The session is approaching, and it's time for us to move from theory to practice. Over the weekend, we sat down and thought that many students would do well to have a collection of basic physics formulas handy. Dry formulas with explanation: short, concise, nothing more. A very useful thing when solving problems, you know. Yes, and at the exam, when exactly what was cruelly memorized the day before can “jump out” of my head, such a selection will serve you well.
Most of the tasks are usually given in the three most popular sections of physics. This is Mechanics, thermodynamics and Molecular physics, electricity. Let's take them!
Basic formulas in physics dynamics, kinematics, statics
Let's start with the simplest. Good old favorite rectilinear and uniform movement.
Kinematic formulas:
Of course, let's not forget about the movement in a circle, and then move on to the dynamics and Newton's laws.
After the dynamics, it's time to consider the conditions for the equilibrium of bodies and liquids, i.e. statics and hydrostatics
Now we give the basic formulas on the topic "Work and energy". Where would we be without them!
Basic formulas of molecular physics and thermodynamics
Let's finish the section of mechanics with formulas for vibrations and waves and move on to molecular physics and thermodynamics.
Efficiency, Gay-Lussac's law, the Clapeyron-Mendeleev equation - all these sweet formulas are collected below.
By the way! There is a discount for all our readers 10% on the .
Basic formulas in physics: electricity
It's time to move on to electricity, although thermodynamics loves it less. Let's start with electrostatics.
And, to the drum roll, we finish with the formulas for Ohm's law, electromagnetic induction and electromagnetic oscillations.
That's all. Of course, a whole mountain of formulas could be given, but this is useless. When there are too many formulas, you can easily get confused, and then completely melt the brain. We hope that our cheat sheet of basic formulas in physics will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or have not found the formula you need: ask the experts student service. Our authors keep hundreds of formulas in their heads and click tasks like nuts. Contact us, and soon any task will be "too tough" for you.
Electricity and magnetism formulas.
Coulomb's Law
1. Coulomb's law
2 . electric field strength
3.
point charge field strength modulus
4 . superposition principle
5. -electric moment vector of the dipole - dipole moment
6. 
2. Gauss's theorem
7
8.
9.
Gauss theorem
10. 
Gauss theorem
11.
12.
- field divergence
13
Electrostatic field potential
14.
- the work of the forces of the electrostatic field on the movement of the test charge q in the electric field of a point charge Q
15. - integral sign of the potentiality of the electrostatic field
16.
- increment of the potential of the electrostatic field
17
. 
- decrease in the potential of the electrostatic field
18 . - potential normalization (selection of reference point)
19 . - superposition principle for
20. - quasi-static work of field forces when moving
along an arbitrary path from v.1 to v.2
21. - local relation between and
22. - potential of a point charge
23. - dipole potential
24. 
is the Hamilton differential operator ("nabla") in polar coordinate system
25
. 
- Laplace operator or Laplacian
26. - Laplace equation
27. - Poisson's equation
4. Energy in electrostatics.
28. - energy of electrostatic interaction of charges with each other
29
. 
- total electrostatic energy of a charged body
30. - volumetric energy density (energy localized in a unit volume)
31. - interaction energy of a point dipole with an external field
5. Electrostatic Conductors
32. - field near the surface of the conductor
33.
- electric capacity of a solitary conductor
34. - capacitance of a flat capacitor
35 . - capacitance of a spherical capacitor formed by spherical conductive surfaces of radii a and b
36
. 
- capacitor energy
6. Electrostatic field in dielectrics
37. , - dielectric susceptibility of the substance
38. - polarization (electric dipole moment per unit volume of a substance)
39. - relationship between tension and polarization
40 . Gauss' theorem for a vector in integral form
41. - Gauss's theorem for a vector in differential form
42. - boundary conditions for the vector
43.
- Gauss's theorem for a vector in dielectrics
44 . - electrical displacement
45. - integral and local Gauss theorem for vector
46. - boundary conditions for the vector , where is the surface density of external charges
47.
- communication and for isotropic media
D.C
48. - current strength
49 . - the charge passing through the cross section of the conductor
50. - continuity equation (law of conservation of charge)
51. - continuity equation in differential form
52
. 
- the potential difference for a conductor in which external forces do not act is identified with the voltage drop
53. - Ohm's law
54.
- Joule-Lenz law
55. - resistance of a wire made of a homogeneous material of the same thickness
56. - Ohm's law in differential form
57 . - the reciprocal of resistivity is called electrical conductivity
58 . - Joule-Lenz law in differential form
59.
- the integral form of Ohm's law, taking into account the field of external forces for a circuit section containing EMF.
60 . Kirchhoff's first law. The algebraic sum of the current strengths for each node in a branched circuit is zero.
61. Kirchhoff's second law. The sum of the voltages along any closed circuit of the circuit is equal to the algebraic sum of the EMF acting in this circuit.
62
. 
- specific thermal current power in an inhomogeneous conducting medium
Law of Bio-Savart
63
. 
- Lorentz force
64 . - if in some reference frame the electromagnetic field is electric
(i.e. ), then in another frame of reference , moving relative to K with a speed , the components of the electromagnetic field are nonzero and are related by the relation 64
65 . - if in some frame of reference an electrically charged body has a speed , then the electric and magnetic components of the electromagnetic field created by its charge are related in this frame of reference by the relation
66 . - if in some reference frame the electromagnetic field is magnetic (), then in any other reference frame moving at a speed relative to the first one, the components and the electromagnetic field are non-zero and are related by the relation
67.
-
magnetic field induction of a moving charge
68
. 
-
magnetic constant
6.
2. Gauss's theorem
7 . - field flow through an arbitrary surface
8. - the principle of additivity of flows
9.
Gauss theorem
10. Gauss theorem
11.
is the Hamilton differential operator ("nabla") in Cartesian coordinate system
12.
- field divergence
13 . local (differential) Gauss theorem
Charged bodies are capable of creating, in addition to electric, another kind of field. If the charges move, then a special kind of matter is created in the space around them, called magnetic field. Therefore, an electric current, which is an ordered movement of charges, also creates a magnetic field. Like the electric field, the magnetic field is not limited in space, it propagates very quickly, but still with a finite speed. It can only be detected by its effect on moving charged bodies (and, as a result, currents).
To describe the magnetic field, it is necessary to introduce the force characteristic of the field, similar to the intensity vector E electric field. Such a characteristic is the vector B magnetic induction. In the SI system of units, 1 Tesla (T) is taken as a unit of magnetic induction. If in a magnetic field with induction B place the conductor length l with current I, then a force called by the power of Ampere, which is calculated by the formula:
where: AT– magnetic field induction, I is the current in the conductor, l- its length. The Ampere force is directed perpendicular to the magnetic induction vector and the direction of the current flowing through the conductor.
To determine the direction of the Ampère force, one usually uses left hand rule: if you position your left hand so that the lines of induction enter the palm, and the outstretched fingers are directed along the current, then the retracted thumb will indicate the direction of the Ampère force acting on the conductor (see figure).
If the angle α between the directions of the vector of magnetic induction and the current in the conductor is different from 90 °, then to determine the direction of the Ampère force, it is necessary to take the component of the magnetic field, which is perpendicular to the direction of the current. It is necessary to solve the problems of this topic in the same way as in dynamics or statics, i.e. by writing the forces along the coordinate axes or by adding the forces according to the rules of vector addition.
The moment of forces acting on the loop with current
Let the loop with current be in a magnetic field, and the plane of the loop is perpendicular to the field. The Ampere forces will compress the frame, and their resultant will be equal to zero. If you change the direction of the current, then the Ampere forces will change their direction, and the frame will not shrink, but stretch. If the lines of magnetic induction lie in the plane of the frame, then a torque of the Ampère forces arises. Rotational moment of Ampere forces equals:
where: S- frame area, α - angle between the normal to the frame and the magnetic induction vector (the normal is a vector perpendicular to the plane of the frame), N- the number of turns, B– magnetic field induction, I- the current strength in the frame.
Lorentz force
Ampere force acting on a piece of conductor of length Δ l with current I located in a magnetic field B can be expressed in terms of the forces acting on individual charge carriers. These forces are called Lorentz forces. Lorentz force acting on a particle with a charge q in a magnetic field B moving at a speed v, is calculated by the following formula:
Injection α in this expression is equal to the angle between the speed and the magnetic induction vector. Direction of the Lorentz force acting on positively a charged particle, as well as the direction of the Ampère force, can be found by the left hand rule or by the gimlet rule (as well as the Ampère force). The magnetic induction vector must be mentally inserted into the palm of the left hand, four closed fingers should be directed along the speed of the charged particle, and the bent thumb will show the direction of the Lorentz force. If the particle has negative charge, then the direction of the Lorentz force, found by the left hand rule, will need to be replaced by the opposite.
The Lorentz force is directed perpendicular to the velocity and magnetic field induction vectors. When a charged particle moves in a magnetic field Lorentz force does no work. Therefore, the modulus of the velocity vector does not change when the particle moves. If a charged particle moves in a uniform magnetic field under the action of the Lorentz force, and its velocity lies in a plane perpendicular to the magnetic field induction vector, then the particle will move in a circle, the radius of which can be calculated by the following formula:
The Lorentz force in this case plays the role of a centripetal force. The period of revolution of a particle in a uniform magnetic field is:
The last expression shows that for charged particles of a given mass m the period of revolution (and hence the frequency and angular velocity) does not depend on the speed (and hence on the kinetic energy) and the radius of the trajectory R.
Magnetic field theory
If two parallel wires carry current in the same direction, they attract; if in opposite directions, they repel each other. The patterns of this phenomenon were experimentally established by Ampère. The interaction of currents is caused by their magnetic fields: the magnetic field of one current acts by the Ampere force on another current and vice versa. Experiments have shown that the modulus of force acting on a segment of length Δ l each of the conductors, is directly proportional to the strength of the current I 1 and I 2 in conductors, segment length Δ l and inversely proportional to the distance R between them:
where: μ 0 is a constant value, which is called magnetic constant. The introduction of the magnetic constant into the SI simplifies the writing of a number of formulas. Its numerical value is:
μ 0 = 4π 10 -7 H / A 2 ≈ 1.26 10 -6 H / A 2.
Comparing the expression just given for the force of interaction of two conductors with current and the expression for the Ampère force, it is easy to obtain an expression for induction of the magnetic field created by each of the rectilinear conductors with current on distance R From him:
where: μ - the magnetic permeability of the substance (more on this below). If current flows in a circular loop, then center of the coil magnetic field induction is determined by the formula:
lines of force The magnetic field is called the lines along the tangents to which the magnetic arrows are located. magnetic needle called a long and thin magnet, its poles are pointed. A magnetic needle suspended on a thread always turns in one direction. At the same time, one end of it is directed towards the north, the other - towards the south. Hence the name of the poles: north ( N) and southern ( S). Magnets always have two poles: north (indicated in blue or the letter N) and southern (in red or letter S). Magnets interact in the same way as charges: like poles repel, and opposite poles attract. It is impossible to get a magnet with one pole. Even if the magnet is broken, each part will have two different poles.
Magnetic induction vector
Magnetic induction vector- a vector physical quantity that is a characteristic of a magnetic field, numerically equal to the force acting on a current element of 1 A and a length of 1 m, if the direction of the field line is perpendicular to the conductor. Denoted AT, unit of measurement - 1 Tesla. 1 T is a very large value, therefore, in real magnetic fields, magnetic induction is measured in mT.
The magnetic induction vector is directed tangentially to the lines of force, i.e. coincides with the direction of the north pole of a magnetic needle placed in a given magnetic field. The direction of the magnetic induction vector does not coincide with the direction of the force acting on the conductor, therefore, the magnetic field lines of force, strictly speaking, are not force lines.
Magnetic field line of permanent magnets directed with respect to the magnets themselves as shown in the figure:
When magnetic field of electric current to determine the direction of field lines use the rule "Right hand": if you take the conductor in your right hand so that the thumb is directed along the current, then four fingers clasping the conductor show the direction of the lines of force around the conductor:
In the case of direct current, the lines of magnetic induction are circles whose planes are perpendicular to the current. The magnetic induction vectors are directed tangentially to the circle.
Solenoid- a conductor wound on a cylindrical surface, through which an electric current flows I similar to the field of a direct permanent magnet. inside solenoid length l and the number of turns N a uniform magnetic field is created with induction (its direction is also determined by the right hand rule):
Magnetic field lines look like closed lines is a common property of all magnetic lines. Such a field is called a vortex field. In the case of permanent magnets, the lines do not end at the surface, but penetrate inside the magnet and close inside. This difference between electric and magnetic fields is explained by the fact that, unlike electric, magnetic charges do not exist.
Magnetic properties of matter
All substances have magnetic properties. The magnetic properties of a substance are characterized relative magnetic permeability μ , for which the following is true:
This formula expresses the correspondence of the magnetic induction vector of the field in vacuum and in a given medium. In contrast to electrical interaction, during magnetic interaction in a medium, both strengthening and weakening of interaction can be observed in comparison with vacuum, in which the magnetic permeability μ = 1. diamagnets magnetic permeability μ slightly less than unity. Examples: water, nitrogen, silver, copper, gold. These substances somewhat weaken the magnetic field. Paramagnets- oxygen, platinum, magnesium - somewhat enhance the field, having μ a little more than one. At ferromagnets- iron, nickel, cobalt - μ >> 1. For example, for iron μ ≈ 25000.
magnetic flux. Electromagnetic induction
Phenomenon electromagnetic induction was discovered by the outstanding English physicist M. Faraday in 1831. It consists in the occurrence of an electric current in a closed conducting circuit with a change in time of the magnetic flux penetrating the circuit. magnetic flux Φ across the square S the contour is called the value:
where: B is the modulus of the magnetic induction vector, α is the angle between the magnetic induction vector B and normal (perpendicular) to the contour plane, S- contour area, N- the number of turns in the circuit. The unit of magnetic flux in the SI system is called Weber (Wb).
Faraday experimentally established that when the magnetic flux changes in a conducting circuit, EMF induction ε ind, equal to the rate of change of the magnetic flux through the surface bounded by the contour, taken with a minus sign:
A change in the magnetic flux penetrating a closed circuit can occur for two possible reasons.
- The magnetic flux changes due to the movement of the circuit or its parts in a time-constant magnetic field. This is the case when conductors, and with them free charge carriers, move in a magnetic field. The occurrence of the induction EMF is explained by the action of the Lorentz force on free charges in moving conductors. The Lorentz force plays the role of an outside force in this case.
- The second reason for the change in the magnetic flux penetrating the circuit is the change in time of the magnetic field when the circuit is stationary.
When solving problems, it is important to immediately determine how the magnetic flux changes. Three options are possible:
- The magnetic field changes.
- The area of the contour changes.
- The orientation of the frame relative to the field changes.
In this case, when solving problems, the EMF is usually considered modulo. Let us also pay attention to one particular case in which the phenomenon of electromagnetic induction occurs. So, the maximum value of the induction emf in a circuit consisting of N turns, area S, rotating with angular velocity ω in a magnetic field with induction AT:
Movement of a conductor in a magnetic field
When moving the conductor length l in a magnetic field B with speed v a potential difference arises at its ends, caused by the action of the Lorentz force on free electrons in the conductor. This potential difference (strictly speaking, EMF) is found by the formula:
where: α - the angle that is measured between the direction of the velocity and the magnetic induction vector. EMF does not occur in the fixed parts of the circuit.
If the rod is long L spins in a magnetic field AT around one of its ends with an angular velocity ω , then at its ends there will be a potential difference (EMF), which can be calculated by the formula:
Inductance. Self-induction. Magnetic field energy
self induction is an important special case of electromagnetic induction, when a changing magnetic flux, causing an EMF of induction, is created by a current in the circuit itself. If the current in the circuit under consideration changes for some reason, then the magnetic field of this current changes, and, consequently, the own magnetic flux penetrating the circuit. In the circuit, an EMF of self-induction occurs, which, according to the Lenz rule, prevents a change in the current in the circuit. Own magnetic flux Φ , penetrating the circuit or coil with current, is proportional to the strength of the current I:
Proportionality factor L in this formula is called the coefficient of self-induction or inductance coils. The SI unit of inductance is the Henry (H).
Remember: the inductance of the circuit does not depend on either the magnetic flux or the strength of the current in it, but is determined only by the shape and size of the circuit, as well as the properties of the environment. Therefore, when the current strength in the circuit changes, the inductance remains unchanged. The inductance of a coil can be calculated using the formula:
where: n- concentration of turns per unit length of the coil:
EMF self-induction, arising in a coil with a constant value of inductance, according to the Faraday formula is equal to:
So the EMF of self-induction is directly proportional to the inductance of the coil and the rate of change of the current strength in it.
The magnetic field has energy. Just as a charged capacitor has a supply of electrical energy, a coil with current flowing through its coils has a supply of magnetic energy. Energy W m magnetic field coil with inductance L generated by current I, can be calculated by one of the formulas (they follow from each other, taking into account the formula Φ = LI):
By correlating the formula for the energy of the magnetic field of the coil with its geometric dimensions, we can obtain a formula for volumetric energy density of the magnetic field(or energy per unit volume):
Lenz's rule
Inertia- a phenomenon that occurs both in mechanics (when accelerating a car, we lean back, counteracting an increase in speed, and when braking, we lean forward, counteracting a decrease in speed), and in molecular physics (when a liquid is heated, the evaporation rate increases, the fastest molecules leave the liquid, reducing speed heating) and so on. In electromagnetism, inertia manifests itself in opposition to a change in the magnetic flux penetrating the circuit. If the magnetic flux increases, then the induction current arising in the circuit is directed so as to prevent the increase in the magnetic flux, and if the magnetic flux decreases, then the induction current arising in the circuit is directed so as to prevent the magnetic flux from decreasing.
On that website. To do this, you need nothing at all, namely: to devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on various topics and varying complexity. The latter can only be learned by solving thousands of problems.
Successful, diligent and responsible implementation of these three points will allow you to show an excellent result on the CT, the maximum of what you are capable of.
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