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

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

Waves and Their Applications in Technologies for Information Transfer

PS.Phy.7.1

Plane Electromagnetic Waves I

yz 평면에 평행한 평면에 의해 두 개의 별개 영역으로 분할된 xyz 좌표를 생각해 보십시오.
+y 및 +z 방향의 균일한 전기장 및 자기장은 왼쪽에 존재하고 오른쪽에는 자기장이 없습니다.
파면이라고 하는 이 경계면은 일정한 속도로 +x 방향으로 이동합니다.
어떤 순간에도, 자기장이 전파 방향에 수직인 모든 평면에 걸쳐 균일한 그러한 파동을 평면파(plane wave)라고 부른다.
이 파동은 맥스웰 방정식을 충족합니다. 직사각형 가우스 상자를 고려하십시오.
전기장이 y 방향을 따르기 때문에 x 방향과 z 방향을 따라 표면에 대한 전기 플럭스는 0입니다.
상단 표면의 경우 플럭스는 하단 표면과 반대편에 있어 순 플럭스가 0입니다.
상자는 전하를 둘러싸지 않기 때문에 전기 플럭스와 자속은 0입니다.
따라서 가우스의 법칙은 전자기 복사에 적용됩니다.
따라서 전기장 벡터와 자기장 벡터는 서로 그리고 전파 방향에 수직이며 횡방향 특성을 보여줍니다.

<ol>
	<li>Young, H.D. 및 Freedman, RA (2012). 현대 물리학을 가진 대학 물리학. 샌프란시스코, 캘리포니아 : 피어슨. 섹션 32.2; 1055–1056쪽.</li>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전]. 원본 주소 <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; 섹션 16.2; 706–707쪽.</li>
</ol>

평면전자기파Ⅰ

전자기(EM)파로 공간을 통해 전파되는 결합된 전기장과 자기장의 존재는 맥스웰 방정식의 가장 중요한 예측입니다. 맥스웰의 방정식은 자유 공간에서 성립하므로 예측된 전자기파는 전파를 위해 매질을 필요로 하지 않습니다. EM파는 정지 전하의 전하당 힘으로 정의되는 전기장과 움직이는 전하의 전하당 힘으로 정의되는 자기장으로 구성됩니다.

EM 필드는 x 좌표와 시간만의 함수로 간주됩니다. 따라서 전기장의 y 구성요소는 Ey(x, t), 자기장의 z 구성요소는 Bz(x, t). 여유 공간이라는 가정으로 인해 자유 전하나 전류가 존재하지 않으므로, 맥스웰 방정식에 포함된 전하와 전류는 0으로 설정됩니다.

전기장에 대한 가우스 법칙의 적용 가능성은 변 l 의 정사각형 단면을 갖고 세 번째 변의 길이가 Δ 인 직사각형 가우스 표면을 가정하여 검사됩니다. x. 전기장의 y 구성요소는 상자의 상단과 하단에서 동일합니다. 따라서 양쪽의 플럭스는 서로 상쇄됩니다. 유사하게, 두 측면을 통과하는 전기장의 z 성분으로부터의 순 플럭스도 상쇄됩니다. 따라서 표면을 통과하는 모든 순 플럭스는 전적으로 전기장의 x 구성 요소에서 비롯됩니다. 전기장은 y- 또는 z 의존성이 없으므로 Ex(x, t)는 면적이 A인 상자의 표면에 걸쳐 일정하며 Ex 의 다른 값을 가질 수 있습니다. (x + Δx, t) 이는 상자의 반대면에서 일정합니다. 가우스 법칙을 적용하면 x 구성요소의 순 플럭스가 제공됩니다.

<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

동봉된 전하 qenc가 0이므로 구성 요소의 순 플럭스도 0이며 위 방정식은 E를 의미합니다. x(x, t) = Ex(x + Δx, t) 모든 Δx에 대해. 이러한 구성 요소 Ex(x, t)는 를 따라 전파되는 전자기파의 일부가 아닙니다. x축이므로 Ex(x, t) = 0입니다. 파도. 따라서 전기장의 0이 아닌 성분은 Ey(x, t)와 Ez(x, t), 파동 전파 방향에 수직.

B를 E로 대체하고 전기장에 대한 가우스 법칙 대신 자기에 대한 가우스 법칙을 사용하면 유사한 주장이 성립됩니다. 이는 B 필드가 파동 전파 방향에 수직임을 보여줍니다. 따라서 전자기파는 전파 방향에 수직으로 진동하는 전기장과 자기장을 갖는 횡파입니다.

전자기파(EM)파로 공간을 통해 전파되는 결합된 전기장과 자기장의 존재는 ...

Education

교육

JoVE Core

물리학

Unit 1

제1단원

Electromagnetic Waves

전자기파

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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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Hertz's Spark Gaps and Radio Waves

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...

the electromagnetic spectrum

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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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How Maxwell Linked Light to Waves

Maxwell's equations show how electric and magnetic fields behave in a vacuum, or empty space. They are written as differential equations and describe fields created by source charges, whether the charges are still or moving. These fields also act on a test charge, and its motion can be found with the right boundary conditions. The key question in empty space is what happens when there are no source charges. In the vacuum form of Maxwell's four equations, the first-order partial differential...

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

Faraday’s law can be used to link the electric and magnetic fields in a plane electromagnetic wave. Here, the wavefront moves in the x-direction at a constant speed. The goal is to show how the field strengths must be related for the wave to stay consistent with Faraday’s law. To apply the law, a rectangle of width a is placed with its area vector in the positive z-direction. The line integral is taken counterclockwise around the rectangle. One side lies outside the wavefront, so the electric...

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

Electromagnetic waves transfer energy through their electric and magnetic fields. This energy can be easy to notice, like the warmth from the summer sun, or harder to feel, like the energy in gamma rays that can damage living cells. The fields in an electromagnetic wave can exert forces on charges in a system. They can move those charges and do work on them. Even if a wave is not absorbed right away, it still carries energy away from its source. If some of the wave energy is absorbed, the...

intensity of electromagnetic waves

Poynting Vector and Light Intensity

The Poynting vector describes the energy flux of an electromagnetic wave. It tells how much energy passes through a unit area in a unit time at a specific moment. For a plane electromagnetic wave moving along the x-axis, the energy flux depends on the peak electric field E0 and the peak magnetic field B0. For high-frequency waves, the energy flux changes very quickly with time. Visible light has a frequency on the order of 10^14 Hz, so its energy flux varies too fast to track directly. Most...

momentum and radiation pressure

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radiation pressure: problem solving

Radiation Pressure in Light and Space

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standing electromagnetic waves

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standing waves in a cavity

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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 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.

Virginia  Standards of Learning

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

High School

HS-PS4-5

Alabama Course of Study Science

9-12.P.3.7.c

Next Generation Science Standards

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)

Earth’s Place in the Universe

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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