Name: transverse fields in electromagnetic waves
Uploaded: 2023-04-30T12:46:03.000Z
Duration: 1 min 30 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

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

考虑一个 xyz 坐标系，其被一个平行于 yz 平面的平面划分为两个不同的区域。
左侧存在沿 +y 和 +z 方向的均匀电场和磁场，而右侧无场。
这个边界平面称为波阵面，它以恒定速度沿 +x 方向传播。
在任何时刻，电场和磁场在垂直于传播方向的平面上均匀分布的这种波称为平面波。
这些波满足麦克斯韦方程组。考虑一个矩形高斯盒子。
由于电场沿 y 方向，因此沿 x 方向和 z 方向的表面的电通量为零。
对于上表面，通量与下表面相反，导致净通量为零。
由于该盒子内部不包含任何电荷，因此电通量和磁通量均为零。
因此，高斯定律适用于电磁辐射。
因此，电场和磁场矢量相互垂直，并且都垂直于传播方向，表现出横波特性。

<ol>
	<li>Young， HD 和 Freedman， RA （2012）。大学物理与现代物理。加利福尼亚州旧金山:皮尔逊。第 32.2 节;第 1055-1056 页。</li>
	<li>OpenStax 的。（2019）. 大学物理学第 2 卷。[Web 版本]。取自 <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>;第 16.2 节;第 706-707 页。</li>
</ol>

平面电磁波 i

以电磁 (EM) 波的形式在空间传播的电场和磁场组合的存在是麦克斯韦方程组最重要的预测。 由于麦克斯韦方程组在自由空间中成立，因此预测的电磁波不需要介质来传播。 电磁波包含电场（定义为每个电荷作用在固定电荷上的力）和磁场（定义为每个电荷作用在移动电荷上的力）。 假设 EM 场仅是 x 坐标和时间的函数。 因此，电场的 y 分量可写为 Ey(x, t），磁场的 z 分量写为 Bz(x，t）。 由于自由空间的假设，不存在自由电荷或电流，因此麦克斯韦方程中封闭的电荷和电流均设置为零。 可以通过假设一个矩形高斯表面，其边长为 l 的正方形横截面，并且其第三边的长度为 Δx，来检验高斯定律对于电场的适用性。 盒子顶部和底部的电场 y 分量相同。 因此，两侧的通量相互抵消。 相同，电场的 z 分量通过两侧的净通量也被抵消。 因此，通过表面的任何净通量完全来自电场的x分量。 由于电场没有 y- 或 z 依赖性，Ex(x, t) 在面积为 A 的盒子表面上是恒定的，并且可能具有不同的 Ex(x + Δx, t) 值在盒子的另一面上是恒定的。 应用高斯定律给出x分量的净通量。 <img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;"> 由于qenc（封闭的电荷）为零，因此组件的净通量也为零，并且上述方程意味着Ex(x, t) = Ex(x + Δx, t) 对于任何 Δx。 这样的分量Ex(x, t)不会是沿x 轴，因此 Ex(x, t) = 0 海浪。 因此，电场的唯一非零分量是 Ey(x, t) 和 Ez(x, t)，垂直于波的传播方向。 通过用 E 代替 B 并使用高斯定律来描述磁力而不是高斯定律来描述电场，也可以得出类似的结论。 这表明B场也垂直于波的传播方向。 因此，电磁波是横波，其振荡电场和磁场垂直于其传播方向。

平面电磁波 I

电磁波在空间中传播时伴随有电场和磁场的共同存在，这是……最显著的预测

Education

教育

JoVE Core

物理学

Unit 1

第一单元

Electromagnetic Waves

电磁波

KEY TERMS AND CONCEPTS

关键术语与概念

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...

generating electromagnetic radiations

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

Electromagnetic Waves in Everyday Technology

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...

electromagnetic wave equation

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

Radiation Pressure in Light and Comets

Radiation pressure is the force that electromagnetic waves can exert on matter. It appears because light carries momentum, so an object that absorbs a wave feels a push in the direction the wave travels. This same force helps explain why sunlight can affect small particles in space. Maxwell predicted radiation pressure, and Nichols and Hull confirmed it in 1903. They used a torsion balance with mirrors suspended from a fiber inside a glass container. When they shone light on one mirror, the...

radiation pressure: problem solving

Radiation Pressure in Light and Space

Radiation pressure is the push that light can exert on matter. When an electromagnetic wave is completely absorbed by a surface, its energy density is transferred as momentum to that surface. The rate of momentum transfer on a surface perpendicular to the wave gives the force, and the force per unit area is the radiation pressure. A perfectly absorbing surface receives this pressure directly from the incoming wave. If the surface is perfectly reflecting, such as a metal surface, and the light...

standing electromagnetic waves

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...

standing waves in a cavity

Electromagnetic Modes in a Microwave Cavity

Electromagnetic waves can form standing patterns inside a cavity. Household microwaves and lasers are common examples of this effect. When two conducting metal plates are placed parallel at the nodal planes, they create a space where standing waves can exist. The cavity between the plates works like a stretched string fixed at x = 0 and x = L. The distance L must be an integer multiple of half a wavelength. The wavelengths that meet this condition have matching frequencies, and each frequency,...

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

new-jersey-student-learning-standards-for-science

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

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

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.

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-4.

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. ...

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be ...

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a ...

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the ...

/files/media/science-education/science-education-thumbs/14721.jpg

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which ...

Speed of a Transverse Wave

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The ...

/files/media/science-education/science-education-thumbs/14722.jpg

problem-solving-tuning-of-a-guitar-string

Problem-Solving: Tuning of a Guitar String

In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or ...

/files/media/science-education/science-education-thumbs/14744.jpg

Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

Sound Waves

Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium&#39;s ...

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As ...

/files/media/science-education/science-education-thumbs/14724.jpg

Perception of Sound Waves

The human ear is not equally sensitive to all frequencies in the audible range. It may perceive sound waves with the same pressure but different ...

Speed of Sound in Solids and Liquids

Most solids and liquids are incompressible&#8212;their densities remain constant throughout. In the presence of an external force, the molecules tend to ...

Speed of Sound in Gases

The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. ...

James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his ...

Electromagnetic Wave Equation

Maxwell&#39;s equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose ...

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of ...

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a ...

Obtain, evaluate, and communicate information to compare mechanical and electromagnetic waves (specifically light and sound) in terms of wave characteristics (frequency, wavelength, period, amplitude, velocity, and energy).

Analyze the behavior of waves and their applications.

Transverse Fields in Electromagnetic Waves

Description

Transcript

More videos by Standards