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

Electromagnetic Wave Equation

Considere la forma diferencial de las cuatro ecuaciones de Maxwell en el vacío, que relacionan mutuamente los campos eléctrico y magnético.
Se pueden encontrar ecuaciones separadas para los campos eléctrico y magnético aplicando el rizo a ambos lados de la tercera y cuarta ecuaciones, usando identidades geométricas, la primera y segunda ecuaciones, la regla de las derivadas parciales y la tercera y cuarta ecuaciones.
La simplificación revela que los campos eléctrico y magnético siguen la misma ecuación. Implica que cada componente cartesiano satisface la ecuación de onda. Entonces, los campos electromagnéticos son ondas tridimensionales.
Se propagan en el vacío con una velocidad determinada por las constantes naturales.
Supongamos que la onda atraviesa en la dirección z. Se escriben las soluciones generales para los campos.
A estas soluciones se les aplica la primera y segunda ecuaciones de Maxwell. La simplificación revela que los componentes z de los campos son cero. Entonces, las ondas electromagnéticas son ondas transversales.
La tercera ecuación de Maxwell aplicada a las soluciones da relaciones entre sus componentes x e y, que se pueden agrupar en forma vectorial. Por lo tanto, los campos eléctrico y magnético que viajan son mutuamente perpendiculares.

<ol>
	<li>Griffiths, David J. (1999). Introducción a la Electrodinámica (3ª ed.). Río Saddle Superior, Nueva Jersey 07458; Sección 9.2; páginas 375-379.</li>
	<li>Young, H.D. y Freedman, R.A. (2012). Física Universitaria con Física Moderna. San Francisco, CA: Pearson; Sección 32.2; Página 1058.</li>
</ol>

ecuación de la onda electromagnética

Las ecuaciones de Maxwell para los campos electromagnéticos están relacionadas con cargas fuente, ya sean estáticas o en movimiento. Estos campos actúan sobre una carga de prueba, cuya trayectoria puede ser determinada utilizando condiciones de frontera adecuadas. El objetivo del electromagnetismo es así teóricamente completo. Sin embargo, aunque los campos eléctrico y magnético fueron introducidos por primera vez como construcciones matemáticas para simplificar la descripción de las fuerzas mutuas entre cargas, surge una pregunta natural a partir de las ecuaciones de Maxwell: ¿Qué sucede con los campos eléctrico y magnético cuando no hay cargas fuente? Considera las formas diferenciales de las cuatro ecuaciones de Maxwell en el vacío. Se observa una simetría natural en las ecuaciones diferenciales parciales de primer orden, excepto por las constantes naturales. Las exploraciones matemáticas revelaron que cada componente del campo eléctrico y magnético sigue la misma ecuación de onda. La velocidad está determinada por una combinación de las constantes naturales: la permitividad del vacío y la permeabilidad del vacío. Sustituyendo sus valores, Maxwell descubrió que esta velocidad es muy cercana al valor experimental de la velocidad de la luz. El resultado es sorprendente dado la independencia de las observaciones: una proveniente de la teoría de la electrodinámica, que surgió del estudio de cargas y corrientes en el laboratorio, y la otra una determinación experimental de la velocidad de la luz. Conectando los puntos, Maxwell hipotetizó que la luz no es más que ondas electromagnéticas. La hipótesis fue posteriormente verificada experimentalmente. Este curso de la historia es una lección esencial sobre la importancia de las matemáticas en la explicación de la naturaleza. Además, los campos eléctrico y magnético no son meras construcciones matemáticas; pueden viajar sin ningún material presente, lo que les otorga un significado físico. Las soluciones generales de las ecuaciones de onda son conocidas. Ya que los campos electromagnéticos siguen el principio de superposición, las soluciones más generales de las ecuaciones de onda pueden escribirse como superposiciones lineales de estas soluciones. Las ecuaciones de Maxwell imponen restricciones adicionales sobre las soluciones generales. Revelan otros hechos notables: los campos eléctrico y magnético están en fase entre sí, son mutuamente perpendiculares y ambos son perpendiculares a la dirección de propagación de la onda. Por lo tanto, las ondas electromagnéticas son ondas transversales.

Ecuación de la Onda Electromagnética

Las ecuaciones de Maxwell para los campos electromagnéticos están relacionadas con las cargas de la fuente, ya sean estáticas o móviles. Estos campos actúan sobre una carga de prueba, cuya ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Electromagnetic Waves

Ondas electromagnéticas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

physics

JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

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

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

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

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

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

South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-3

P-PS4-5

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-1.

E-ESS1-2.

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

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PS.PSc.8.1

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Intensity Of Electromagnetic Waves

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Interference: Path Lengths

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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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