Name: electromagnetic wave reflection at conductors
Uploaded: 2023-09-18T17:11:17.000Z
Duration: 1 min 15 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.7

PS.7.a

Standing Electromagnetic Waves

Lembre-se das ondas estacionárias formadas em uma corda apertada. 
As ondas estacionárias são a combinação de duas ondas que se movem na direção oposta, mas têm a mesma amplitude e frequência.
Considere uma folha condutora perfeita colocada no plano y-z. Uma onda eletromagnética polarizada linearmente atinge a folha, enquanto viaja na direção x negativa.
A onda incidente induz a corrente na superfície do condutor, resultando em campos elétricos adicionais, produzindo uma onda refletida com a mesma frequência e amplitude da onda incidente.
A superposição dessas duas ondas gera a onda estacionária. Simplificando essas expressões, forneça os pontos na onda onde as magnitudes do campo elétrico e do campo magnético são zero. Estes são chamados de nós ou planos nodais.
Um antinó é um ponto onde a amplitude vai do deslocamento positivo máximo para o deslocamento negativo máximo.
Os nós do campo elétrico coincidem com os antinós dos campos magnéticos e vice-versa. Portanto, eles estão 90 graus fora de fase em cada ponto.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Física Universitária com Física Moderna. São Francisco, CA: Pearson. Seção 32.5; páginas 1069–1070.</li>
</ol>

ondas eletromagnéticas estacionárias

As ondas eletromagnéticas podem ser refletidas; a superfície de um condutor, ou de um dielétrico, pode atuar como um refletor. Assim como os campos elétrico e magnético obedecem ao princípio da superposição, as ondas eletromagnéticas também o fazem. A superposição de uma onda incidente e uma onda eletromagnética refletida produz uma onda estacionária análoga às ondas estacionárias criadas em uma corda esticada.

Suponha que uma folha de um condutor perfeito seja colocada no plano yz, e uma onda eletromagnética linearmente polarizada viajando na direção negativa do eixo x a atinja. Como o campo elétrico não pode ter uma componente paralela à superfície de um condutor perfeito, o campo elétrico deve ser zero em todos os lugares no plano yz. O campo elétrico da onda eletromagnética incidente não é zero a todo momento no plano yz, mas essa onda incidente induz correntes oscilantes na superfície do condutor, dando origem a um campo elétrico adicional. O campo elétrico líquido, que é a soma vetorial deste campo e do campo incidente, é zero em todos os lugares dentro e na superfície do condutor. As correntes induzidas na superfície do condutor também geram uma onda refletida que se propaga para fora do plano. O princípio da superposição afirma que o campo total em qualquer ponto é a soma vetorial dos campos elétricos das ondas incidente e refletida, assim como o campo magnético. A superposição das ondas incidente e refletida gera ondas estacionárias.

<img alt="Equation1" src="/files/ftp_upload/13829/13829_Equation_1.png" style="text-align: center; height: 24px;" />

<img alt="Equation2" src="/files/ftp_upload/13829/13829_Equation_2.png" style="text-align: center; height: 22px;" />

Simplificando essas expressões, obtemos os pontos na onda onde as magnitudes do campo elétrico e do campo magnético são zero. Esses pontos são chamados de nós, ou planos nodais. Na metade do caminho entre quaisquer dois planos nodais adjacentes estão os planos de amplitude máxima; estes são os planos antinodais.

O campo elétrico total é uma função seno, e o campo magnético total é uma função cosseno. Portanto, as variações senoidais dos dois campos estão fora de fase em cada ponto. Os nós do campo elétrico coincidem com os antinós dos campos magnéticos e vice-versa. Portanto, eles estão fora de fase em 90 graus em cada ponto. Isso é em contraste com uma onda que viaja em uma direção, para a qual as variações senoidais dos campos elétrico e magnético estão em fase em todos os pontos.

Ondas Eletromagnéticas Estacionárias

As ondas eletromagnéticas podem ser refletidas; A superfície de um condutor ou dielétrico pode atuar como um refletor. Como os campos elétricos e magnéticos obedecem ao ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Electromagnetic Waves

Ondas Eletromagnéticas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

electromagnetic wave reflection at conductors

Electromagnetic waves can reflect from a conductor or a dielectric. When the reflected wave combines with the incoming wave, the result is a standing electromagnetic wave. This is similar to the standing waves formed on a stretched string.

To see how this happens, consider a perfect conductor placed in the yz-plane. A linearly polarized electromagnetic wave moving in the negative x-direction strikes the surface. The electric field cannot have a component parallel to the surface of a perfect conductor, so the electric field must be zero everywhere in the yz-plane.

The incident wave is not zero at the surface, but it induces oscillating currents on the conductor. These currents create an additional electric field. The net electric field is the vector sum of the incident and induced fields, and it is zero everywhere inside and on the conductor's surface. The same surface currents also produce a reflected wave that moves away from the plane.

The total field at any point is the vector sum of the incident and reflected electric fields, and the same idea applies to the magnetic field. This superposition creates standing waves. The places where the electric or magnetic field magnitude is zero are called nodes, or nodal planes. The planes halfway between adjacent nodes have maximum amplitude and are called antinodal planes.

For these standing waves, the total electric field follows a sine function, while the total magnetic field follows a cosine function. The two fields are therefore 90° out of phase at each point. Electric field nodes line up with magnetic field antinodes, and magnetic field nodes line up with electric field antinodes. This is different from a wave traveling in one direction, where the electric and magnetic fields are in phase at a given point.

Electromagnetic Wave Reflection at Conductors

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Explore how reflected electromagnetic waves form standing patterns at conductors, with nodes, antinodes, and electric and magnetic fields out of phase.

Electromagnetic Wave Reflection at Conductors | JoVE K12

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Minnesota Academic Standards in Science

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4.2.1 9P.3.2.2.1

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PS.7.b

Electromagnetic Wave Reflection at Conductors

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