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

Рассмотрим координату xyz, разделенную на две отдельные области плоскостью, параллельной плоскости yz.
Однородное электрическое и магнитное поле в направлениях +y и +z присутствуют с левой стороны, в то время как правая сторона не имеет поля.
Эта граничная плоскость, называемая волновым фронтом, движется в направлении +x с постоянной скоростью.
Такие волны, в которых в любой момент времени поля равномерны на любой плоскости, перпендикулярной направлению распространения, называются плоскими волнами.
Эти волны удовлетворяют уравнениям Максвелла. Рассмотрим прямоугольный гауссов ящик.
Поскольку электрическое поле находится вдоль y-направления, электрические потоки для поверхности вдоль x-направления и z-направления равны нулю.
Для верхней поверхности флюс противоположен нижней поверхности, что дает нулевой чистый флюс.
Поскольку коробка не содержит электрического заряда, электрический, а также магнитный поток равны нулю.
Таким образом, закон Гаусса справедлив для электромагнитного излучения.
Поэтому векторы электрического и магнитного поля перпендикулярны друг другу и направлению распространения, проявляя поперечный характер.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. Статья 32.2; Страницы 1055–1056.</li>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Получено из <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; раздел 16.2; стр. 706–707.</li>
</ol>

ПЛОСКИЕ ЭЛЕКТРОМАГНИТНЫЕ ВОЛНЫ i

Существование комбинированного электрического и магнитного поля, распространяющегося через пространство как электромагнитные волны (EM волны), является наиболее значительным предсказанием уравнений Максвелла. Поскольку уравнения Максвелла справедливы в свободном пространстве, предсказанные электромагнитные волны не требуют среды для своего распространения. (ЭМ) волна включает в себя электрическое поле, определяемое как сила на единицу заряда неподвижного заряда, и магнитное поле, определяемое как сила на единицу заряда движущегося заряда.

(ЭМ) поле считается функцией только координаты x и времени. Таким образом, y компонента электрического поля записывается как Ey(x, а z компонента магнитного поля записывается как Bz(x, t). В связи с предположением свободного пространства, отсутствуют свободные заряды или токи, и, следовательно, заряд, заключённый и ток в уравнении Максвелла, принимаются равными нулю.

Применимость закона Гаусса для электрических полей проверяется при предположении прямоугольной гауссовой поверхности с квадратным поперечным сечением стороной l и третьей стороной длиной Δx. y компонента электрического поля на верхней и нижней стороне коробки одинакова. Поэтому потоки с обеих сторон сбрасывают друг друга. Аналогично, суммарный поток от z-компоненты электрического поля через боковые стороны также уничтожается. Любой чистый поток через поверхность, следовательно, полностью происходит от x компоненты электрического поля. Поскольку электрическое поле не зависит от y- или z, Ex(x, t) является постоянным на лице коробки с площадью A и имеет, возможно, другое значение Ex(x + Δx, t), которое также является постоянным на противоположной стороне коробки. Применение закона Гаусса даёт чистый поток x-компоненты.

<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

Поскольку заключённый заряд qenc , равен нулю, чистый поток компонента также равен нулю, и вышеуказанное уравнение подразумевает Ex(x, t) = Ex(x + Δx, t для любой Δx. Такая компонента Ex(x, t) не будет частью распространяющейся вдоль оси x электромагнитной волны, поэтому Ex(x, t) = 0 для этой волны. Таким образом, единственные ненулевые компоненты электрического поля - Ey(x, t) и Ez(x, t), перпендикулярные направлению распространения волны.

Аналогичный аргумент применим, заменив E на B и используя закон Гаусса для магнитизма вместо закона Гаусса для электрических полей. Это показывает, что магнитное поле B также перпендикулярно направлению распространения волны. Следовательно, электромагнитная волна является поперечной волной, с колеблющимися электрическими и магнитными полями, перпендикулярными направлению распространения.

ПЛОСКИЕ ЭЛЕКТРОМАГНИТНЫЕ ВОЛНЫ I

Существование комбинированных электрических и магнитных полей, которые распространяются в пространстве в виде электромагнитных (ЭМ) волн, является наиболее значимым предсказанием ...

Education

JoVE Core

Физика

Unit 1

Раздел 1

Electromagnetic Waves

Электромагнитные волны

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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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

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

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energy carried by electromagnetic waves

How EM Waves Transfer Energy

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intensity of electromagnetic waves

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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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JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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HIgh School

Physical Science

PS.7

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

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HS-PS4-5

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9-12.P.3.7.c

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HS-PS4-3

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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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E-ESS1-2.

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New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-4.

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Transverse Fields in Electromagnetic Waves

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