Name: maxwell’s equations and light speed
Uploaded: 2023-04-30T12:46:19.000Z
Duration: 1 min 30 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Waves and Their Applications

PS.PSc.8.2

propagation-speed-of-electromagnetic-waves

Propagation Speed of Electromagnetic Waves

Les ondes électromagnétiques sont compatibles avec la loi d'Ampère.
Considérons un front d’onde plan se déplaçant dans la direction +x. Considérons au-dessus de celui-ci un rectangle dans le plan xz, avec un vecteur aire dans la direction +y.
L’intégration s’effectue dans le sens inverse des aiguilles d’une montre autour du rectangle.
Le champ magnétique est soit nul, soit perpendiculaire aux éléments de longueur, à l’exception de la longueur « RS », où le champ est parallèle et contribue à l’intégrale.
Cela implique que le membre droit de la loi d'Ampère doit également être non nul. Par conséquent, le champ électrique doit avoir une composante y qui peut fournir une dérivée temporelle non nulle du flux électrique.
Il établit également que les champs électrique et magnétique doivent être mutuellement perpendiculaires.
Le flux électrique augmente jusqu’à une valeur positive dans le temps « dt ». Le taux de variation du flux électrique peut être substitué dans la loi d'Ampère.
Comme les ondes électromagnétiques sont cohérentes avec toutes les équations de Maxwell, l'expression obtenue est comparée à l'expression dérivée de la loi de Faraday, qui donne la vitesse de propagation des ondes dans le vide.
En substituant les valeurs de perméabilité et de permittivité, la vitesse de propagation est égale à la vitesse de la lumière.

<ol>
	<li>Young, H.D. et Freedman, R.A. (2012). La physique universitaire avec la physique moderne. San Francisco, Californie : Pearson. L’article 32.2 ; page 1057.</li>
	<li>OpenStax. (2019). Physique universitaire Vol. 2. [Version Web]. Récupéré de <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a> ; l’article 16.2 ; Pages 707 à 709.</li>
</ol>

vitesse de propagation des ondes électromagnétiques

Les ondes électromagnétiques sont conformes à la loi d'Ampère. En supposant qu'il n'y ait aucun courant de conduction, la loi d'Ampère s'exprime de la manière suivante :

<img alt="Equation1" src="/files/ftp_upload/13824/13824_Equation_PT_1.svg" style="text-align: center; height: 38px;" />

<img alt="Figure1" src="/files/ftp_upload/13824/13824_Figure_PT_1.svg" style="text-align: center; height: 220px;" />

Considérons une onde plane se déplaçant dans la direction positive de l'axe x, comme le montre la figure. Dessus, considérons un rectangle dans le plan xz, avec un vecteur d'aire orienté dans la direction positive de l'axe y. L'intégration s'effectue dans le sens inverse des aiguilles d'une montre autour du rectangle pour résoudre le membre de gauche de la loi d'Ampère. Le champ magnétique est soit nul, soit perpendiculaire aux éléments de longueur, à l'exception d'une longueur où le champ est parallèle. Cette longueur contribue à l'intégrale en lui donnant une valeur non nulle.

Pour satisfaire la loi d'Ampère, le membre de droite de la loi d'Ampère doit également être non nul. Par conséquent, le champ électrique doit avoir une composante dans la direction y qui peut fournir une dérivée temporelle non nulle du flux électrique. Cela établit également que les champs électrique et magnétique doivent être mutuellement perpendiculaires. Le flux électrique augmente à une valeur positive en fonction du temps dt. Le taux de variation du flux électrique peut être substitué dans la loi d'Ampère.

<img alt="Equation2" src="/files/ftp_upload/13824/13824_Equation_PT_2.svg" style="text-align: center; height: 17px;" />

Étant donné que les ondes électromagnétiques sont conformes à toutes les équations de Maxwell, l'expression obtenue est comparée à l'expression dérivée de la loi de Faraday, qui donne la vitesse de propagation des ondes dans le vide.

<img alt="Equation3" src="/files/ftp_upload/13824/13824_Equation_PT_3.svg" style="text-align: center; height: 45px;" />

Lorsque les valeurs numériques de la perméabilité et de la permittivité sont substituées, la vitesse de propagation obtenue est égale à la vitesse de la lumière.

<img alt="Equation4" src="/files/ftp_upload/13824/13824_Equation_PT_4.svg" style="text-align: center; height: 17px;" />

Cela implique que l'onde supposée est conforme à toutes les équations de Maxwell, à condition que le front d'onde se déplace à la vitesse indiquée ci-dessus, qui est reconnue comme étant la vitesse de la lumière. Notez que la valeur exacte de la vitesse de la lumière est définie comme étant de 299 792 458 m/s.

Vitesse de propagation des ondes électromagnétiques

Les ondes électromagnétiques sont compatibles avec la loi d'Ampère. En supposant qu'il n'y a pas de courant de conduction, la loi d'Ampère est donnée comme suit :

Prenons l’exemple d’un avion...

Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

Electromagnetic Waves

Ondes électromagnétiques

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

maxwell’s equations and light speed

Electromagnetic waves follow Ampere’s law when there is no conduction current. A plane wavefront moves in the positive x-direction. To analyze it, a rectangle is placed in the xz-plane with its area vector pointing in the positive y-direction.

The line integral around the rectangle is taken counterclockwise. The magnetic field is zero on some sides and perpendicular on others. It is parallel to one side, and that side gives a non-zero contribution to the integral.

Because the left side of Ampere’s law is non-zero, the right side must also be non-zero. That means the electric field needs a y-component. This component creates a changing electric flux, and it also shows that the electric and magnetic fields are mutually perpendicular.

The increase in electric flux over time dt is placed into Ampere’s law as a time derivative. The result is then compared with the expression from Faraday’s law. From this comparison, the wave speed in vacuum is obtained.

When the permeability and permittivity values are substituted, the calculated speed matches the speed of light. This shows that the assumed wavefront is consistent with Maxwell’s equations if it moves at that speed. The exact speed of light is defined as 299,792,458 m/s.

Maxwell’s Equations and Light Speed

electromagnetic waves

Maxwell’s Equations Behind EM Waves

Maxwell’s equations explain how electric and magnetic fields work together to create electromagnetic waves. James Clerk Maxwell brought together the ideas of Oersted, Coulomb, Gauss, and Faraday and built a single theory of electromagnetism. Together with the Lorentz force law, his equations describe the laws of electricity and magnetism. A key part of Maxwell’s work is the symmetry in the equations. Faraday’s law shows that a changing magnetic field produces an electric field. Maxwell added...

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plane electromagnetic waves ii

Faraday’s Law in a Plane Wave

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propagation speed of electromagnetic waves

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electromagnetic waves in matter

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intensity of electromagnetic waves

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Maxwell’s Equations and Light Speed | JoVE K12

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JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

Pennsylvania State Academic Standards

Waves and Electromagnetic Radiation

3.2.9-12.V

Louisiana Student Standards for Science

High School

waves-and-their-applications-in-technologies-for-information-transfer

Waves And Their Applications In Technologies For Information Transfer

HS-PS4-1

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Energy And Waves

Waves

Tennessee Academic Standards

Waves and Their Applications in Technologies for Information Transfer

PHYS.PS4.2

Virginia  Standards of Learning

HIgh School

PS.7

PS.7.a

PH.5

PH.5.c

PH.6

PH.6.b

Minnesota Academic Standards in Science

3.2.2 9P.3.1.1.2

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

HS-PS4-5

Arizona Science Standards

HS.P4

HS.P4U1.10

Alabama Course of Study Science

9-12.PS.2.2

9-12.PS.2.2.c

Earth and Space Science

Earth's Place in the Universe

9-12.ESS.1.2.b

9-12.P.3.7.c

Next Generation Science Standards

HS-PS4-3

HS-PS4-4

Florida Department of Education

SC.912.P.10

SC.912.P.10.18

SC.912.P.12

SC.912.P.12.7

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.B

Chemistry and Physics

IPC.6

IPC.6.E

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS4-1

P-PS4-3

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-2.

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-4.

Georgia Standards of Excellence

SPS9.

electromagnetic-waves-and-mechanical-waves

Electromagnetic Waves and Mechanical Waves

SP4.

mechanical-and-electromagnetic-waves-properties

Mechanical and Electromagnetic Waves Properties

Travelling Waves

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Wave Parameters

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Equations of Wave Motion

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Graphing the Wave Function

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Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which ...

Speed of a Transverse Wave

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Problem-Solving: Tuning of a Guitar String

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Kinetic and Potential Energy of a Wave

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Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

Carry out investigations to explain the quantitative and qualitative relationships among wave frequency, wave velocity, wavelength, and wave energy.

PS.PSc.8.1

James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his ...

Electromagnetic Wave Equation

Maxwell&#39;s equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose ...

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


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Electromagnetic Waves in Matter

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Energy Carried By Electromagnetic Waves

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Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a ...

Use models to compare the characteristics of mechanical and electromagnetic waves.

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect ...

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at ...

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second ...

Sound Waves: Interference

Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure ...

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two ...

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Use models to explain the wave interactions of reflection, refraction, diffraction, and interference.

PS.PSc.8.3

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a ...

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Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. ...

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Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions ...

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Obtain, evaluate, and communicate information to explain how instruments that transmit and detect waves are used in everyday life.

PS.PSc.8.4

Analyze the nature of waves and their applications.

Maxwell’s Equations and Light Speed

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