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

Considérons une coordonnée xyz divisée en deux régions distinctes par un plan parallèle au plan yz.
Un champ électrique et magnétique uniforme dans les directions +y et +z est présent sur le côté gauche, tandis que le côté droit est sans champ.
Ce plan limite, appelé front d’onde, se déplace dans la direction +x avec une vitesse constante.
De telles ondes où, à tout instant, les champs sont uniformes sur tout plan perpendiculaire à la direction de propagation sont appelées ondes planes.
Ces ondes satisfont aux équations de Maxwell. Considérons une boîte gaussienne rectangulaire.
Comme le champ électrique se trouve dans la direction y, les flux électriques pour la surface dans les directions x et z sont nuls.
Pour la surface supérieure, le flux est opposé à la surface inférieure, ce qui donne un flux net nul.
Étant donné que la boîte n’enferme aucune charge électrique, le flux électrique ainsi que le flux magnétique sont nuls.
Ainsi, la loi de Gauss s'applique au rayonnement électromagnétique.
Par conséquent, les vecteurs de champ électrique et magnétique sont perpendiculaires l’un à l’autre et à la direction de propagation, montrant une nature transversale.

<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 ; Pages 1055 et 1056.</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 706 et 707.</li>
</ol>

les ondes électromagnétiques planes i

L'existence de champs électriques et magnétiques combinés qui se propagent dans l'espace sous forme d'ondes électromagnétiques (EM) est la prédiction la plus significative des équations de Maxwell. Comme les équations de Maxwell s'appliquent dans l'espace libre, les ondes électromagnétiques prédites ne nécessitent pas de support pour leur propagation. Une onde EM comprend un champ électrique, défini comme la force par charge sur une charge stationnaire, et un champ magnétique, qui est la force par charge sur une charge en mouvement.

On suppose que le champ EM est une fonction uniquement de la coordonnée x et du temps. Ainsi, la composante y du champ électrique est alors écrite comme Ey(x, t), et la composante z du champ magnétique est écrite comme Bz(x, t). En raison de l'hypothèse de l'espace libre, il n'y a pas de charges ou de courants libres, et donc la charge enfermée et le courant dans les équations de Maxwell sont fixés à zéro.

L'applicabilité de la loi de Gauss pour les champs électriques est examinée en supposant une surface gaussienne rectangulaire avec une section transversale carrée de côté l et dont le troisième côté a une longueur Δx. La composante y du champ électrique est la même sur les côtés supérieur et inférieur de la boîte. Par conséquent, les flux des deux côtés s'annulent mutuellement. De même, le flux net de la composante z du champ électrique à travers les deux côtés latéraux est également annulé. Tout flux net à travers la surface provient donc entièrement de la composante x du champ électrique. Comme le champ électrique ne dépend pas de y ou de z, Ex(x, t) est constant sur la face d'une boîte d'aire A et a une éventuellement une valeur différente de Ex(x + Δx, t) qui est constante sur la face opposée de la boîte. En appliquant la loi de Gauss, on obtient le flux net de la composante x.

<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

Depuis que qenc, la charge enfermée, est nulle, le flux net de cette composante est également nul, et l'équation ci-dessus implique Ex(x, t) = Ex(x + Δx, t) pour tout Δx. Une telle composante Ex(x, t) ne ferait pas partie d'une onde électromagnétique se propageant le long de l'axe x, donc Ex(x, t) = 0 pour cette onde. Par conséquent, les seules composantes non nulles du champ électrique sont Ey(x, t) et Ez(x, t), perpendiculaires à la direction de propagation de l'onde.

Un argument similaire est valable en substituant E pour B et en utilisant la loi de Gauss pour le magnétisme au lieu de la loi de Gauss pour les champs électriques. Cela montre que le champ B est également perpendiculaire à la direction de propagation de l'onde. L'onde électromagnétique est donc une onde transversale, avec ses champs électrique et magnétique oscillants perpendiculaires à sa direction de propagation.

Les ondes électromagnétiques planes I

L’existence de champs électriques et magnétiques combinés qui se propagent dans l’espace sous forme d’ondes électromagnétiques (EM) est la prédiction la plus significative de ...

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Unit 1

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Electromagnetic Waves

Ondes électromagnétiques

KEY TERMS AND CONCEPTS

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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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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

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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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energy carried by electromagnetic waves

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intensity of electromagnetic waves

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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

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3.2.2 9P.3.1.1.2

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Transverse Fields in Electromagnetic Waves

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