Electrostatics -this is a branch of physics that studies the interaction and properties of systems of electric charges that are stationary relative to a chosen inertial frame of reference.

The whole variety of natural phenomena is based on four fundamental interactions between elementary particles

gravitational,

electromagnetic,

Electric charge - carrier electromagnetic interaction.

Fundamental properties of charges

1. Electric charge can be of two types: positive(when skin is rubbed against glass) and negative(during friction of fur with ebonite). Bodies with electric charges of the same sign repel each other, bodies with charges of opposite signs attract.

2. Carriers electric charge are charged elementary particles with elementary charge(Coulomb is the SI unit of electric charge)

proton is a positive charge carrier (+ e), (m p\u003d 1.6710 -27 kg);

electron – negative charge carrier (– e), (m e\u003d 9.1110 -31 kg).

The charge of any other body is an integer multiple of elementary electric charge.

3. The fundamental law of conservation of electric charge(performed in any processes of birth and destruction elementary particles): in any electrically isolated system, the algebraic sum of charges does not change .

4. Electric charge is relativistcki invariant: its value does not depend on the frame of reference, and therefore does not depend on whether it is moving or at rest.

So, to charge a body positively means to take away a certain number of electrons from it, and to charge it negatively means to give the body a certain number of extra electrons. Note that the charges of bodies of the order of 1 nC = 10 -9 C can already be considered quite significant. In order for a body to have such a charge, the number of electrons in it must differ from the number of protons by ! things.

Classification of bodies depending on the concentration of free charges

conductors(bodies with free movement of charges throughout the volume);

1. conductorsIkind- metals (charges move without chemical transformations);

   conductorsIIkind- electrolytes (the movement of charges is accompanied by chemical transformations);

Semiconductors(bodies with limited movement of charges);

Dielectrics(bodies in which there are practically no free charges);

The unit of electric charge Coulomb is a derivative of the unit of current, it is an electric charge passing through the cross section of the conductor at a current of 1 A in a time of 1 s (1Cl = 1A1s).

Coulomb's law. Dielectric permittivity and its physical meaning

Rice. 1. Scheme of interaction of point charges

, (1)

where k– coefficient of proportionality, depending on the choice of units of measure. In the SI system

- electrical constant.

Strength F called Coulomb force, it is an attractive force if the charges have different signs (Fig. 1), and a repulsive force if the charges are of the same sign.

If electric charges are placed inside the dielectric, then the strength of the electrical interaction decreases in accordance with the expression:

, (2)

where - dielectric permittivity of the medium, showing how many times the force of interaction of point charges in a dielectric is less than the force of their interaction in vacuum.

Dielectric Constant Values ​​for Some Substances

Electric charge- this is physical quantity characterizing the ability of particles or bodies to enter into electromagnetic interactions. Electric charge is usually denoted by the letters q or Q. In the SI system, electric charge is measured in Coulomb (C). A free charge of 1 C is a gigantic amount of charge, practically not found in nature. As a rule, you will have to deal with microcoulombs (1 μC = 10 -6 C), nanocoulombs (1 nC = 10 -9 C) and picocoulombs (1 pC = 10 -12 C). Electric charge has the following properties:

1. Electric charge is a kind of matter.

2. The electric charge does not depend on the movement of the particle and on its speed.

3. Charges can be transferred (for example, by direct contact) from one body to another. Unlike body mass, electric charge is not an inherent characteristic of a given body. The same body in different conditions can have a different charge.

4. There are two types of electric charges, conventionally named positive and negative.

5. All charges interact with each other. At the same time, like charges repel each other, unlike charges attract. The forces of interaction of charges are central, that is, they lie on a straight line connecting the centers of charges.

6. There is the smallest possible (modulo) electric charge, called elementary charge. Its meaning:

e= 1.602177 10 -19 C ≈ 1.6 10 -19 C

The electric charge of any body is always a multiple of the elementary charge:

where: N is an integer. Please note that it is impossible to have a charge equal to 0.5 e; 1,7e; 22,7e and so on. Physical quantities that can take only a discrete (not continuous) series of values ​​are called quantized. elementary charge e is the quantum (smallest portion) of electric charge.

7. The law of conservation of electric charge. In an isolated system, the algebraic sum of the charges of all bodies remains constant:

The law of conservation of electric charge states that closed system bodies, processes of the birth or disappearance of charges of only one sign cannot be observed. It also follows from the law of conservation of charge if two bodies of the same size and shape that have charges q 1 and q 2 (it doesn’t matter what sign the charges are), bring into contact, and then back apart, then the charge of each of the bodies will become equal:

From the modern point of view, charge carriers are elementary particles. All ordinary bodies are made up of atoms, which include positively charged protons, negatively charged electrons and neutral particles neutrons. Protons and neutrons are part of atomic nuclei, the electrons form electron shell atoms. The electric charges of the proton and electron modulo are exactly the same and equal to the elementary (that is, the minimum possible) charge e.

In a neutral atom, the number of protons in the nucleus is equal to the number of electrons in the shell. This number is called the atomic number. An atom of a given substance can lose one or more electrons, or acquire an extra electron. In these cases, the neutral atom turns into a positively or negatively charged ion. Please note that positive protons are part of the nucleus of an atom, so their number can only change during nuclear reactions. Obviously, when electrifying bodies nuclear reactions not happening. Therefore, in any electrical phenomena, the number of protons does not change, only the number of electrons changes. So, giving a body a negative charge means transferring extra electrons to it. And the message of a positive charge, contrary to a common mistake, does not mean the addition of protons, but the subtraction of electrons. Charge can be transferred from one body to another only in portions containing an integer number of electrons.

Sometimes in problems the electric charge is distributed over some body. To describe this distribution, the following quantities are introduced:

1. Linear charge density. Used to describe the distribution of charge along the filament:

where: L- thread length. Measured in C/m.

2. Surface charge density. Used to describe the distribution of charge over the surface of a body:

where: S is the surface area of ​​the body. Measured in C / m 2.

3. Bulk charge density. Used to describe the distribution of charge over the volume of a body:

where: V- volume of the body. Measured in C / m 3.

Please note that electron mass is equal to:

me\u003d 9.11 ∙ 10 -31 kg.

Coulomb's law

point charge called a charged body, the dimensions of which can be neglected under the conditions of this problem. Based on numerous experiments, Coulomb established the following law:

The forces of interaction of fixed point charges are directly proportional to the product of charge modules and inversely proportional to the square of the distance between them:

where: ε – dielectric permittivity of the medium – a dimensionless physical quantity showing how many times the force of electrostatic interaction in a given medium will be less than in vacuum (that is, how many times the medium weakens the interaction). Here k- coefficient in the Coulomb law, the value that determines the numerical value of the force of interaction of charges. In the SI system, its value is taken equal to:

k= 9∙10 9 m/F.

The forces of interaction of point motionless charges obey Newton's third law, and are the forces of repulsion from each other at the same signs charges and forces of attraction to each other with different signs. The interaction of fixed electric charges is called electrostatic or Coulomb interaction. The section of electrodynamics that studies the Coulomb interaction is called electrostatics.

Coulomb's law is valid for point charged bodies, uniformly charged spheres and balls. In this case, for distances r take the distance between the centers of spheres or balls. In practice, Coulomb's law is well fulfilled if the dimensions of the charged bodies are much smaller than the distance between them. Coefficient k in the SI system is sometimes written as:

where: ε 0 \u003d 8.85 10 -12 F / m - electrical constant.

Experience shows that the forces of the Coulomb interaction obey the principle of superposition: if a charged body interacts simultaneously with several charged bodies, then the resulting force acting on this body is equal to vector sum forces acting on this body from all other charged bodies.

Remember also two important definitions:

conductors- substances containing free carriers of electric charge. Inside the conductor it is possible free movement electrons - charge carriers (on conductors can flow electricity). Conductors include metals, electrolyte solutions and melts, ionized gases, and plasma.

Dielectrics (insulators)- substances in which there are no free charge carriers. The free movement of electrons inside dielectrics is impossible (electric current cannot flow through them). It is dielectrics that have a certain permittivity not equal to unity ε .

For the permittivity of a substance, the following is true (about what an electric field is a little lower):

Electric charge and its main properties.

The law of conservation of electric charge.

Electric charge is a scalar physical quantity that determines the intensity electromagnetic interactions. The unit of charge is [q] pendant.

Electric charge properties:

1. Electric charge is not a definite quantity, there are both positive and negative charges.

2. Electric charge- the value is invariant. It does not change when the charge carrier moves.

3. Electric charge additive.

4. Electric charge multiple of elementary. q = Ne. This property of charge is called discreteness (quantization).

5. Total electric charge any isolated system is saved. This property is the law of conservation of electric charge.

The law of conservation of electric charge - electric charges are not created and do not disappear, but are only transferred from one body to another or redistributed within the body.

Electrostatics. point charge. Coulomb's law. The principle of superposition of forces. Volume surface and linear charge density.

Electrostatics- a section of the doctrine of electricity that studies the interaction of motionless electric charges.

point charge is a charged body, size and shape, which can be neglected.

The formulation of Coulomb's law: The strength of the electrostatic interaction between two point electric charges is directly proportional to the product of the magnitudes of the charges, inversely proportional to the square of the distance between them and is directed along the straight line connecting them so that like charges repel and unlike charges attract.

The principle of superposition of forces is that the action of several forces can be replaced by the action of one - the resultant. The resultant is the only force, the result of which is equivalent to the simultaneous action of all the forces applied to this body.

Linear charge density: charge per unit length.

Surface charge density: the charge per unit area.

Volumetric charge density: the charge per unit volume.

tension electric field. lines of force electrostatic field. The field strength of the stationary point charge. electrostatic field. The principle of superposition.

Electric field strength- a vector physical quantity characterizing the electric field at a given point and numerically equal to the ratio of the force acting on a fixed point charge placed in given point field, to the value of this charge q.

Electrostatic field lines have the following properties:

1. Always open: start with positive charges(or at infinity) and end with negative charges(or at infinity).

2 . They do not intersect or touch each other.

3 . The density of lines is the greater, the greater the intensity, that is, the field strength is directly proportional to the number lines of force passing through a platform of unit area located perpendicular to the lines.

Potentiality of the electrostatic field. Circulation of the field of the vector E. The theorem on the circulation of the vector E of the electrostatic field in int. and diff. forms and their content.

Since the principle of superposition is valid for the strength of the electrostatic field, then any electrostatic field is potential.

The theorem on the circulation of the vector E of the electrostatic field: Circulation E in a closed loop, L is always zero.

In diff. form:

The electrostatic field is potential.

Potential energy point charge in an electrostatic field. The potential of the electrostatic field. equipotential surfaces. Potential of the field of a point immobile charge. Superposition principle for potential.

The potential energy of a charge in a uniform electrostatic field is:

Potential - scalar value, is the energy characteristic of the field at a given point and is equal to the ratio of the potential energy possessed by the test charge to this charge.

Equipotential surface is the surface on which the potential of a given field takes on the same value.

Field potential of a point immobile charge:

Superposition principle for potentials- The potential of the field created by the GRU with a number of charges at an arbitrary point is equal to the sum of the potentials of the fields created by each charge.

moment

and acquires potential energy

The dipole has:

minimum sweat. energy:

in position (position of stable equilibrium);

maximum sweat. energy:

in position (position of unstable equilibrium);

In all other cases, a moment of forces arises, turning the dipole into a position of stable equilibrium.

In an external inhomogeneous electrostatic field, a moment of forces acts on a point dipole and this dipole has a potential energy

The force acting on a point dipole in a nonuniform. email stat. field:

In the external heterogeneous email. stat. The field of a point dipole under the simultaneous action of the moment of forces rotates in the direction of the field and force, moves in the direction where the modulus is greater (it stretches towards a stronger field).

In the conductor.

In the conductor there are free. charges - current carriers, capable of moving under the influence of an arbitrarily small force. throughout the conductor.

Electrostatic induction is the phenomenon of redistribution of charges on the surface of a conductor under the action of a stor. electrostatic field.

Redistribution charges stop., when any point of the conductor will be fulfilled. condition:

Because , then the strength of the electrostatic field at any point inside the conductor:

Because then

- the potential of the conductor is the same. in all its internal points and on the surface

Conditions for stationary distribution of charges in a conductor:

2.Ed. there are no charges inside the conductor, and the induced charges are distributed

on its surface ()

3. Near the outer side of the surface. conductor vector is directed along the normal to this

surface at each point ()

4. The entire volume of the conductor is yavl. equipotential region, and its surface is equipotential

Circuit with current in a magnetic field. The moment of forces acting on a circuit with current, and the potential energy of a circuit with current in a uniform magnetic field. The work of forces magnetic field when moving a circuit with current.

Magnetic moment line current I, going along a closed flat contour (all points of which lie in the same plane):

S is the surface area bounded by the contour; in SI = A*

The resulting Ampère force acting on a current-carrying circuit in a uniform magnetic field is 0.

Therefore, the total moment of ampere forces does not depend on the choice of point O, relative to which it is calculated:

Moment of forces acting on a closed circuit with current I in a magnetic field of induction:

When M=0 (i.e., the current-carrying circuit is in the equilibrium position).

When the maximum moment of forces acts on the contour.

Potential energy of a closed loop with current in a magnetic field:

The work of the Ampere forces:

In this case, the direction of the positive normal forms a right-handed system. This formula is valid in the case of arbitrary displacement of a contour of any shape in a magnetic field.

29. Magnetic field in matter. Magnetization of dia- and paramagnets. Magnetization vector . Vector field circulation theorem in the integral and differential form.

Any substance is magnetic (i.e., capable of being magnetized under the influence of an external magnetic field)

Conduction current (I, ) is the current due to the directed movement of current carriers in the substance.

Molecular currents () - currents associated with the orbital motion and spin of elementary particles in the atoms of matter. Every molecular current has a magnetic moment.

Diamagnets are substances whose magnetic moments of atoms in the absence of an external magnetic field are equal to zero, i.e. magnetic moments of all elementary particles of an atom (molecule) are compensated.

Paramagnets are substances whose atoms in the absence of an external magnetic field have a non-zero magnetic moment, but their direction is randomly oriented, therefore.

When a diamagnet is introduced into an external magnetic field, an additional moment is induced in each of its atoms, directed against the external magnetic field.

When a paramagnet is introduced into an external magnetic field, the magnetic moment of its atoms (molecules) becomes oriented in the direction of the external field.

The magnetization of a substance is due to the predominant orientation or induction of individual molecules in one direction. The magnetization of a substance leads to the appearance of magnetization currents (molecular currents averaged over the macroscopic region):

where is the density vector of the magnetizing current passing through the oriented surface S.

According to the principle of superposition:

where is the induction of the external field;

Magnetic field induction of magnetizing currents.

The magnetization vector is quantitative characteristic magnetized state of a substance, equal to the ratio of the total magnetic moment of a physically small volume of a magnet for this volume:

In SI [J] = A/m.

The magnetostatic field vector circulation theorem in differential form:

at any point of the magnetostatic field, the rotor of the vector is equal to the magnetization current density vector at the same point.