Name: transverse fields in electromagnetic waves
Uploaded: 2023-04-30T12:46:03.000Z
Duration: 1 min 30 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physics

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Waves and Their Applications in Technologies for Information Transfer

PS.Phy.7.1

Plane Electromagnetic Waves I

Considere una coordenada xyz dividida en dos regiones distintas por un plano paralelo al plano yz.
Un campo eléctrico y magnético uniforme en las direcciones +y y +z está presente en el lado izquierdo, mientras que el lado derecho está libre de campo.
Este plano límite, llamado frente de onda, se mueve en la dirección +x con una velocidad constante.
Las ondas en las que, en cualquier instante, los campos son uniformes en cualquier plano perpendicular a la dirección de propagación se denominan ondas planas.
Estas ondas satisfacen las ecuaciones de Maxwell. Considere una caja gaussiana rectangular.
Dado que el campo eléctrico está a lo largo de la dirección y, los flujos eléctricos para la superficie a lo largo de la dirección x y la dirección z son cero.
Para la superficie superior, el flujo es opuesto a la superficie inferior, lo que da un flujo neto cero.
Dado que la caja no contiene carga eléctrica, el flujo eléctrico y magnético es cero.
Por lo tanto, la ley de Gauss es válida para la radiación electromagnética.
Por lo tanto, los vectores del campo eléctrico y magnético son perpendiculares entre sí y en la dirección de propagación, mostrando la naturaleza transversal.

<ol>
	<li>Young, H.D. y Freedman, R.A. (2012). Física Universitaria con Física Moderna. San Francisco, CA: Pearson. Sección 32.2; páginas 1055-1056.</li>
	<li>OpenStax. (2019). Física Universitaria Vol. 2. [Versión web]. Obtenido de <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; Sección 16.2; páginas 706-707.</li>
</ol>

ondas electromagnéticas planas i

La existencia de campos eléctricos y magnéticos combinados que se propagan a través del espacio como ondas electromagnéticas (EM) es la predicción más significativa de las ecuaciones de Maxwell. Como las ecuaciones de Maxwell se cumplen en el espacio libre, las ondas electromagnéticas predichas no requieren un medio para su propagación. Una onda EM comprende un campo eléctrico, definido como la fuerza por carga en una carga estacionaria, y un campo magnético, que es la fuerza por carga en una carga en movimiento.

Se asume que el campo EM es una función solo de la coordenada x y el tiempo. Por lo tanto, la componente y del campo eléctrico se escribe como Ey(x, t), y la componente z del campo magnético se escribe como Bz(x, t). Debido a la suposición de espacio libre, no hay cargas ni corrientes libres, por lo que la carga encerrada y la corriente en la ecuación de Maxwell se establecen en cero.

La aplicabilidad de la ley de Gauss para campos eléctricos se examina al asumir una superficie gaussiana rectangular con una sección transversal cuadrada de lado l y cuyo tercer lado tiene una longitud de Δx. La componente y del campo eléctrico es la misma en los lados superior e inferior de la caja. Por lo tanto, los flujos en ambos lados se cancelan entre sí. De manera similar, el flujo neto de la componente z del campo eléctrico a través de los dos lados laterales también se cancela. Por lo tanto, cualquier flujo neto a través de la superficie proviene enteramente de la componente x del campo eléctrico. Como el campo eléctrico no tiene dependencia de y o z, Ex(x, t) es constante sobre la cara de una caja con área A y tiene un valor posiblemente diferente de Ex(x + Δx, t) que es constante sobre la cara opuesta de la caja. Aplicando la ley de Gauss se obtiene el flujo neto de la componente x.

<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;"> Dado que qenc, la carga encerrada, es cero, el flujo neto de la componente también es cero, y la ecuación anterior implica que Ex(x, t) = Ex(x + Δx, t) para cualquier Δx. Una componente Ex(x, t) no sería parte de una onda electromagnética que se propaga a lo largo del eje x, por lo que Ex(x, t) = 0 para esta onda. Por lo tanto, las únicas componentes no nulas del campo eléctrico son Ey(x, t) y Ez(x, t), perpendiculares a la dirección de propagación de la onda. Un argumento similar se aplica al sustituir E por B y usar la ley de Gauss para el magnetismo en lugar de la ley de Gauss para campos eléctricos. Esto muestra que el campo B también es perpendicular a la dirección de propagación de la onda. Por lo tanto, la onda electromagnética es una onda transversal, con sus campos eléctrico y magnético oscilando perpendicularmente a su dirección de propagación.

Ondas electromagnéticas planas I

La existencia de campos eléctricos y magnéticos combinados que se propagan a través del espacio como ondas electromagnéticas (EM) es la predicción más significativa de ...

Education

Educación

JoVE Core

Física

Unit 1

Unidad 1

Electromagnetic Waves

Ondas electromagnéticas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 set to zero. This lets us test which field components can remain in the wave.

To apply Gauss's law for electric fields, a rectangular Gaussian surface with a square cross-section of side l and a third side of length Δx is used. The y-component of the electric field is the same on the top and bottom sides, so those fluxes cancel. The z-component through the two lateral sides also cancels, so any net flux comes only from Ex.

Because Ex depends only on x and time, it is constant over one face of the box and may have a different value on the opposite face. Gauss's law gives zero net flux because the enclosed charge is zero. That means Ex(x, t) = Ex(x + Δx, t) for any Δx, so Ex(x, t) is not part of the wave and must be zero. The electric field components left in the wave are Ey(x, t) and Ez(x, t), both perpendicular to the direction of travel.

A similar argument applies to the magnetic field by using Gauss's law for magnetism instead of Gauss's law for electric fields. This shows that the magnetic field is also perpendicular to the direction of propagation. An electromagnetic wave is therefore a transverse wave, with oscillating electric and magnetic fields at right angles to the wave's motion.

Transverse Fields in Electromagnetic Waves

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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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Heinrich Hertz used sparks and tuned circuits to show that electromagnetic waves could be produced in the lab. Starting in 1887, the German physicist ran experiments that confirmed electromagnetic waves exist and travel at the speed of light. Hertz built an alternating-current RLC circuit. RLC stands for resistor, inductor, and capacitor. The circuit was set to a known resonant frequency and connected to a loop of wire. High voltage across the gap in the loop created sparks. Those sparks gave...

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plane electromagnetic waves i

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

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propagation speed of electromagnetic waves

propagation-speed-of-electromagnetic-waves

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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

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key terms and concepts

See why electromagnetic waves are transverse. Learn how Maxwell’s equations show that electric and magnetic fields stay perpendicular to the direction of travel.

Transverse Fields in Electromagnetic 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.

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South Carolina College and Career Ready Science Standards

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Transverse Fields in Electromagnetic Waves

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