Name: how maxwell linked light to waves
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 24 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Waves and Their Applications

PS.PSc.8.2

Electromagnetic Wave Equation

Betrachten Sie die Differentialform der vier Maxwell-Gleichungen im Vakuum, die die elektrischen und magnetischen Felder miteinander in Beziehung setzen.
Getrennte Gleichungen für das elektrische und das magnetische Feld können gefunden werden, indem die Krümmung auf beide Seiten der dritten und vierten Gleichung angewendet wird, wobei geometrische Identitäten, die erste und zweite Gleichung, die Regel der partiellen Ableitungen und die dritte und vierte Gleichung verwendet werden.
Die Vereinfachung zeigt, dass das elektrische und das magnetische Feld der gleichen Gleichung folgen. Es impliziert, dass jede kartesische Komponente die Wellengleichung erfüllt. Die elektromagnetischen Felder sind also dreidimensionale Wellen.
Sie breiten sich im Vakuum mit einer Geschwindigkeit aus, die durch Naturkonstanten bestimmt wird.
Angenommen, die Welle verläuft in z-Richtung. Die allgemeinen Lösungen für die Felder sind geschrieben.
Auf diese Lösungen werden die erste und zweite Maxwell-Gleichung angewendet. Die Vereinfachung zeigt, dass die Z-Komponenten der Felder Null sind. Elektromagnetische Wellen sind also Transversalwellen.
Die dritte Gleichung von Maxwell, die auf die Lösungen angewendet wird, ergibt Beziehungen zwischen ihren x- und y-Komponenten, die in Vektorform zusammengefasst werden können. Die wandernden elektrischen und magnetischen Felder stehen also senkrecht zueinander.

<ol>
	<li>Griffiths, David J. (1999). Einführung in die Elektrodynamik (3. Aufl.). Upper Saddle River, New Jersey 07458; Abschnitt 9.2; Seiten 375–379.</li>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson; Abschnitt 32.2; Seite 1058.</li>
</ol>

elektromagnetische wellengleichung

Maxwells Gleichungen für elektromagnetische Felder stehen in Beziehung zu ursächlichen Ladungen, sei es statische oder bewegte. Diese Felder wirken auf eine Testladung, deren Bahn mithilfe geeigneter Randbedingungen bestimmt werden kann. Das Ziel des Elektromagnetismus ist damit theoretisch erreicht.

Allerdings taucht aus Maxwells Gleichungen eine natürliche Frage auf: Was passiert mit den elektrischen und magnetischen Feldern, wenn es keine ursächlichen Ladungen gibt?

Betrachten wir die Differentialformen der vier Maxwellschen Gleichungen im Vakuum. In den partiellen Differentialgleichungen erster Ordnung wird eine natürliche Symmetrie beobachtet, mit Ausnahme der Naturkonstanten.

Mathematische Untersuchungen ergaben, dass jede elektrische und magnetische Feldkomponente der gleichen Wellengleichung folgt. Die Geschwindigkeit wird durch eine Kombination der Naturkonstanten bestimmt: die Permittivität des Vakuums und die Permeabilität des Vakuums. Durch die Substitution ihrer Zahlen entdeckte Maxwell, dass diese Geschwindigkeit sehr nahe am experimentellen Wert der Lichtgeschwindigkeit liegt.

Das Ergebnis ist verblüffend, wenn man bedenkt, dass die Beobachtungen unabhängig voneinander gemacht wurden: zum einen durch die Theorie der Elektrodynamik, die aus der Untersuchung von Ladungen und Strömen im Labor hervorging, und zum anderen durch eine experimentelle Bestimmung der Lichtgeschwindigkeit.

Durch die Verknüpfung der Punkte stellte Maxwell die Hypothese auf, dass Licht nichts anderes als elektromagnetische Wellen ist. Die Hypothese wurde später experimentell verifiziert. Dieser Verlauf der Geschichte ist eine wichtige Lektion über die Bedeutung der Mathematik für die Erklärung der Natur. Außerdem sind elektrische und magnetische Felder keine rein mathematischen Konstrukte; sie können sich auch ohne Material fortbewegen, was ihnen eine physikalische Bedeutung verleiht.

Die allgemeinen Lösungen der Wellengleichungen sind bekannt. Da elektromagnetische Felder dem Prinzip der Überlagerung folgen, können allgemeinere Lösungen der Wellengleichungen als lineare Überlagerungen dieser Lösungen geschrieben werden.

Maxwells Gleichungen legen zusätzliche Einschränkungen auf die allgemeinen Lösungen fest. Sie enthüllen weitere bemerkenswerte Tatsachen: Die elektrischen und magnetischen Felder sind in Phase miteinander und stehen senkrecht zueinander sowie senkrecht zur Ausbreitungsrichtung der Welle. Elektromagnetische Wellen sind also transversale Wellen.

Elektromagnetische Wellengleichung

Die Maxwell-Gleichungen für elektromagnetische Felder beziehen sich auf Quellenladungen, entweder statisch oder bewegend. Diese Felder wirken auf eine Testladung, deren ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Electromagnetic Waves

Elektromagnetische Wellen

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

how maxwell linked light to waves

Maxwell's equations show how electric and magnetic fields behave in a vacuum, or empty space. They are written as differential equations and describe fields created by source charges, whether the charges are still or moving. These fields also act on a test charge, and its motion can be found with the right boundary conditions.

The key question in empty space is what happens when there are no source charges. In the vacuum form of Maxwell's four equations, the first-order partial differential equations have a clear symmetry, except for the natural constants. From this symmetry, mathematicians found that each component of the electric field and magnetic field satisfies the same wave equation.

The wave speed depends on two vacuum constants: permittivity and permeability. When Maxwell used their values, he found a speed very close to the measured speed of light. That was a striking match because the two results came from very different places: one from electrodynamics in the lab and the other from experiments on light.

Maxwell then proposed that light is an electromagnetic wave. Later experiments confirmed this idea. This story also shows why mathematics matters in science, because it can reveal links that are not obvious from experiments alone.

The fields are not just mathematical ideas. They can travel through space without any material medium, so they have real physical meaning. The general solutions of the wave equation are known, and because electromagnetic fields follow superposition, more complex waves can be built from linear combinations of those solutions.

Maxwell's equations add more rules to these solutions. They show that the electric and magnetic fields are in phase with each other, meaning their peaks and valleys line up. They are also perpendicular to each other and both are perpendicular to the direction the wave travels, so electromagnetic waves are transverse waves.

How Maxwell Linked Light to Waves

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key terms and concepts

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How Maxwell Linked Light to Waves | JoVE K12

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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.

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Waves and Their Applications in Technologies for Information Transfer

PS.Phy.7.1

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

HS-PS4-1

Tennessee Academic Standards

PHYS.PS4.5

Virginia  Standards of Learning

HIgh School

PS.7

PS.7.a

PH.5

PH.5.c

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New Jersey Student Learning Standards for Science

HS-PS4-5

Alabama Course of Study Science

9-12.P.3.7.c

Next Generation Science Standards

HS-PS4-3

Florida Department of Education

SC.912.P.10

SC.912.P.10.18

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South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-3

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Earth’s Place in the Universe

E-ESS1-1.

E-ESS1-2.

Georgia Standards of Excellence

SPS9.

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Electromagnetic Waves and Mechanical Waves

SP4.

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Mechanical and Electromagnetic Waves Properties

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Energy and Power of a Wave

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

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Reflection of Waves

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Interference: Path Lengths

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

PS.PSc.8.3

Standing Waves

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Modes of Standing Waves - I

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Modes of Standing Waves: II

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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.

How Maxwell Linked Light to Waves

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