given point in the field.
If we take a negatively charged plate (Fig. 124) as the zero level of potential energy, and therefore 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 reading the potential. What is of practical importance is not the potential itself at a point, but the change in potential, which does not depend on the choice of the zero level of the potential reference.
Since potential energy, the work is equal to:
In the future, instead of changing the potential, which is the difference in potential values at the final and initial points of the trajectory, we will use another value - the potential difference. By potential difference we mean the difference in potential values at the initial and final points of the trajectory:
Often the potential difference is also called voltage.
It is more convenient to deal with potential difference, or voltage, than with potential change, especially when studying electric current.
According to formulas (8.22) and (8.23), the potential difference
Thus, the potential difference (voltage) between two points is equal to the ratio of the work done by the field to move a charge from the starting point to the final point to this charge.
Knowing the voltage in the lighting network, we thereby know the work that an electric field can do when moving a unit charge from one socket contact to another along any electrical circuit. We will deal with the concept of potential difference throughout the entire physics course.
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 coulombs. Therefore, the potential difference between two points is equal to unity if, when moving a charge of 1 C from one point to another, the electric field does 1 J of work. This unit is called a volt
1. What fields are called potential? 2. How is the change in potential energy related to work? 3. What is the potential energy of a charged particle in a uniform electric field? 4. Define potential. What is the potential difference between two points in the field?
Potential difference
It is known that one body can be heated more, and another less. The degree to which a body heats up is called its temperature. Likewise, one body can be electrified more than another. The degree of electrification of a body is characterized by a quantity called electrical potential or simply the potential of the body.
What does it mean to electrify the body? This means telling him electric charge, that is, add a certain number of electrons to it if we charge the body negatively, or subtract them from it if we charge the body positively. In both cases, the body will have a certain degree of electrification, i.e., one or another potential, and a body charged positively has a positive potential, and a body charged negatively has a negative potential.
Difference in electric charge levels two bodies are usually called electrical 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 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 zero) is numerically equal to the potential of this body.
So, if two bodies are charged in such a way that their potentials are unequal, a potential difference inevitably exists between them.
Everyone knows electrification phenomenon rubbing a comb against hair is nothing more than creating a potential difference between the comb and human hair.
Indeed, when a comb rubs against hair, some of the electrons transfer to the comb, charging it negatively, while the hair, having lost some electrons, becomes 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 hair with a comb. This reverse transition of electrons is easily detected by ear if an electrified comb is brought close to the ear. A characteristic crackling sound will indicate a discharge is occurring.
Speaking above about the potential difference, we meant two charged bodies, however A potential difference can also be obtained between different parts (points) of the same body.
So, for example, let's consider what will happen if, under the influence of some external force, we manage to move the free electrons located in the wire to one end of it. Obviously, at the other end of the wire there will be a shortage of electrons, 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 will immediately, due to the attraction of opposite charges, rush to the positively charged end of the wire, i.e., to the place where they are missing, and electrical equilibrium will again occur in the wire.
Electromotive force and voltage
D To maintain an electric current in a conductor, some external source of energy is needed, which would always maintain a potential difference at the ends of this conductor.
These energy sources 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.
Electromotive force (abbreviated EMF) is denoted by the letter E. The unit of measurement for EMF is the volt. In our country, the volt is abbreviated as “B”, and in the international designation – by the letter “V”.
So, to obtain a continuous flow, you need an electromotive force, that is, you need a source of electric current.
The first such source of current 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 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 electromotive force is created in this way are called chemical current sources.
Currently, chemical current sources are galvanic cells and batteries - widely used in electrical engineering and power engineering.
Another main source of current, widely used in all areas of electrical engineering and power engineering, are generators.
Generators are installed at power stations and serve as the only source of current to supply electricity to industrial enterprises, electric lighting of cities, electric railways, trams, subways, trolleybuses, etc.
Both with chemical sources of electric current (cells and batteries) and with generators, the action of 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 terminals are called current source poles. One pole of the current source always experiences a lack 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 using conductors to the poles of the current source, forming a closed electrical circuit. The potential difference that is established between the poles of a current source in a closed electrical circuit is called voltage and is designated by the letter U.
The unit of measurement for 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 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 it is open, the voltmeter will show the EMF of the current source. If you close the circuit, the voltmeter will no longer show the EMF, but the voltage at the terminals of the current source.
The EMF developed by a current source is always greater than the voltage at its terminals.
Let's consider the situation: charge q 0 enters an electrostatic field. This electrostatic field is also created by some charged body or system of bodies, but we are not interested in this. A force acts on the charge q 0 from the field, which can do work and move this charge in the field.
The work of the electrostatic field does not depend on the trajectory. The work done by the field when a charge moves along a closed path is zero. For this reason, electrostatic field forces are called conservative, and the field itself is called potential.
Potential
The "charge - electrostatic field" or "charge - charge" system has potential energy, just as the "gravitational field - body" system has potential energy.
A physical scalar quantity characterizing the energy state of the field is called potential a given point in the field. A charge q is placed in a field, it has potential energy W. Potential is a characteristic of an electrostatic field.
Let's remember potential energy in mechanics. Potential energy is zero when the body is on the ground. And when a body is raised to a certain height, it is said that the body has potential energy.
Regarding potential energy in electricity, there is no zero level of potential energy. It is chosen randomly. Therefore, potential is a relative physical quantity.
In mechanics, bodies tend to occupy a position with the least potential energy. In electricity, under the influence of field forces, a positively charged body tends to move from a point with a higher potential to a point with a lower potential, and a negatively charged body, vice versa.
Potential field energy is the work done by the electrostatic force when moving a charge from a given point in the field to a point with zero potential.
Let us consider the special case when an electrostatic field is created by an electric charge Q. To study the potential of such a field, there is no need to introduce a charge q into it. You can calculate the potential of any point in such a field located at a distance r from the charge Q.
The dielectric constant of the medium has a known value (tabular) and characterizes the medium in which the field exists. For air it is equal to unity.
Potential difference
The work done by a field to move a charge from one point to another is called potential difference
This formula can be presented in another form
Equipotential surface (line)- surface of equal potential. The work done to move a charge along an equipotential surface is zero.
Voltage
The potential difference is also called electrical voltage provided that external forces do not act or their effect can be neglected.
The voltage between two points in a uniform electric field located along the same line of intensity is equal to the product of the modulus of the field strength vector and the distance between these points.
The current in the circuit and the energy of the charged particle depend on the voltage.
Superposition principle
The potential of a field created by several charges is equal to the algebraic (taking into account the sign of the potential) sum of the potentials of the fields of each field separately
When solving problems, a lot of confusion arises when determining the sign of potential, potential difference, and work.
The figure shows tension lines. At which point in the field is the potential greater?
The correct answer is point 1. Let us remember that the tension lines begin on a positive charge, which means the positive charge is on the left, therefore the leftmost point has the maximum potential.
If a field is being studied that is created by a negative charge, then the field potential near the charge has a negative value; this can be easily verified if a charge with a minus sign is substituted into the formula. The further away from the negative charge, the greater the field potential.
If a positive charge moves along the tension lines, then the potential difference and work are positive. If a negative charge moves along the tension lines, then the potential difference has a “+” sign, and the work has a “-” sign.