Physics formulas for the exam. Electrodynamics, formulas Oscillations and waves

Definition 1

Electrodynamics is a huge and important area of physics that studies the classical, non-quantum properties of the electromagnetic field and the motion of positively charged magnetic charges interacting with each other through 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 united into one whole by general initial laws and equations. The latter, constituting the bulk of classical electrodynamics, are presented in detail in Maxwell's formulas. Currently, scientists continue to study the principles of this field in physics, the skeleton of its relationship with other scientific areas.

Coulomb's law in electrodynamics is denoted as follows: $F= \frac (kq1q2) (r2)$, where $k= \frac (9 \cdot 10 (H \cdot m)) (Kl)$. The electric field strength equation 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, first of all, free charges and systems of charges are studied, which contribute to the activation of a continuous energy spectrum. The classical description of the electromagnetic interaction is favored by the fact that it is effective even in the low-energy limit, when the energy potential of particles and photons is small compared to the rest energy of the 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 an 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 a field by sources.

Among these positions in physics it is possible to distinguish:

the Gauss theorem for the electric field - designed to determine the generation of an electrostatic field by positive charges;
the hypothesis of closed field lines - 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 Ampère-Maxwell theorem is a unique idea about the circulation of lines in a magnetic field with the gradual addition of displacement currents introduced by Maxwell himself, precisely determines the transformation of a 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 an 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 idealization of a point charge moving at a certain speed) is written with the change of speed $v$.

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

If we study 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 fields systematically change from point to point on a particular site, then in the expressions and formulas for partial flows, as in the case of a liquid, the average values $E ⃗ $ and $B ⃗$ on the site are necessarily put down.

Special position of electrodynamics in physics

The significant position of electrodynamics in modern science can be confirmed by the well-known work of A. Einstein, in which the principles and foundations of the special theory of relativity were detailed. The scientific work of an 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 the magnetic field and electromagnetic induction;
the doctrine of electromagnetic waves and oscillations.

All the above sections are combined 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 that functions 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 investigates all the patterns of electromagnetic interactions, but also describes them in detail using mathematical formulas. Deep and long-term studies of electrodynamics have opened up new ways for the use of electromagnetic phenomena in practice, for the benefit of all mankind.

Cheat sheet with formulas in physics for the exam

And not only (may need 7, 8, 9, 10 and 11 classes). For starters, a picture that can be printed in a compact form.

A cheat sheet with formulas in physics for the Unified State Examination and not only (grades 7, 8, 9, 10 and 11 may need it).

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

And then the Word file, which contains all the formulas to print them, which are at the bottom of the article.

Mechanics

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

X=X0 + υ 0∙t+(a∙t 2)/2 S=( υ 2 -υ 0 2) /2а S=( υ +υ 0) ∙t /2

Velocity equation 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 period and frequency ν=1/T=ω/2π
Newton's II law F=ma
Hooke's law Fy=-kx
Law of universal gravitation F=G∙M∙m/R 2
The weight of a body moving with acceleration a P \u003d m (g + a)
The weight of a body moving with acceleration a ↓ P \u003d m (g-a)
Friction force Ffr=µN
Body momentum p=m υ
Force impulse Ft=∆p
Moment M=F∙ℓ
Potential energy of a body raised above the ground Ep=mgh
Potential energy of 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
Oscillation period of the mathematical pendulum T=2π√ℓ/g
Oscillation period of a spring pendulum T=2 π √m/k
The equation of harmonic oscillations Х=Хmax∙cos ωt
Relationship of the wavelength, its speed and period λ= υ T

Molecular physics and thermodynamics

Amount of substance ν=N/ Na
Molar mass M=m/ν
Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
Basic equation of MKT P=nkT=1/3nm 0 υ 2
Gay-Lussac law (isobaric process) V/T =const
Charles' law (isochoric process) P/T =const
Relative humidity φ=P/P 0 ∙100%
Int. ideal energy. 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 \u003d 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
The equation of state for an ideal gas is PV=m/M∙RT
First law of thermodynamics ΔU=A+Q
Efficiency of heat engines η= (Q 1 - Q 2) / Q 1
Ideal efficiency. engines (Carnot cycle) η \u003d (T 1 - T 2) / T 1

Electrostatics and electrodynamics - formulas in physics

Coulomb's law F=k∙q 1 ∙q 2 /R 2
Electric field strength E=F/q
Email tension. field of a point charge E=k∙q/R 2
Surface charge density σ = q/S
Email tension. fields of the infinite plane E=2πkσ
Dielectric constant ε=E 0 /E
Potential energy of 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
Capacitance 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 the circuit section I=U/R
The laws of the last compounds I 1 \u003d I 2 \u003d I, U 1 + U 2 \u003d U, R 1 + R 2 \u003d R
Parallel laws. conn. U 1 \u003d U 2 \u003d U, I 1 + I 2 \u003d I, 1 / R 1 + 1 / R 2 \u003d 1 / R
Electric current power P=I∙U
Joule-Lenz law Q=I 2 Rt
Ohm's law for a complete chain 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 Fл=Bqυsin α
Magnetic flux Ф=BSсos α Ф=LI
Law of electromagnetic induction Ei=ΔФ/Δt
EMF of induction in moving conductor Ei=Вℓ υ sinα
EMF of self-induction Esi=-L∙ΔI/Δt
The energy of the magnetic field of the coil Wm \u003d LI 2 / 2
Oscillation period count. contour T=2π ∙√LC
Inductive reactance X L =ωL=2πLν
Capacitance Xc=1/ωC
The current value of the current Id \u003d Imax / √2,
RMS voltage Ud=Umax/√2
Impedance Z=√(Xc-X L) 2 +R 2

Optics

The law of refraction of light n 21 \u003d n 2 / n 1 \u003d 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 grating d∙sin φ=k λ

The quantum physics

Einstein's formula for the photoelectric effect hν=Aout+Ek, Ek=U ze
Red border of the photoelectric effect ν to = Aout/h
Photon momentum P=mc=h/ λ=E/s

Physics of the atomic nucleus

Law of radioactive decay N=N 0 ∙2 - t / T
Binding energy of atomic nuclei

E CB \u003d (Zm p + Nm n -Mya)∙c 2

ONE HUNDRED

t \u003d t 1 / √1-υ 2 / c 2
ℓ=ℓ 0 ∙√1-υ 2 /c 2
υ 2 \u003d (υ 1 + υ) / 1 + υ 1 ∙υ / c 2
E = m With 2

Cheat sheet with formulas in physics for the exam

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

For starters, 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 Ft=mg
5. Archimedean force Fa=ρ w ∙g∙Vt
Equation of motion for uniformly accelerated motion

X=X0 + υ 0∙t+(a∙t 2)/2 S=( υ 2 -υ 0 2) /2а S=( υ +υ 0) ∙t /2

Velocity equation 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 period and frequency ν=1/T=ω/2π
Newton's II law F=ma
Hooke's law Fy=-kx
Law of universal gravitation F=G∙M∙m/R 2
The weight of a body moving with acceleration a P \u003d m (g + a)
The weight of a body moving with acceleration a ↓ P \u003d m (g-a)
Friction force Ffr=µN
Body momentum p=m υ
Force impulse Ft=∆p
Moment M=F∙ℓ
Potential energy of a body raised above the ground Ep=mgh
Potential energy of 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
Oscillation period of the mathematical pendulum T=2π√ℓ/g
Oscillation period of a spring pendulum T=2 π √m/k
The equation of harmonic oscillations Х=Хmax∙cos ωt
Relationship of the wavelength, its speed and period λ= υ T

Molecular physics and thermodynamics

Amount of substance ν=N/ Na
Molar mass M=m/ν
Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
Basic equation of MKT P=nkT=1/3nm 0 υ 2
Gay-Lussac law (isobaric process) V/T =const
Charles' law (isochoric process) P/T =const
Relative humidity φ=P/P 0 ∙100%
Int. ideal energy. 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 \u003d 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
The equation of state for an ideal gas is PV=m/M∙RT
First law of thermodynamics ΔU=A+Q
Efficiency of heat engines η= (Q 1 - Q 2) / Q 1
Ideal efficiency. engines (Carnot cycle) η \u003d (T 1 - T 2) / T 1

Electrostatics and electrodynamics - formulas in physics

Coulomb's law F=k∙q 1 ∙q 2 /R 2
Electric field strength E=F/q
Email tension. field of a point charge E=k∙q/R 2
Surface charge density σ = q/S
Email tension. fields of the infinite plane E=2πkσ
Dielectric constant ε=E 0 /E
Potential energy of 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
Capacitance 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 the circuit section I=U/R
The laws of the last compounds I 1 \u003d I 2 \u003d I, U 1 + U 2 \u003d U, R 1 + R 2 \u003d R
Parallel laws. conn. U 1 \u003d U 2 \u003d U, I 1 + I 2 \u003d I, 1 / R 1 + 1 / R 2 \u003d 1 / R
Electric current power P=I∙U
Joule-Lenz law Q=I 2 Rt
Ohm's law for a complete chain 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 Fл=Bqυsin α
Magnetic flux Ф=BSсos α Ф=LI
Law of electromagnetic induction Ei=ΔФ/Δt
EMF of induction in moving conductor Ei=Вℓ υ sinα
EMF of self-induction Esi=-L∙ΔI/Δt
The energy of the magnetic field of the coil Wm \u003d LI 2 / 2
Oscillation period count. contour T=2π ∙√LC
Inductive reactance X L =ωL=2πLν
Capacitance Xc=1/ωC
The current value of the current Id \u003d Imax / √2,
RMS voltage Ud=Umax/√2
Impedance Z=√(Xc-X L) 2 +R 2

Optics

The law of refraction of light n 21 \u003d n 2 / n 1 \u003d 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 grating d∙sin φ=k λ

The quantum physics

Einstein's formula for the photoelectric effect hν=Aout+Ek, Ek=U ze
Red border of the photoelectric effect ν to = Aout/h
Photon momentum P=mc=h/ λ=E/s

Physics of the atomic nucleus

Electrodynamics- this is the science of the properties and patterns of a special type of matter - an electromagnetic field that 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 the absorption and emission of photons by particles.

2. Characteristics of the electromagnetic field

Electromagnetic field - E \u003d N / Kl \u003d W / M

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

D- electric field induction - is 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

IN- magnetic field induction vector = N/A*m= 1Tl

Induction is a vector whose modulus is the ratio of the modulus of force acting from the side of the field on a current-carrying conductor, on the current strength in the conductor and its length . B= | F|/ I* l(Us) H- magnetic field strength (A / m) \u003d 80 oersteds \u003d) 80 Gauss, is called a vector parallel to the induction vector, but independent of the properties of the medium. H= 1/µ, where µ = µ 0* µ’

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

4. THEOREM OF OSTROGRADSKY-GAUSS AND STOKES

5. LAW OF THE PENDANT

6. GAUSS THEOREM

7.VECTOR STREAM

8. EQUATIONS OF CONTINUITY

9.BIAS CURRENT

10. LAW OF TOTAL CURRENT

11. LAW OF CONTINUITY OF THE MAGNETIC FLOW

12. BOUNDARY CONDITIONS

13. JOULE-LETZ 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:

Applying this law to an infinitesimal cylinder whose axis coincides with the direction of the current, we obtain

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

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

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

14. Complete system of Maxwell 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 intensity and induction vectors of the electric and magnetic fields by the following relationships:

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 allows us to "hide" in ,, and then in P, M and, consequently, in D, B, the complex microscopic nature of the electromagnetic field in the medium.