Graphical representation of the electric field. School Encyclopedia
1. Vector lines. For a graphical representation of electrostatic fields, vector lines are used - they are drawn so that at each point of the line the vector is directed tangentially to it (Fig. 3.6). The lines do not intersect anywhere, they start on positive charges, end on negative charges, or go to infinity. Examples of a graphical representation of the fields of point charges are shown in Fig. 3.6, b, c, d. It's clear that
for a single point charge, the lines are straight lines leaving or entering the charge. In the case of a homogeneous electric field(Fig. 3.6, e), at each point of which the vector is the same both in absolute value and in direction, the lines are straight lines parallel to each other and spaced from each other at the same distance.
The graphic representation of the fields using lines makes it possible to visually see the direction of the Coulomb force acting on a point charge placed at a given point in the field, which is convenient for a qualitative analysis of the behavior of the charge.
Usually, the lines are drawn in such a way that their density (the number of lines penetrating a flat surface of a fixed area perpendicular to them) at each point of the field determines numerical value vector . Therefore, according to the degree of proximity of the lines to each other, one can judge the change in the modulus and, accordingly, the change in the modulus of the Coulomb force acting on a charged particle in electric field.
2. Equipotential surfaces. An equipotential surface is a surface of equal potential, at each point of the surface the potential φ remains constant. Therefore, the elementary work of moving the charge q on such a surface will be equal to zero: . It follows from this that the vector at each point of the surface will be perpendicular to it, i.e. will be directed along the normal vector (Fig. 3.6, d). Indeed, if this were not the case, then there would be a component of the vector () directed tangentially to the surface, and, consequently, a potential in different points surfaces would be different ( 
¹const), which contradicts the definition of an equipotential surface.
Figure 3.6 shows a graphical representation of electric fields using equipotential surfaces (dashed lines) for a point charge (Figure 3.6, b, c, these are spheres in the center of which there is a point charge), for a field created simultaneously by negative and positive charges ( Fig. 3.6, d), for a uniform electric field (Fig. 3.6, e, these are planes perpendicular to the lines).
We agreed to draw equipotential surfaces so that the potential difference between adjacent surfaces was the same. This allows you to visually see the change potential energy charge as it moves in an electric field.
The fact that the vector is perpendicular to the equipotential surface at each of its points makes it quite easy to switch from the graphic representation of the electric field using lines to equipotential surfaces and vice versa. So, by drawing dotted lines in Fig. 3.6, b, c, d, e, perpendicular to the lines, you can get a graphic image of the field using equipotential surfaces in the plane of the picture.
1. Electric charge. Coulomb's law.
2. Electric field. Tension, potential, potential difference. Graphic representation of electric fields.
3. Conductors and dielectrics, relative permittivity.
4. Current, current strength, current density. Thermal action current.
5. Magnetic field, magnetic induction. Power lines. Action magnetic field for conductors and charges. The action of a magnetic field on a circuit with current. Magnetic permeability.
6. Electromagnetic induction. Toki Fuko. Self-induction.
7. Capacitor and inductor. Energy of electric and magnetic fields.
8. Basic concepts and formulas.
9. Tasks.
The characteristics of the electric and magnetic fields that are created by biological systems or act on them are a source of information about the state of the organism.
10.1. Electric charge. Coulomb's Law
The charge of a body is made up of the charges of its electrons and protons, whose own charges are the same in magnitude and opposite in sign (e = 1.67x10 -19 C).
Bodies in which the number of electrons and protons is the same are called uncharged.
If for some reason the equality between the number of electrons and protons is violated, the body is called charged and its electric charge is given by
Coulomb's law
Interaction motionless point charges obey Coulomb's law and called Coulomb or electrostatic.
The power of interaction two fixed point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them:
10.2. Electric field. Tension, potential, potential difference. Graphical representation of electric fields
Electric field is a form of matter through which the interaction between electric charges is carried out.
The electric field is created by charged bodies. The power characteristic of the electric field is a vector quantity called the field strength.
Electric field strength(E) at some point in space is equal to the force acting on a unit point charge placed at this point:
Potential, potential difference
When moving a charge from one point of the field to another, the field forces do work that does not depend on the shape of the path. To calculate this work, a special physical quantity is used, called potential.
Graphical representation of electric fields
For a graphical representation of the electric field, use lines of force or equipotential surfaces(usually one or the other). force line- a line, the tangents to which coincide with the direction of the tension vector at the corresponding points.
The density of field lines is proportional to the field strength. Equipotential surface- a surface, all points of which have the same potential.
These surfaces are carried out so that the potential difference between adjacent surfaces is constant.
Rice. 10.1. Field lines and equipotential surfaces of charged spheres
The lines of force are perpendicular to the equipotential surfaces.
Figure 10.1 shows lines of force and equipotential surfaces for the fields of charged spheres.
Figure 10.2, a shows lines of force and equipotential surfaces for a field created by two plates, the charges of which are the same in magnitude and opposite in sign. Figure 10.2, b shows the lines of force and equipotential surfaces for the Earth's electric field near standing man.
Rice. 10.2. Electric field of two plates (a); electric field of the Earth near a standing person (b).
10.3. Conductors and dielectrics, relative permittivity
Substances that have free charges are called conductors.
The main types of conductors are metals, electrolyte solutions and plasma. In metals, free charges are the electrons of the outer shell separated from the atom. In electrolytes, the free charges are the ions of the solute. In plasma, free charges are electrons that are separated from atoms when high temperatures, and positive ions.
Substances that do not have free charges are called dielectrics.
All gases are dielectrics. low temperatures, resins, rubber, plastics and many other non-metals. Dielectric molecules are neutral, but the centers of positive and negative charges do not coincide. Such molecules are called polar and are depicted as dipoles. Figure 10.3 shows the structure of a water molecule (H 2 O) and its corresponding dipole.
Rice. 10.3. The water molecule and its image as a dipole
If there is a conductor in the electrostatic field (charged or uncharged - it does not matter), then the free charges are redistributed in such a way that the electric field created by them compensates outer field. Therefore, the electric field strength inside the conductor equals zero.
If a dielectric is in an electrostatic field, then its polar molecules "tend" to settle down along the field. This leads to a decrease in the field inside the dielectric.
The dielectric constant (ε) - a dimensionless scalar value showing how many times the electric field strength in the dielectric decreases compared to the field in vacuum:
10.4. Current, current strength, current density. Thermal effect of current
electric shock called the ordered movement of free charges in matter. The direction of current is taken as the direction of movement positive charges.
An electric current occurs in a conductor, between the ends of which an electric voltage (U) is maintained.
Quantitatively, the electric current is characterized using a special quantity - current strength.
current strength in a conductor is called a scalar quantity showing what charge passes through the cross section of the conductor in 1 s.
In order to show the distribution of current in conductors of complex shape, use the current density (j).
current density in the conductor is equal to the ratio of the current strength to the cross-sectional area of the conductor:
Here R is a characteristic of the conductor, called resistance. Unit of measurement - Ohm.
The resistance value of a conductor depends on its material, shape and size. For a cylindrical conductor, the resistance is directly proportional to its length (l) and inversely proportional to the cross-sectional area (S):
The coefficient of proportionality ρ is called specific electrical resistance conductor material; its dimension is ohm.
The flow of current through the conductor is accompanied by the release of heat Q. The amount of heat released in the conductor during time t is calculated by the formulas
The thermal effect of the current at a certain point of the conductor is characterized by specific thermal power q.
Specific thermal power - the amount of heat released per unit volume of the conductor per unit time.
To find this value, you need to calculate or measure the amount of heat dQ released in a small neighborhood of the point, and then divide it by the time and volume of the neighborhood:
where ρ is the resistivity of the conductor.
10.5. Magnetic field, magnetic induction. Power lines. Magnetic permeability
A magnetic field is a form of matter through which the interaction of moving electric charges is carried out.
In the microcosm, magnetic fields are created individual moving charged particles. At chaotic movement of charged particles in matter, their magnetic fields compensate each other and the magnetic field in the macrocosm does not occur. If the movement of particles in a substance is somehow arrange, the magnetic field also appears in the macrocosm. For example, a magnetic field arises around any current-carrying conductor. The special ordered rotation of electrons in some substances also explains the properties of permanent magnets.
The force characteristic of the magnetic field is the vector magnetic inductionb. Unit of magnetic induction - tesla(Tl).
lines of force
The magnetic field is graphically represented using lines of magnetic induction(magnetic lines of force). Tangents to lines of force show the direction of the vector AT at the respective points. The density of lines is proportional to the modulus of the vector AT. Unlike lines of force electrostatic field, the lines of magnetic induction are closed (Fig. 10.4).
Rice. 10.4. Magnetic lines of force
The action of a magnetic field on conductors and charges
Knowing the value of magnetic induction (V) in this place, you can calculate the force acting from the magnetic field on a current-carrying conductor or a moving charge.
a) ampere power, acting on straight section current-carrying conductor, perpendicular to both direction B and current-carrying conductor (Fig. 10.5, a):
where I is the current strength; l- conductor length; α is the angle between the direction of the current and the vector B.
b) Lorentz force, acting on a moving charge, is perpendicular to both the direction B and the direction of the charge velocity (Fig. 10.5, b):
where q is the amount of charge; v- its speed; α - angle between direction v and V.
Rice. 10.5. Ampere (a) and Lorentz forces (b).
Magnetic permeability
Just as a dielectric placed in an external electric field polarized and creates its own electric field, any substance placed in an external magnetic field, magnetized and creates its own magnetic field. Therefore, the magnitude of the magnetic induction inside the substance (B) differs from the magnitude of the magnetic induction in vacuum (B 0). The magnetic induction in a substance is expressed in terms of the magnetic field induction in vacuum by the formula
where μ is the magnetic permeability of the substance. For vacuum μ = 1
Magnetic permeability of a substance(μ) is a dimensionless quantity showing how many times the magnetic field induction in a substance changes compared to the magnetic field induction in vacuum.
According to the ability to magnetize, substances are divided into three groups:
1) diamagnets, for which μ< 1 (вода, стекло и др.);
2) paramagnets, in which μ > 1 (air, ebonite, etc.);
3) ferromagnets, for which μ >>1 (nickel, iron, etc.).
For dia- and paramagnets, the difference in magnetic permeability from unity is very insignificant (~0.0001). The magnetization of these substances when removed from a magnetic field disappears.
In ferromagnets, the magnetic permeability can reach several thousand (for example, in iron, μ \u003d 5,000-10,000). When removed from the magnetic field, the magnetization of ferromagnets is partially is saved. Ferromagnets are used to make permanent magnets.
10.6. Electromagnetic induction. Toki Fuko. self induction
In a closed conducting circuit placed in a magnetic field, under certain conditions, an electric current arises. To describe this phenomenon, a special physical quantity is used - magnetic flux. The magnetic flux through the contour of the area S, the normal of which (n) forms an angle α with the direction of the field (Fig. 10.6), is calculated by the formula
Rice. 10.6. Magnetic flux through the loop
Magnetic flux is a scalar quantity; unit weber[Wb].
According to Faraday's law, with any change in the magnetic flux penetrating the circuit, an electromotive force arises in it E(emf of induction), which is equal to the rate of change of the magnetic flux penetrating the circuit:
emf induction occurs in a circuit that is in variable magnetic field or revolves in a constant magnetic field. In the first case, the change in the flux is due to a change in the magnetic induction (B), and in the second case, it is due to a change in the angle α. The rotation of a wireframe between the poles of a magnet is used to generate electricity.
Toki Foucault
In some cases, electromagnetic induction manifests itself even in the absence of a specially created circuit. If in variable If there is a conducting body in the magnetic field, then eddy currents arise throughout its volume, the flow of which is accompanied by the release of heat. Let us explain the mechanism of their occurrence using the example of a conducting disk located in a changing magnetic field. A disk can be thought of as a "set" of nested closed loops. On fig. 10.7 nested contours are circular segments between
Rice. 10.7. Foucault currents in a conducting disk located in a uniform alternating magnetic field. The direction of the currents corresponds to the increase in V
circles. When the magnetic field changes, the magnetic flux also changes. Therefore, the current shown by the arrow is induced in each circuit. The totality of all such currents is called Foucault currents.
In technology, Foucault currents have to be fought (energy losses). However, in medicine, these currents are used to warm tissues.
self induction
Phenomenon electromagnetic induction can also be observed when external there is no magnetic field. For example, if you skip along a closed loop variable current, then it will create an alternating magnetic field, which, in turn, will create an alternating magnetic flux through the circuit, and emf will appear in it.
Self induction is called the emergence electromotive force in the circuit through which alternating current.
The electromotive force of self-induction is directly proportional to the rate of change in the current strength in the circuit:
The “-” sign means that the self-induction emf prevents a change in the current strength in the circuit. The proportionality factor L is a characteristic of the circuit, called inductance. Unit of inductance - henry (Gn).
10.7. Capacitor and inductor. Energy of electric and magnetic fields
In radio engineering, special devices are used to create electric and magnetic fields concentrated in a small area of \u200b\u200bspace - capacitors and inductors.
Capacitor It consists of two conductors separated by a dielectric layer, on which charges of the same magnitude and opposite in sign are placed. These conductors are called plates capacitor.
Capacitor charge is called the charge of the positive plate.
The plates have the same shape and are located at a distance that is very small compared to their dimensions. In this case, the electric field of the capacitor is almost completely concentrated in the space between the plates.
electrical capacitance capacitor is the ratio of its charge to the potential difference between the plates:
Capacity unit - farad(F \u003d Cl / V).
A flat capacitor consists of two parallel plates of area S, separated by a dielectric layer of thickness d with permittivity ε. The distance between the plates is much less than their radii. The capacitance of such a capacitor is calculated by the formula:
Inductor is a wire coil with a ferromagnetic core (to enhance the magnetic field). The diameter of the coil is much smaller than its length. In this case, the magnetic field created by the flowing current is almost completely concentrated inside the coil. The ratio of magnetic flux (F) to current strength (I) is a characteristic of the coil, called its inductance(L):
Unit of inductance - Henry(Hn = Wb/A).
Energy of electric and magnetic fields
Electric and magnetic fields are material and therefore have energy.
The energy of the electric field of a charged capacitor:
where I is the current in the coil; L is its inductance.
10.8. Basic concepts and formulas
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10.9. Tasks
1. What force attracts charges of 1 C, located at a distance of 1 m from each other?
Solution
According to the formula (10.1) we find: F \u003d 9 * 10 9 * 1 * 1/1 \u003d 9x10 9 N. Answer: F \u003d 9x10 9 N.
2. With what force does the nucleus of an iron atom (serial number 26) attract an electron on the inner shell with a radius of r = 1x10 -12 m?
Solution
Nuclear charge q = +26e. We find the force of attraction by the formula (10.1). Answer: F = 0.006 N.
3. Estimate the electric charge of the Earth (it is negative) if the electric field strength at the Earth's surface is E = 130 V/m. The radius of the Earth is 6400 km.
Solution
The field strength near the Earth is the field strength of the charged sphere:
E \u003d k * q | / R 2, where k \u003d 1/4πε 0 \u003d 910 9 Nm 2 / C 2.
From here we find |q| = ER 2 /k = )
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