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

Вспомним стоячие волны, сформированные в тугую струну. 
Стоячие волны — это комбинация двух волн, которые движутся в противоположном направлении, но имеют одинаковую амплитуду и частоту.
Рассмотрим идеальный проводящий лист, размещенный в плоскости y-z. Линейно поляризованная электромагнитная волна ударяется о лист, при этом перемещаясь в отрицательном направлении x.
Падающая волна индуцирует ток на поверхности проводника, в результате чего образуются дополнительные электрические поля, в результате чего образуется отраженная волна с той же частотой и амплитудой, что и падающая волна.
Наложение этих двух волн порождает стоячую волну. Упрощая эти выражения, можно определить точки на волне, где величины электрического поля и магнитного поля равны нулю. Они называются узлами или узловыми плоскостями.
Пучность — это точка, в которой амплитуда идет от максимального положительного к максимальному отрицательному смещению.
Узлы электрического поля совпадают с пучностями магнитных полей, и наоборот. Следовательно, они находятся на 90 градусов в противофазе в каждой точке.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. Статья 32.5; Страницы 1069–1070.</li>
</ol>

Стоячие электромагнитные волны

Электромагнитные волны могут отражаться; поверхность проводника или диэлектрика может действовать как отражатель. Так же, как и электрические и магнитные поля, электромагнитные волны подчиняются принципу суперпозиции. Суперпозиция падающей волны и отражённой электромагнитной волны создаёт стоячую волну, аналогичную стоячей волне, созданной на натянутой струне.

Предположим, что лист идеального проводника помещён в плоскость yz, а линейно поляризованная электромагнитная волна, движущаяся в отрицательном направлении оси x, попадает на него. Поскольку электрическое поле не может иметь компоненту, параллельную поверхности идеального проводника, электрическое поле должно быть равным нулю во всей плоскости yz. Электрическое поле падающей электромагнитной волны не равно нулю во всём времени в плоскости yz, но эта падающая волна вызывает колеблющиеся токи на поверхности проводника, вызывая дополнительное электрическое поле. Суммарное электрическое поле, которое является векторной суммой этого поля и падающего поля, равно нулю везде внутри и на поверхности проводника. Индуцированные на поверхности проводника токи также создают отражённую волну, которая выходит из плоскости. Принцип суперпозиции утверждает, что общее поле в любой точке является векторной суммой электрических полей падающих и отражённых волн, аналогично магнитному полю. Суперпозиция падающих и отражённых волн вызывает возникновение стоячих волн.

<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;" />

Упрощение этих выражений позволяет найти точки волны, в которых амплитуда электрического и магнитного поля равна нулю. Их называют узлами или нодальными плоскостями. По середине между любыми двумя соседними нодальными плоскостями находятся плоскости с максимальной амплитудой; они называются антиузловыми плоскостями.

Общее электрическое поле - это синусоидальная функция, а общее магнитное поле - это косинусоидальная функция. Поэтому синусоидальные изменения двух полей смещены в фазе на каждой точке. Узлы электрического поля совпадают с антиузлами магнитного поля и наоборот. Следовательно, они смещены на 90° в фазе на каждой точке. Это в отличие от волны, движущейся в одном направлении, для которой синусоидальные изменения электрических и магнитных полей совпадают по фазе в конкретной точке.

Электромагнитные волны могут отражаться; Поверхность проводника или диэлектрика может выступать в качестве отражателя. Поскольку электрические и магнитные поля подчиняются ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Electromagnetic Waves

Электромагнитные волны

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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key terms and concepts

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

physics

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Minnesota Academic Standards in Science

9-12

4.2.1 9P.3.2.2.1

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New Jersey Student Learning Standards for Science

High School

waves-and-their-applications-in-technologies-for-information-transfer

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HS-PS4-5

Alabama Course of Study Science

9-12.PS.2.2.e

9-12.P.3.7.c

Florida Department of Education

SC.912.P.10

SC.912.P.10.17

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-4

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-2.

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PS.7.b

Electromagnetic Wave Reflection at Conductors

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