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 uma coordenada xyz dividida em duas regiões distintas por um plano paralelo ao plano yz.
Um campo elétrico e magnético uniforme nas direções +y e +z está presente no lado esquerdo, enquanto o lado direito é livre de campo.
Este plano de fronteira, chamado de frente de onda, move-se na direção +x com uma velocidade constante.
Tais ondas onde, a qualquer instante, os campos são uniformes em qualquer plano perpendicular à direção de propagação são chamadas de ondas planas.
Essas ondas satisfazem as equações de Maxwell. Considere uma caixa gaussiana retangular.
Como o campo elétrico está ao longo da direção y, os fluxos elétricos para a superfície ao longo da direção x e z são zero.
Para a superfície superior, o fluxo é oposto à superfície inferior, dando fluxo líquido zero.
Como a caixa não contém carga elétrica, o fluxo elétrico e magnético é zero.
Assim, a lei de Gauss vale para a radiação eletromagnética.
Portanto, os vetores de campo elétrico e magnético são perpendiculares entre si e à direção de propagação, apresentando natureza transversal.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Física Universitária com Física Moderna. São Francisco, CA: Pearson. Seção 32.2; páginas 1055–1056.</li>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão Web]. Obtido de <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; seção 16.2; páginas 706–707.</li>
</ol>

ondas eletromagnéticas planas i

A existência de campos elétricos e magnéticos combinados que se propagam pelo espaço como ondas eletromagnéticas (EM) é a previsão mais significativa das equações de Maxwell. Como as equações de Maxwell valem no espaço livre, as ondas eletromagnéticas previstas não requerem um meio para sua propagação. Uma onda EM é composta por um campo elétrico, definido como a força por carga em uma carga estacionária, e um campo magnético, que é a força por carga em uma carga em movimento.

Assume-se que o campo EM é uma função apenas da coordenada x e do tempo. Assim, a componente y do campo elétrico é então escrita como Ey(x, t), e a componente z do campo magnético é escrita como Bz(x, t). Devido à suposição de espaço livre, não existem cargas ou correntes livres e, portanto, a carga contida e a corrente na equação de Maxwell são definidas como zero.

A aplicabilidade da lei de Gauss para campos elétricos é examinada ao se assumir uma superfície gaussiana retangular com uma seção transversal quadrada de lado l e cujo terceiro lado tem comprimento Δx. A componente y do campo elétrico é a mesma nas faces superior e inferior da caixa. Portanto, os fluxos em ambos os lados se cancelam. Da mesma forma, o fluxo líquido da componente z do campo elétrico através das duas faces laterais também é cancelado. Qualquer fluxo líquido através da superfície, portanto, vem inteiramente da componente x do campo elétrico. Como o campo elétrico não tem dependência em y nem em z, Ex(x, t) é constante sobre a face de uma caixa com área A e tem um valor possivelmente diferente de Ex(x + Δx, t) que é constante sobre a face oposta da caixa. Aplicando a lei de Gauss, obtém-se o fluxo líquido da componente x.

<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

Desde que qenc, a carga contida, seja zero, o fluxo líquido da componente também é zero, e a equação acima implica que Ex(x, t) = Ex(x + Δx, t) para qualquer Δx. Uma componente Ex(x, t) assim não faria parte de uma onda eletromagnética que se propaga ao longo do eixo x, então Ex(x, t) = 0 para essa onda. Portanto, as únicas componentes não nulas do campo elétrico são Ey(x, t) e Ez(x, t), perpendiculares à direção de propagação da onda.

Um argumento similar vale substituindo E por B e usando a lei de Gauss para magnetismo em vez da lei de Gauss para campos elétricos. Isso mostra que o campo B também é perpendicular à direção de propagação da onda. A onda eletromagnética é, portanto, uma onda transversal, com seus campos elétricos e magnéticos oscilantes perpendiculares à sua direção de propagação.

Ondas eletromagnéticas planas I

A existência de campos elétricos e magnéticos combinados que se propagam pelo espaço como ondas eletromagnéticas (EM) é a previsão mais significativa de ...

Education

JoVE Core

Física

Unit 1

Unidade 1

Electromagnetic Waves

Ondas Eletromagnéticas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

transverse-fields-in-electromagnetic-waves

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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Electromagnetic waves are grouped by wavelength and frequency. This set of waves is called the electromagnetic spectrum. It includes radio waves, microwaves, infrared, visible light, X-rays, and gamma rays. Radio waves have wavelengths from millimeters to kilometers. They are often used for audio communication, such as radios. In many cases, they come from alternating current in the wires of a broadcast antenna. Radio waves also carry AM and FM radio, cellular phone signals, and TV signals. <br...

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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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propagation speed of electromagnetic waves

propagation-speed-of-electromagnetic-waves

Maxwell’s Equations and Light Speed

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

How Light Slows in Materials

Electromagnetic waves can travel through matter as well as through vacuum. Light is one example. It can move through air, water, or glass. When an electromagnetic wave passes through a dielectric medium, the equations that describe it change. In Ampere's law, the permittivity of free space, ε0, is replaced by the permittivity of the dielectric, ε. The vacuum permeability, μ0, is also replaced by the permeability of the medium, μ. The wave speed c in vacuum is then replaced by a lower speed, v,...

energy carried by electromagnetic waves

How EM Waves Transfer Energy

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intensity of electromagnetic waves

Poynting Vector and Light Intensity

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momentum and radiation pressure

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radiation pressure: problem solving

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standing 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

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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HIgh School

Physical Science

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PS.7.a

Minnesota Academic Standards in Science

3.2.2 9P.3.1.1.2

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New Jersey Student Learning Standards for Science

High School

HS-PS4-5

Alabama Course of Study Science

9-12.P.3.7.c

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HS-PS4-3

Florida Department of Education

SC.912.P.10

SC.912.P.10.17

SC.912.P.10.18

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South Carolina College and Career Ready Science Standards

P-PS4-3

Earth and Space Science (ESS)

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New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

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Transverse Fields in Electromagnetic Waves

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