Electrostatics- This is a branch of physics that studies the properties and interactions of electrically charged bodies or particles that are motionless relative to the inertial reference frame and have an electric charge.
Electric charge- this is a physical quantity that characterizes the property of bodies or particles to enter into electromagnetic interactions and determines the values of forces and energies during these interactions. In the International System of Units, the unit of electric charge is the pendant (C).
There are two types of electric charges:
- positive;
- negative.
A body is electrically neutral if the total charge of the negatively charged particles that make up the body is equal to the total charge of the positively charged particles.
Stable carriers of electric charges are elementary particles and antiparticles.
Positive charge carriers are proton and positron, and negative charge carriers are electron and antiproton.
The total electric charge of the system is equal to the algebraic sum of the charges of the bodies included in the system, i.e.:
Law of conservation of charge: in a closed, electrically isolated system, the total electric charge remains unchanged, no matter what processes take place inside the system.
isolated system- this is a system into which electrically charged particles or any bodies do not penetrate from the external environment through its boundaries.
Law of conservation of charge- this is a consequence of the conservation of the number of particles, a redistribution of particles in space takes place.
conductors- These are bodies that have electric charges that can move freely over considerable distances.
Examples of conductors: metals in solid and liquid states, ionized gases, electrolyte solutions.
Dielectrics- these are bodies that have charges that cannot move from one part of the body to another, that is, bound charges.
Examples of dielectrics: quartz, amber, ebonite, gases under normal conditions.
Electrification- this is such a process, as a result of which bodies acquire the ability to take part in electromagnetic interaction, that is, they acquire an electric charge.
Electrification of bodies- this is such a process of redistribution of electric charges in bodies, as a result of which the charges of the bodies become of opposite signs.
Types of electrification:
- Electrification due to electrical conductivity. When two metallic bodies come into contact, one charged and the other neutral, then a certain number of free electrons pass from the charged body to the neutral one if the body's charge was negative, and vice versa if the body's charge is positive.
As a result of this, in the first case, the neutral body will receive a negative charge, in the second - a positive one.
- Electrification by friction. As a result of contact during friction of some neutral bodies, electrons are transferred from one body to another. Electrification by friction is the cause of static electricity, discharges of which can be seen, for example, when combing your hair with a plastic comb or removing a synthetic shirt or sweater.
- Electrification through influence arises if a charged body is brought to the end of a neutral metal rod, while a violation of the uniform distribution of positive and negative charges occurs in it. Their distribution occurs in a peculiar way: an excess negative charge arises in one part of the rod, and a positive one in the other. Such charges are called induced, the occurrence of which is explained by the movement of free electrons in the metal under the action of the electric field of a charged body brought to it.
point charge is a charged body whose dimensions under given conditions can be neglected.
point charge is a material point that has an electric charge.
Charged bodies interact with each other in the following way: oppositely charged bodies attract, and similarly charged bodies repel.
Coulomb's law: the force of interaction of two point stationary charges q1 and q2 in vacuum is directly proportional to the product of the values of the charges and inversely proportional to the square of the distance between them:
The main property of the electric field is that an electric field exerts an influence on electric charges with some force. The electric field is a special case of the electromagnetic field.
electrostatic field is the electric field of stationary charges. The electric field strength is a vector quantity that characterizes the electric field at a given point. The field strength at a given point is determined by the ratio of the force acting on a point charge placed at a given point in the field to the magnitude of this charge:
tension is the power characteristic of the electric field; it allows you to calculate the force acting on this charge: F = qE.
In the International System of Units, the unit of tension is volts per meter. Tension lines are imaginary lines needed to use a graphic representation of an electric field. The tension lines are drawn so that the tangents to them at each point in space coincide in direction with the field strength vector at a given point.
The principle of superposition of fields: the field strength from several sources is equal to the vector sum of the field strengths of each of them.
electric dipole- this is a set of two equal in absolute value of opposite point charges (+q and -q), located at a certain distance from each other.
Dipole (electric) moment is a vector physical quantity, which is the main characteristic of the dipole.
In the International System of Units, the unit of dipole moment is the coulomb meter (C/m).
Types of dielectrics:
- Polar, which include molecules whose centers of distribution of positive and negative charges do not coincide (electric dipoles).
- non-polar, in molecules and atoms of which the centers of distribution of positive and negative charges coincide.
Polarization is the process that occurs when dielectrics are placed in an electric field.
Polarization of dielectrics- this is the process of displacement of the bound positive and negative charges of the dielectric in opposite directions under the action of an external electric field.
The dielectric constant is a physical quantity that characterizes the electrical properties of a dielectric and is determined by the ratio of the electric field strength modulus in vacuum to the strength modulus of this field inside a homogeneous dielectric.
The permittivity is a dimensionless quantity and is expressed in dimensionless units.
Ferroelectrics- this is a group of crystalline dielectrics that do not have an external electric field and instead of it there is a spontaneous orientation of the dipole moments of the particles.
Piezoelectric effect- this is an effect during mechanical deformations of some crystals in certain directions, where electrical opposite charges arise on their faces.
Electric field potential. Electrical capacity
Electrostatic potential- this is a physical quantity characterizing the electrostatic field at a given point, it is determined by the ratio of the potential energy of the interaction of the charge with the field to the value of the charge placed at a given point of the field: 
In the International System of Units, the unit of measurement is the volt (V).
The field potential of a point charge is determined by: 
Under the conditions if q > 0, then k > 0; if q
The principle of superposition of fields for potential: if an electrostatic field is created by several sources, then its potential at a given point in space is defined as the algebraic sum of the potentials:
The potential difference between two points of an electric field is a physical quantity determined by the ratio of the work of electrostatic forces to move a positive charge from the starting point to the final one to this charge: 
Equipotential surfaces- this is the geometric area of points of the electrostatic field, where the potential values are the same.
Electrical capacitance- This is a physical quantity that characterizes the electrical properties of a conductor, a quantitative measure of its ability to hold an electric charge.
The electrical capacitance of a solitary conductor is determined by the ratio of the charge of the conductor to its potential, while we assume that the potential of the conductor field is taken equal to zero at an infinitely distant point:
Ohm's law
Homogeneous section of the chain- This is the section of the circuit that does not have a current source. The voltage in such a section will be determined by the potential difference at its ends, i.e.: 
In 1826, the German scientist G. Ohm discovered a law that determines the relationship between the current strength in a homogeneous section of the circuit and the voltage across it: the current strength in a conductor is directly proportional to the voltage across it. , where G is the coefficient of proportionality, which is called in this law the electrical conductivity or conductivity of the conductor, which is determined by the formula.
Conductor conductivity is a physical quantity that is the reciprocal of its resistance.
In the International System of Units, the unit of electrical conductivity is the Siemens (Sm).
The physical meaning of Siemens: 1 cm is the conductivity of a conductor with a resistance of 1 ohm.
To obtain Ohm's law for a circuit section, it is necessary to substitute the resistance R in the formula above, instead of electrical conductivity, then:
Ohm's law for a circuit section: the current strength in a circuit section is directly proportional to the voltage on it and inversely proportional to the resistance of the circuit section.
Ohm's law for a complete circuit: the current strength in an unbranched closed circuit, including a current source, is directly proportional to the electromotive force of this source and inversely proportional to the sum of the external and internal resistances of this circuit:
Sign rules:
- If, when bypassing the circuit in the selected direction, the current inside the source goes in the direction of the bypass, then the EMF of this source is considered positive.
- If, when bypassing the circuit in the selected direction, the current inside the source flows in the opposite direction, then the EMF of this source is considered negative.
Electromotive Force (EMF)- this is a physical quantity that characterizes the action of external forces in current sources, this is the energy characteristic of the current source. For a closed loop, EMF is defined as the ratio of the work of external forces to move a positive charge along a closed loop to this charge: 
In the International System of Units, the unit of measure for EMF is the volt. With an open circuit, the EMF of the current source is equal to the electrical voltage at its terminals.
Joule-Lenz law: the amount of heat released by a conductor with current is determined by the product of the square of the current strength, the resistance of the conductor and the time it takes the current to pass through the conductor: 
When moving the electric field of the charge along the section of the circuit, it does work, which is determined by the product of the charge and the voltage at the ends of this section of the circuit:
DC power- this is a physical quantity that characterizes the rate of work performed by the field on the movement of charged particles along the conductor and is determined by the ratio of the work of the current over time to this period of time: 
Kirchhoff rules, which are used to calculate branched DC circuits, the essence of which is to find, by given resistances, sections of the circuit and the EMF of currents applied to them in each section.
The first rule is the node rule: the algebraic sum of the currents that converge at a node is the point at which there are more than two possible current directions, it is equal to zero
The second rule is the rule of circuits: in any closed circuit, in a branched electrical circuit, the algebraic sum of the products of the current strengths and the resistance of the corresponding sections of this circuit is determined by the algebraic sum of the EMF applied in it: 
A magnetic field- this is one of the manifestations of the electromagnetic field, the specificity of which is that this field affects only moving particles and bodies that have an electric charge, as well as magnetized bodies, regardless of the state of their movement.
Magnetic induction vector- this is a vector quantity that characterizes the magnetic field at any point in space, which determines the ratio of the force acting from the magnetic field on the conductor element with electric current to the product of the current strength and the length of the conductor element, equal in absolute value to the ratio of the magnetic flux through the cross section of the area to area of this cross section.
In the International System of Units, the unit of induction is the tesla (T).
Magnetic circuit is a collection of bodies or regions of space where a magnetic field is concentrated.
Magnetic flux (flux of magnetic induction)- this is a physical quantity, which is determined by the product of the modulus of the magnetic induction vector by the area of a flat surface and by the cosine of the angle between the normal vectors to the flat surface / the angle between the normal vector and the direction of the induction vector.
In the International System of Units, the unit of magnetic flux is the weber (Wb).
Ostrogradsky-Gauss theorem for the flux of magnetic induction: the magnetic flux through an arbitrary closed surface is zero:
Ohm's law for a closed magnetic circuit: 
Magnetic permeability- this is a physical quantity that characterizes the magnetic features of a substance, which is determined by the ratio of the modulus of the magnetic induction vector in the medium to the modulus of the induction vector at the same point in space in vacuum:
Magnetic field strength is a vector quantity that defines and characterizes the magnetic field and is equal to: 
Amp power is the force exerted by a magnetic field on a current-carrying conductor. The elemental force of Ampere is determined by the ratio:
Ampère's law: the modulus of force acting on a small piece of conductor through which current flows, from the side of a uniform magnetic field with induction making an angle with the element
Superposition principle: when at a given point in space, diverse sources form magnetic fields, the inductions of which are B1, B2, .., then the resulting field induction at this point is equal to: 
Gimlet rule or right screw rule: if the direction of the translational movement of the tip of the gimlet during screwing coincides with the direction of the current in space, then the direction of the rotational movement of the gimlet at each point coincides with the direction of the magnetic induction vector.
Biot-Savart-Laplace law: determines the magnitude and direction of the magnetic induction vector at any point of the magnetic field created in vacuum by a conductor element of a certain length with current: 
The movement of charged particles in electric and magnetic fields The Lorentz force is the force that affects a moving particle from the magnetic field: 
left hand rule:
- It is necessary to position the left hand so that the lines of magnetic induction enter the palm, and the outstretched four fingers are co-directed with the current, then the thumb bent 90 ° will indicate the direction of the Ampere force.
- It is necessary to position the left hand so that the lines of magnetic induction enter the palm, and four outstretched fingers coincide with the direction of the particle velocity with a positive particle charge or are directed in the direction opposite to the particle velocity with a negative particle charge, then the thumb bent by 90 ° will show the direction Lorentz force acting on a charged particle.
If there is a joint action on a moving charge of electric and magnetic fields, then the resulting force will be determined by: 
Mass spectrographs and mass spectrometers- These are instruments that are designed specifically for accurate measurements of the relative atomic masses of elements.
Faraday's law. Lenz's rule
Electromagnetic induction- this is a phenomenon that consists in the fact that an EMF of induction occurs in a conducting circuit located in an alternating magnetic field.
Faraday's Law: EMF of electromagnetic induction in the circuit is numerically equal and opposite in sign of the rate of change of the magnetic flux Ф through the surface bounded by this circuit: 
Induction current- this is the current that is formed if the charges under the action of the Lorentz forces begin to move.
Lenz's rule: the induction current that appears in a closed circuit always has such a direction that the magnetic flux created by it through the area bounded by the circuit tends to compensate for the change in the external magnetic field that caused this current.
How to use the Lenz rule to determine the direction of the inductive current:
Vortex field- this is a field in which the lines of tension are closed lines, the cause of which is the generation of an electric field by a magnetic one.
The work of the vortex electric field when moving a single positive charge along a closed fixed conductor is numerically equal to the induction EMF in this conductor.
Toki Foucault- these are large induction currents that appear in massive conductors due to the fact that their resistance is small. The amount of heat that is released per unit time by eddy currents is directly proportional to the square of the frequency of the change in the magnetic field.
Self-induction. Inductance
self induction- this is a phenomenon consisting in the fact that a changing magnetic field induces an EMF in the very conductor through which the current flows that forms this field.
The magnetic flux Ф of the circuit with current I is determined by:
Ф \u003d L, where L is the coefficient of self-induction (current inductance).
Inductance- this is a physical quantity, which is a characteristic of the EMF of self-induction that appears in the circuit when the current strength changes, is determined by the ratio of the magnetic flux through the surface bounded by the conductor to the direct current strength in the circuit:
In the International System of Units, the unit for inductance is the henry (H).
EMF of self-induction is determined by: 
The energy of the magnetic field is determined by:
The volumetric energy density of the magnetic field in an isotropic and non-ferromagnetic medium is determined by: 
Definition 1
Electrostatics is an extensive branch of electrodynamics that studies and describes electrically charged bodies at rest in a certain system.
In practice, there are two types of electrostatic charges: positive (glass on silk) and negative (ebonite on wool). The elementary charge is the minimum charge ($e = 1.6 ∙10^( -19)$ C). The charge of any physical body is a multiple of the whole number of elementary charges: $q = Ne$.
Electrification of material bodies is the redistribution of charge between bodies. Methods of electrification: touch, friction and influence.
The law of conservation of electric positive charge - in a closed concept, the algebraic sum of the charges of all elementary particles remains stable and unchanged. $q_1 + q _2 + q _3 + …..+ q_n = const$. The test charge in this case is a point positive charge.
Coulomb's law
This law was established experimentally in 1785. According to this theory, the force of interaction of two point charges at rest in a medium is always directly proportional product of positive modules and inversely the square of the total distance between them.
The electric field is a unique kind of matter that interacts between stable electric charges, is formed around charges, affects only charges.
Such a process of fixed point elements is completely subject to Newton's third law, and is considered the result of repulsion of particles from each other with the same force of attraction to each other. The relationship of stable electric charges in electrostatics is called the Coulomb interaction.
Coulomb's law is quite fair and accurate for charged material bodies, uniformly charged balls and spheres. In this case, the distances are mainly taken as the parameters of the centers of spaces. In practice, this law is well and quickly fulfilled if the magnitudes of the charged bodies are much less than the distance between them.
Remark 1
Conductors and dielectrics also act in an electric field.
The former represent substances containing free carriers of an electromagnetic charge. Inside the conductor, free movement of electrons can occur. These elements include solutions, metals and various melts of electrolytes, ideal gases and plasma.
Dielectrics are substances in which there can be no free carriers of electric charge. The free movement of electrons within the dielectrics themselves is impossible, since no electric current flows through them. It is these physical particles that have a permeability that is not equal to the dielectric unit.
Field lines and electrostatics
The lines of force of the initial strength of the electric field are continuous lines, the tangent points to which in each medium through which they pass completely coincide with the axis of tension.
The main characteristics of the lines of force:
- do not intersect;
- not closed;
- stable;
- the end direction is the same as the direction of the vector;
- start at $+ q$ or at infinity, end at $– q$;
- are formed near the charges (where there is more tension);
- perpendicular to the surface of the main conductor.
Definition 2
The electrical potential difference or voltage (Ф or $U$) is the magnitude of the potentials at the starting and ending points of the positive charge trajectory. The less the potential changes along the path, the lower the field strength as a result.
The electric field strength is always directed in the direction of decreasing the initial potential.
Figure 2. Potential energy of a system of electric charges. Author24 - online exchange of student papers
Electric capacity characterizes the ability of any conductor to accumulate the necessary electric charge on its own surface.
This parameter does not depend on the electric charge, however, it can be affected by the geometric dimensions of the conductors, their shape, location and properties of the medium between the elements.
A capacitor is a universal electrical device that helps to quickly accumulate an electric charge for transferring it to a circuit.
Electric field and its intensity
According to modern ideas of scientists, electric stable charges do not directly affect each other. Each charged physical body in electrostatics creates an electric field in the environment. This process has a forceful effect on other charged substances. The main property of an electric field is to act on point charges with a certain force. Thus, the interaction of positively charged particles is carried out through the fields that surround the charged elements.
This phenomenon can be investigated by means of the so-called test charge - a small electric charge that does not introduce a significant redistribution of the studied charges. For quantitative detection of the field, a force feature is introduced - the electric field strength.
The intensity is called a physical indicator, which is equal to the ratio of the force with which the field acts on the trial charge placed at a given point in the field to the magnitude of the charge itself.
The electric field strength is a vector physical quantity. The direction of the vector in this case coincides at each material point of the surrounding space with the direction of the force acting on the positive charge. The electric field of elements that do not change with time and are stationary is considered to be electrostatic.
To understand the electric field, lines of force are used, which are drawn in such a way that the direction of the main axis of tension in each system coincides with the direction of the tangent to the point.
Potential difference in electrostatics
An electrostatic field includes one important property: the work of the forces of all moving particles when moving a point charge from one point of the field to another does not depend on the direction of the trajectory, but is determined solely by the position of the initial and final lines and the charge parameter.
The result of the independence of work from the form of movement of charges is the following statement: the functional of the forces of the electrostatic field during the transformation of the charge along any closed trajectory is always equal to zero.
Figure 4. Potentiality of the electrostatic field. Author24 - online exchange of student papers
Property potentiality of the electrostatic field helps to introduce the concept of potential and internal energy of a charge. And the physical parameter equal to the ratio of the potential energy in the field to the magnitude of this charge is called the constant potential of the electric field.
In many complex problems of electrostatics, when determining potentials beyond a reference material point, where the magnitude of the potential energy and the potential itself vanish, it is convenient to use an infinitely distant point. In this case, the significance of the potential is defined as follows: the potential of the electric field at any point in space is equal to the work that internal forces perform when a positive unit charge is removed from a given system to infinity.
