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

Si consideri una coordinata xyz divisa in due regioni distinte da un piano parallelo al piano yz.
Un campo elettrico e magnetico uniforme nelle direzioni +y e +z è presente sul lato sinistro, mentre il lato destro è privo di campo.
Questo piano limite, chiamato fronte d'onda, si muove nella direzione +x con una velocità costante.
Tali onde in cui, in ogni istante, i campi sono uniformi su qualsiasi piano perpendicolare alla direzione di propagazione sono chiamate onde piane.
Queste onde soddisfano le equazioni di Maxwell. Consideriamo una scatola gaussiana rettangolare.
Poiché il campo elettrico si trova lungo la direzione y, i flussi elettrici per la superficie lungo la direzione x e la direzione z sono nulli.
Per la superficie superiore, il flusso è opposto alla superficie inferiore, dando un flusso netto pari a zero.
Poiché la scatola non contiene alcuna carica elettrica, il flusso elettrico e magnetico è zero.
Quindi, la legge di Gauss vale per la radiazione elettromagnetica.
Pertanto, i vettori del campo elettrico e magnetico sono perpendicolari tra loro e alla direzione di propagazione, mostrando una natura trasversale.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson. Sezione 32.2; pagine 1055-1056.</li>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. Estratto da <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; sezione 16.2; pagine 706-707.</li>
</ol>

onde elettromagnetiche piane i

L'esistenza di campi elettrici e magnetici combinati che si propagano nello spazio come onde elettromagnetiche (EM) è la più significativa previsione delle equazioni di Maxwell. Poiché le equazioni di Maxwell valgono nello spazio libero, le onde elettromagnetiche previste non richiedono un mezzo per la loro propagazione. Un'onda EM comprende un campo elettrico, definito come la forza per carica su una carica stazionaria, e un campo magnetico, che è la forza per carica su una carica in movimento.

Si assume che il campo EM sia una funzione solo della coordinata x e del tempo. Quindi, la componente y del campo elettrico viene scritta come Ey(x, t), e la componente z del campo magnetico viene scritta come Bz(x, t). A causa dell'assunzione dello spazio libero, non ci sono cariche libere o correnti, e quindi la carica inclusa e la corrente nelle equazioni di Maxwell vengono impostate su zero.

L'applicabilità della legge di Gauss per i campi elettrici viene esaminata assumendo una superficie gaussiana rettangolare con una sezione trasversale quadrata di lato l e il cui terzo lato ha lunghezza Δx. La componente y del campo elettrico è la stessa sui lati superiore e inferiore della scatola. Pertanto, i flussi su entrambi i lati si annullano reciprocamente. Allo stesso modo, il flusso netto dalla componente z del campo elettrico attraverso i due lati laterali viene anche annullato. Qualsiasi flusso netto attraverso la superficie, quindi, proviene interamente dalla componente x del campo elettrico. Poiché il campo elettrico non ha dipendenza da y o z, Ex(x, t) è costante sulla faccia di una scatola con area A e ha un valore possibilmente diverso di Ex(x + Δx, t) che è costante sulla faccia opposta della scatola. Applicando la legge di Gauss si ottiene il flusso netto della componente x.

<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

Dato che qenc, la carica inclusa, è zero, anche il flusso netto della componente è zero, e l'equazione sopra implica Ex(x, t) = Ex(x + Δx, t) per qualsiasi Δx. Una tale componente Ex(x, t) non sarebbe parte di un'onda elettromagnetica che si propaga lungo l'asse x, quindi Ex(x, t) = 0 per questa onda. Pertanto, le uniche componenti non nulle del campo elettrico sono Ey(x, t) e Ez(x, t), perpendicolari alla direzione di propagazione dell'onda.

Un argomento simile vale sostituendo E con B e utilizzando la legge di Gauss per il magnetismo invece della legge di Gauss per i campi elettrici. Ciò mostra che il campo B è anche perpendicolare alla direzione di propagazione dell'onda. L'onda elettromagnetica è quindi un'onda trasversale, con i suoi campi elettrici e magnetici oscillanti perpendicolari alla sua direzione di propagazione.

Onde elettromagnetiche piane I

L'esistenza di campi elettrici e magnetici combinati che si propagano nello spazio come onde elettromagnetiche (EM) è la previsione più significativa di ...

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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

Faraday’s Law in a Plane Wave

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electromagnetic waves in matter

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How EM Waves Transfer Energy

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radiation pressure: problem solving

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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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Transverse Fields in Electromagnetic Waves

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