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

Elektromagnetische Wellen stimmen mit dem Ampereschen Gesetz überein.
Stellen Sie sich eine ebene Wellenfront vor, die sich in +x-Richtung bewegt. Betrachten Sie darüber ein Rechteck in der xz-Ebene mit einem Flächenvektor in +y-Richtung.
Die Integration erfolgt gegen den Uhrzeigersinn um das Rechteck herum.
Das Magnetfeld ist entweder Null oder senkrecht zu den Längenelementen, mit Ausnahme der Länge "RS", bei der das Feld parallel ist und zum Integral beiträgt.
Es impliziert, dass die rechte Seite des Ampereschen Gesetzes ebenfalls ungleich Null sein muss. Daher muss das elektrische Feld eine y-Komponente haben, die eine Zeitableitung des elektrischen Flusses ungleich Null liefern kann.
Es legt auch fest, dass das elektrische und das magnetische Feld senkrecht zueinander stehen müssen.
Der elektrische Fluss steigt auf einen positiven Wert in der Zeit "dt" an. Die Änderungsrate des elektrischen Flusses kann im Ampereschen Gesetz substituiert werden.
Da elektromagnetische Wellen mit allen Maxwell-Gleichungen konsistent sind, wird der erhaltene Ausdruck mit dem Ausdruck verglichen, der nach dem Faradayschen Gesetz abgeleitet wurde, das die Ausbreitungsgeschwindigkeit der Welle im Vakuum angibt.
Setzt man die Werte für Permeabilität und Permittivität ein, so ist die Ausbreitungsgeschwindigkeit gleich der Lichtgeschwindigkeit.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson. Abschnitt 32.2; Seite 1057.</li>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion]. Abgerufen von <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; Abschnitt 16.2; Seiten 707–709.</li>
</ol>

ausbreitungsgeschwindigkeit elektromagnetischer wellen

Elektromagnetische Wellen stehen im Einklang mit dem Ampèreschen Gesetz. Unter der Annahme, dass kein Leitungsstrom vorliegt, lautet das Ampèresche Gesetz wie folgt:

<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;" />

Betrachten wir eine ebene Wellenfront, die sich in positiver x-Richtung bewegt, wie in der Abbildung gezeigt. Darüber hinaus betrachten wir ein Rechteck in der xz-Ebene mit einem Flächenvektor in positiver y-Richtung. Die Integration erfolgt gegen den Uhrzeigersinn um das Rechteck herum, um die linke Seite des Ampereschen Gesetzes zu lösen. Das Magnetfeld ist entweder Null oder senkrecht zu den Längenelementen, mit Ausnahme einer Länge, wo das Feld parallel ist. Diese Länge trägt zum Integral bei und ergibt einen Wert ungleich Null.

Um das Ampèresche Gesetz zu erfüllen, muss auch die rechte Seite des Ampèreschen Gesetzes von null verschieden sein. Daher muss das elektrische Feld eine y-Komponente haben, die eine von null verschiedene Zeitableitung des elektrischen Flusses liefern kann. Zudem ist festgelegt, dass das elektrische und magnetische Feld senkrecht zueinander stehen müssen. Der elektrische Fluss nimmt mit der Zeit dt einen positiven Wert an. Die Änderungsrate des elektrischen Flusses kann in das Ampèresche Gesetz eingesetzt werden.

<img alt="Equation2" src="/files/ftp_upload/13824/13824_Equation_PT_2.svg" style="text-align: center; height: 17px;" />

Da elektromagnetische Wellen mit allen Maxwellschen Gleichungen übereinstimmen, wird der erhaltene Ausdruck mit dem Ausdruck verglichen, der unter Verwendung des Faradayschen Gesetzes hergeleitet wurde und die Wellenausbreitungsgeschwindigkeit im Vakuum liefert.

<img alt="Equation3" src="/files/ftp_upload/13824/13824_Equation_PT_3.svg" style="text-align: center; height: 45px;" />

Wenn die numerischen Werte der Permeabilität und Permittivität eingesetzt werden, ergibt sich die erhaltene Ausbreitungsgeschwindigkeit gleich der Lichtgeschwindigkeit.

<img alt="Equation4" src="/files/ftp_upload/13824/13824_Equation_PT_4.svg" style="text-align: center; height: 17px;" />

Das bedeutet, dass die angenommene Welle mit allen Maxwellschen Gleichungen übereinstimmt, vorausgesetzt, dass sich die Wellenfront mit der oben angegebenen Geschwindigkeit bewegt, die als Lichtgeschwindigkeit bezeichnet wird. Beachten Sie, dass der genaue Wert der Lichtgeschwindigkeit als 299.792.458 m/s definiert ist.

Ausbreitungsgeschwindigkeit elektromagnetischer Wellen

Elektromagnetische Wellen stimmen mit dem Ampereschen Gesetz überein. Unter der Annahme, dass kein Leitungsstrom vorhanden ist, wird das Amperesche Gesetz wie folgt angegeben:

Stellen Sie sich ein Flugzeug vor ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Electromagnetic Waves

Elektromagnetische Wellen

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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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the electromagnetic spectrum

Electromagnetic Waves in Everyday Technology

Electromagnetic waves are grouped by wavelength and frequency. This set of waves is called the electromagnetic spectrum. It includes radio waves, microwaves, infrared, visible light, X-rays, and gamma rays. Radio waves have wavelengths from millimeters to kilometers. They are often used for audio communication, such as radios. In many cases, they come from alternating current in the wires of a broadcast antenna. Radio waves also carry AM and FM radio, cellular phone signals, and TV signals. <br...

electromagnetic wave equation

How Maxwell Linked Light to Waves

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plane electromagnetic waves i

Transverse Fields in Electromagnetic Waves

Electromagnetic waves are made of electric and magnetic fields that move through space together. Maxwell's equations predict these waves, and they can travel in free space without a medium. The electric field acts on a stationary charge, while the magnetic field acts on a moving charge. For a wave traveling along the x-axis, the fields are written as Ey(x, t) and Bz(x, t). In free space, there are no free charges or currents, so the charge enclosed and current terms in Maxwell's equations are...

plane electromagnetic waves ii

Faraday’s Law in a Plane Wave

Faraday’s law can be used to link the electric and magnetic fields in a plane electromagnetic wave. Here, the wavefront moves in the x-direction at a constant speed. The goal is to show how the field strengths must be related for the wave to stay consistent with Faraday’s law. To apply the law, a rectangle of width a is placed with its area vector in the positive z-direction. The line integral is taken counterclockwise around the rectangle. One side lies outside the wavefront, so the electric...

propagation speed of electromagnetic waves

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...

electromagnetic waves in matter

How Light Slows in Materials

Electromagnetic waves can travel through matter as well as through vacuum. Light is one example. It can move through air, water, or glass. When an electromagnetic wave passes through a dielectric medium, the equations that describe it change. In Ampere's law, the permittivity of free space, ε0, is replaced by the permittivity of the dielectric, ε. The vacuum permeability, μ0, is also replaced by the permeability of the medium, μ. The wave speed c in vacuum is then replaced by a lower speed, v,...

energy carried by electromagnetic waves

How EM Waves Transfer Energy

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intensity of electromagnetic waves

Poynting Vector and Light Intensity

The Poynting vector describes the energy flux of an electromagnetic wave. It tells how much energy passes through a unit area in a unit time at a specific moment. For a plane electromagnetic wave moving along the x-axis, the energy flux depends on the peak electric field E0 and the peak magnetic field B0. For high-frequency waves, the energy flux changes very quickly with time. Visible light has a frequency on the order of 10^14 Hz, so its energy flux varies too fast to track directly. Most...

momentum and radiation pressure

Radiation Pressure in Light and Comets

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radiation pressure: problem solving

Radiation Pressure in Light and Space

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standing electromagnetic waves

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standing waves in a cavity

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key terms and concepts

See how Ampere’s law and Faraday’s law lead to the vacuum speed of electromagnetic waves and show why it matches the speed of light.

Maxwell’s Equations and Light Speed | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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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Equations of Wave Motion

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Graphing the Wave Function

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Velocity and Acceleration of a Wave

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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

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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

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

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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