Electrodynamics, formulas. Electromagnetism

Electrodynamics Is the science of the properties and laws of a special type of matter - the electromagnetic field, which interacts between electrically charged bodies or particles.

Quantum electrodynamics(QED) - quantum field theory of electromagnetic interactions; the most developed part of quantum field theory. Classical electrodynamics takes into account only the continuous properties of the electromagnetic field, while quantum electrodynamics is based on the idea that the electromagnetic field also has discontinuous (discrete) properties, the carriers of which are field quanta - photons. The interaction of electromagnetic radiation with charged particles is considered in quantum electrodynamics as absorption and emission of photons by particles.

2.Characteristics of the electromagnetic field

Electromagnetic field - E = N / Kl = B / M

E= F/ q – the ratio of the force acting from the field to the magnitude of this charge.

D- induction of an electric field - called a vector proportional to the intensity vector, but independent of the properties of the medium

D = 𝞮 E; 𝞮 = 𝞮 0 𝞮 ’ 0 = 8.85 * 10 -12 F / m

V- magnetic induction vector = N / A * m = 1T

Induction is a vector, the modulus of which is the ratio of the modulus of force acting from the side of the field to the conductor with current, to the current in the conductor and its length . B= | F|/ I* l(US) N- magnetic field strength (A / m) = 80 oersted =) 80 Gauss, called a vector parallel to the induction vector, but independent of the properties of the medium. Н = 1 / μ, where μ = μ 0* µ’

3.Vector fields. Integral and differential characteristics of a vector field

4 THEOREM OF OSTROGRAD-GAUSS AND STOKS

5.LAW OF PENDANT

6 GAUSS'S THEOREM

7.VECTOR FLOW

8 EQUATIONS OF CONTINUITY

9. DISPLACEMENT CURRENT

10 THE LAW OF FULL CURRENT

11.LAW OF CONTINUITY OF MAGNETIC FLUX

12.BOUNDARY CONDITIONS

13 JOLE-LENTZ'S LAWS IN DIFFERENTIAL FORM

The amount of heat released per unit time in a conductor with resistance R at current strength I, according to the Joule-Lenz law, is equal to:

Applying this law to an infinitely small cylinder, the axis of which coincides with the direction of the current, we obtain

Considering that - the volume of an infinitely small cylinder, and - the amount of heat released in a unit of volume per unit of time, we find

Where expressed in watts per cubic meter. Considering that j 2 = j * j and using an expression for j, we can write the ratio in the form:

This equality expresses the Joule-Lenz law in differential form.

14. Complete system of Maxwell's equations in matter

In a medium, external electric and magnetic fields cause polarization and magnetization of the substance, which are macroscopically described by the polarization vector P and the magnetization vector M of the substance, respectively, and are caused by the appearance of bound charges and currents. As a result, the field in the medium turns out to be the sum of external fields and fields caused by bound charges and currents.

The polarization P and the magnetization of the substance M are related to the vectors of the strength and induction of the electric and magnetic fields by the following relations:

Therefore, expressing the vectors D and H in terms of E, B, and, one can obtain a mathematically equivalent system of Maxwell's equations:

The index here denotes free charges and currents. Maxwell's equations in this form are fundamental, in the sense that they do not depend on the model of the electromagnetic device of matter. The division of charges and currents into free and bound ones allows one to "hide" in, and then in P, M and, consequently, in D, B, the complex microscopic nature of the electromagnetic field in the medium.

Definition 1

Electrodynamics is a huge and important area of physics, which investigates the classical, non-quantum properties of the electromagnetic field and the motion of positively charged magnetic charges interacting with each other using this field.

Figure 1. Briefly about electrodynamics. Author24 - online exchange of student papers

Electrodynamics is represented by a wide range of various problem statements and their competent solutions, approximate methods and special cases, which are combined into a single whole by common initial laws and equations. The latter, constituting the main part of classical electrodynamics, are presented in detail in Maxwell's formulas. At present, scientists continue to study the principles of this area in physics, the skeleton of its construction of relationships with other scientific areas.

Coulomb's law in electrodynamics is denoted as follows: $ F = \ frac (kq1q2) (r2) $, where $ k = \ frac (9 \ cdot 10 (H \ cdot m)) (Cl) $. The equation of the electric field strength is written as follows: $ E = \ frac (F) (q) $, and the flux of the magnetic field induction vector is $ ∆Ф = В∆S \ cos (a) $.

In electrodynamics, free charges and charge systems are primarily studied, which contribute to the activation of a continuous energy spectrum. The classical description of electromagnetic interaction is favored by the fact that it is effective already in the low-energy limit, when the energy potential of particles and photons is small in comparison with the rest energy of an electron.

In such situations, there is often no annihilation of charged particles, since there is only a gradual change in the state of their unstable motion as a result of the exchange of a large number of low-energy photons.

Remark 1

However, even at high energies of particles in a medium, despite the significant role of fluctuations, electrodynamics can be successfully used for a comprehensive description of average statistical, macroscopic characteristics and processes.

Basic equations of electrodynamics

The main formulas that describe the behavior of the electromagnetic field and its direct interaction with charged bodies are Maxwell's equations, which determine the probable actions of a free electromagnetic field in a medium and vacuum, as well as the general generation of the field by sources.

Among these provisions in physics, it is possible to distinguish:

Gauss's theorem for an electric field - designed to determine the generation of an electrostatic field by positive charges;
the hypothesis of the closedness of the lines of force - promotes the interaction of processes within the magnetic field itself;
Faraday's law of induction - establishes the generation of electric and magnetic fields by variable properties of the environment.

In general, the Ampere - Maxwell theorem is a unique idea of the circulation of lines in a magnetic field with a gradual addition of displacement currents introduced by Maxwell himself, accurately determines the transformation of the magnetic field by moving charges and the alternating action of an electric field.

Charge and force in electrodynamics

In electrodynamics, the interaction of the force and charge of the electromagnetic field proceeds from the following joint definition of the electric charge $ q $, energy $ E $ and magnetic $ B $ fields, which are approved as a fundamental physical law based on the entire set of experimental data. The formula for the Lorentz force (within the limits of idealization of a point charge moving at a certain speed) is written with the replacement of the speed $ v $.

Conductors often contain a huge amount of charges, therefore, these charges are fairly well compensated: the number of positive and negative charges is always equal to each other. Consequently, the total electrical force that constantly acts on the conductor is also zero. As a result, the magnetic forces operating on individual charges in the conductor are not compensated, because in the presence of current, the velocities of the charges are always different. The equation of action of a conductor with a current in a magnetic field can be written as follows: $ G = | v ⃗ | s \ cos (a) $

If we investigate not a liquid, but a full-fledged and stable flow of charged particles as a current, then the entire energy potential passing linearly through the area in $ 1s $ will be the current strength equal to: $ I = ρ | \ vec (v) | s \ cos (a) $, where $ ρ $ is the charge density (per unit volume in the total flow).

Remark 2

If the magnetic and electric field systematically changes from point to point on a specific site, then in expressions and formulas for partial flows, as in the case of a liquid, the average values $ E ⃗ $ and $ B ⃗ $ at the site are mandatory.

The special position of electrodynamics in physics

The significant position of electrodynamics in modern science can be confirmed through the well-known work of A. Einstein, which detailed the principles and foundations of the special theory of relativity. The scientific work of the outstanding scientist is called "On the electrodynamics of moving bodies", and includes a huge number of important equations and definitions.

As a separate area of physics, electrodynamics consists of the following sections:

the doctrine of the field of motionless, but electrically charged physical bodies and particles;
the doctrine of the properties of electric current;
the doctrine of the interaction of magnetic field and electromagnetic induction;
the doctrine of electromagnetic waves and vibrations.

All the above sections are united into one whole by the theorem of D. Maxwell, who not only created and presented a coherent theory of the electromagnetic field, but also described all its properties, proving its real existence. The work of this particular scientist showed the scientific world that the electric and magnetic fields known at that time are just a manifestation of a single electromagnetic field functioning in different reference systems.

An essential part of physics is devoted to the study of electrodynamics and electromagnetic phenomena. This area largely claims the status of a separate science, since it not only explores all the laws of electromagnetic interactions, but also describes them in detail by means of mathematical formulas. Deep and long-term studies of electrodynamics have opened new ways for using electromagnetic phenomena in practice, for the benefit of all mankind.

Electrodynamics is a branch of physics that studies the theory of the electromagnetic field, as well as the interaction between electric charges. Electrodynamics has become another stage in the rapid development of physics. There are formulas for electrodynamics, as well as spurs and problems in electrodynamics.

How science was born as a result of numerous discoveries and experiments. The branch of electrodynamics that studies interactions and electric fields of resting electric charges is electrostatics.

Classical electrodynamics

Electrodynamics developed at a rapid pace, many famous scientists have contributed to the development of electrodynamics. In 1785, the French physicist C. Coulomb experimentally established the law of interaction of two stationary point charges. Pendant Charles Augustin In 1820 the Danish physicist H. Oersted showed that the current flowing through wires creates a magnetic field around itself.

Oersted Hans Christian In 1831 M. Faraday discovered electromagnetic induction.

Faraday Michael Electrodynamics is the science that studies the electromagnetic field. This field manifests itself through forceful interaction with those particles of matter that have an electric charge. attracted the English scientist J. Maxwell. Based on empirical data, he proposed equations sufficient to describe all electromagnetic phenomena.

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Title: Electrodynamics and Radio Wave Propagation

The session draws near, and it's time for us to move from theory to practice. Over the weekend, we sat down and thought that many students would like to have a selection of basic physical formulas on hand. Dry formulas with an explanation: brief, concise, nothing superfluous. A very useful thing when solving problems, you know. Yes, and at the exam, when exactly what was most brutally memorized the day before can "jump out" of the head, such a selection will serve an excellent service.

Most of the problems are usually assigned to the three most popular areas of physics. This Mechanics, thermodynamics and Molecular physics, electricity... Let's take them!

Basic formulas in physics - dynamics, kinematics, statics

Let's start with the simplest. A good old-fashioned favorite straight and steady motion.

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 will give the basic formulas on the topic "Work and Energy". Where are we without them!

Basic formulas of molecular physics and thermodynamics

Let us finish the section of mechanics with formulas for vibrations and waves and move on to molecular physics and thermodynamics.

Efficiency, Gay-Lussac's law, Clapeyron-Mendeleev's equation - all these lovely formulas are collected below.

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Basic physics formulas: electricity

It's time to move on to electricity, although thermodynamics love it less. We start with electrostatics.

And, under 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 brought up, but this is useless. When there are too many formulas, you can easily get confused, and then completely melt the brain. We hope our cheat sheet for basic physics formulas will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or did not find the required formula: ask the experts student service... Our authors keep hundreds of formulas in their heads and crack problems like nuts. Contact us, and soon any task will be too tough for you.

Cheat sheet with formulas in physics for the exam

and not only (may need 7, 8, 9, 10 and 11 grades).

First, a picture that can be printed in a compact form.

Mechanics

Pressure P = F / S
Density ρ = m / V
Pressure at the depth of the liquid P = ρ ∙ g ∙ h
Gravity Fт = mg
5. Archimedean force Fa = ρ w ∙ g ∙ Vт
Equation of motion for uniformly accelerated motion

X = X 0 + υ 0 ∙ t + (a ∙ t 2) / 2 S = ( υ 2 -υ 0 2) / 2а S = ( υ +υ 0) ∙ t / 2

Equation of speed for uniformly accelerated motion υ =υ 0 + a ∙ t
Acceleration a = ( υ -υ 0) / t
Circular speed υ = 2πR / T
Centripetal acceleration a = υ 2 / R
Relationship between the period and the frequency ν = 1 / T = ω / 2π
II Newton's law F = ma
Hooke's law Fy = -kx
The law of gravitation F = G ∙ M ∙ m / R 2
Weight of a body moving with acceleration a P = m (g + a)
Weight of a body moving with acceleration a ↓ P = m (g-a)
Friction force Ffr = µN
Body momentum p = m υ
Force impulse Ft = ∆p
Moment of force M = F ∙ ℓ
Potential energy of a body raised above the ground Ep = mgh
Potential energy of an elastically deformed body Ep = kx 2/2
Kinetic energy of the body Ek = m υ 2 /2
Work A = F ∙ S ∙ cosα
Power N = A / t = F ∙ υ
Efficiency η = Ap / Az
The oscillation period of the mathematical pendulum T = 2π√ℓ / g
The period of oscillation of a spring pendulum T = 2 π √m / k
Equation of harmonic vibrations X = Xmax ∙ cos ωt
Relationship between wavelength, its speed and period λ = υ T

Molecular physics and thermodynamics

Amount of substance ν = N / Na
Molar mass М = m / ν
Wed kin. energy of molecules of a monatomic gas Ek = 3/2 ∙ kT
Basic equation of MKT P = nkT = 1 / 3nm 0 υ 2
Gay - Lussac's law (isobaric process) V / T = const
Charles's law (isochoric process) P / T = const
Relative humidity φ = P / P 0 ∙ 100%
Int. energy is ideal. monatomic gas U = 3/2 ∙ M / µ ∙ RT
Gas work A = P ∙ ΔV
Boyle's law - Mariotte (isothermal process) PV = const
The amount of heat during heating Q = Cm (T 2 -T 1)
The amount of heat during melting Q = λm
The amount of heat during vaporization Q = Lm
The amount of heat during fuel combustion Q = qm
Ideal gas equation of state PV = m / M ∙ RT
The first law of thermodynamics ΔU = A + Q
Efficiency of heat engines η = (Q 1 - Q 2) / Q 1
Efficiency is ideal. engines (Carnot cycle) η = (T 1 - T 2) / T 1

Electrostatics and electrodynamics - physics formulas

Coulomb's law F = k ∙ q 1 ∙ q 2 / R 2
Electric field strength E = F / q
The tension of the email field of a point charge E = k ∙ q / R 2
Surface charge density σ = q / S
The tension of the email field of the infinite plane E = 2πkσ
Dielectric constant ε = E 0 / E
Potential energy interaction. charges W = k ∙ q 1 q 2 / R
Potential φ = W / q
Point charge potential φ = k ∙ q / R
Voltage U = A / q
For a uniform electric field U = E ∙ d
Electric capacity C = q / U
Electric capacity of a flat capacitor C = S ∙ ε ∙ε 0 / d
Energy of a charged capacitor W = qU / 2 = q² / 2С = CU² / 2
Current I = q / t
Conductor resistance R = ρ ∙ ℓ / S
Ohm's law for a section of a circuit I = U / R
The laws of the last. compounds I 1 = I 2 = I, U 1 + U 2 = U, R 1 + R 2 = R
Parallel laws conn. U 1 = U 2 = U, I 1 + I 2 = I, 1 / R 1 + 1 / R 2 = 1 / R
Electric current power P = I ∙ U
Joule-Lenz law Q = I 2 Rt
Ohm's law for the complete circuit I = ε / (R + r)
Short-circuit current (R = 0) I = ε / r
Magnetic induction vector B = Fmax / ℓ ∙ I
Ampere force Fa = IBℓsin α
Lorentz force Fl = Bqυsin α
Magnetic flux Ф = BSсos α Ф = LI
The law of electromagnetic induction Ei = ΔФ / Δt
EMF of induction in the motion conductor Ei = Bℓ υ sinα
EMF of self-induction Esi = -L ∙ ΔI / Δt
The magnetic field energy of the coil Wm = LI 2/2
Oscillation period qty. contour T = 2π ∙ √LC
Inductive resistance X L = ωL = 2πLν
Capacitive resistance Xc = 1 / ωC
The effective value of the current Id = Imax / √2,
RMS voltage value Uд = Umax / √2
Impedance Z = √ (Xc-X L) 2 + R 2

Optics

The law of refraction of light n 21 = n 2 / n 1 = υ 1 / υ 2
Refractive index n 21 = sin α / sin γ
Thin lens formula 1 / F = 1 / d + 1 / f
Optical power of the lens D = 1 / F
max interference: Δd = kλ,
min interference: Δd = (2k + 1) λ / 2
Differential lattice d ∙ sin φ = k λ

The quantum physics

F-la Einstein for the photoeffect hν = Aout + Ek, Ek = U s e
Red border of the photoelectric effect ν к = Aout / h
Photon momentum P = mc = h / λ = E / s

Atomic Nuclear Physics