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

Rozważmy współrzędną xyz podzieloną na dwa odrębne regiony płaszczyzną równoległą do płaszczyzny yz.
Jednolite pole elektryczne i magnetyczne w kierunkach +y i +z występuje po lewej stronie, podczas gdy prawa strona jest wolna od pola.
Ta płaszczyzna graniczna, zwana czołem fali, porusza się w kierunku +x ze stałą prędkością.
Takie fale, w których w dowolnym momencie pola są jednorodne na dowolnej płaszczyźnie prostopadłej do kierunku rozchodzenia się, nazywane są falami płaskimi.
Fale te spełniają równania Maxwella. Weźmy pod uwagę prostokątne pudełko Gaussa.
Ponieważ pole elektryczne przebiega wzdłuż kierunku y, strumienie elektryczne dla powierzchni wzdłuż kierunku x i z wynoszą zero.
W przypadku górnej powierzchni strumień jest przeciwny do dolnej powierzchni, co daje zerowy strumień netto.
Ponieważ pudełko nie zawiera ładunku elektrycznego, strumień elektryczny i magnetyczny wynosi zero.
Tak więc prawo Gaussa odnosi się do promieniowania elektromagnetycznego.
Dlatego wektory pola elektrycznego i magnetycznego są prostopadłe do siebie i do kierunku rozchodzenia się, co wskazuje na charakter poprzeczny.

<ol>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson. Sekcja 32.2; strony 1055–1056.</li>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 2. [Wersja internetowa]. Źródło: <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; sekcja 16.2; strony 706–707.</li>
</ol>

płaskie fale elektromagnetyczne i

Istnienie połączonych pól elektrycznych i magnetycznych, które rozchodzą się w przestrzeni jako fale elektromagnetyczne (EM), jest najważniejszym przewidywaniem równań Maxwella. Ponieważ równania Maxwella obowiązują w wolnej przestrzeni, przewidywane fale elektromagnetyczne nie wymagają ośrodka do ich propagacji. Fala EM składa się z pola elektrycznego, zdefiniowanego jako siła przypadająca na ładunek ładunku stacjonarnego, oraz pola magnetycznego, które oznacza siłę przypadającą na ładunek poruszającego się ładunku.

Przyjmuje się, że pole EM jest funkcją tylko współrzędnej x i czasu. Zatem składowa y pola elektrycznego jest wówczas zapisywana jako Ey(x, t), a składowa z pola magnetycznego jest zapisywana jako Bz(x, t). Ze względu na założenie o wolnej przestrzeni nie ma swobodnych ładunków ani prądów, dlatego zawarty ładunek i prąd w równaniu Maxwella są ustawione na zero.

Zastosowanie prawa Gaussa dla pól elektrycznych bada się zakładając prostokątną powierzchnię Gaussa o kwadratowym przekroju poprzecznym boku l i której trzeci bok ma długość Δx. Składowa y pola elektrycznego jest taka sama na górze i na dole pudełka. Dlatego strumienie po obu stronach znoszą się nawzajem. Podobnie, strumień wypadkowy składowej z pola elektrycznego przez dwie boczne strony jest również eliminowany. Zatem wszelki strumień netto przez powierzchnię pochodzi w całości ze składowej x pola elektrycznego. Ponieważ pole elektryczne nie ma zależności y- ani z, Ex(x, t) jest stała na powierzchni pudełka o polu A i ma prawdopodobnie różną wartość Ex (x + Δx, t) który jest stały po przeciwnej stronie pudełka. Zastosowanie prawa Gaussa daje strumień netto składowej x.

<img alt="Równanie1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;" />

Ponieważ qenc, zawarty w nim ładunek, wynosi zero, strumień wypadkowy składnika również wynosi zero, a z powyższego równania wynika E x(x, t) = Ex(x + `x, t) dla dowolnego `x. Taka składowa Ex(x, t) nie byłaby częścią fali elektromagnetycznej rozchodzącej się wzdłuż Δx, więc Ex(x, t) = 0 w tym przypadku fala. Dlatego jedynymi niezerowymi składowymi pola elektrycznego są Ey(x, t) i Ez(x, t), prostopadle do kierunku propagacji fali.

Podobny argument można zastosować, zastępując E B i stosując prawo Gaussa dla magnetyzmu zamiast prawa Gaussa dla pól elektrycznych. To pokazuje, że pole B jest również prostopadłe do kierunku propagacji fali. Fala elektromagnetyczna jest zatem falą poprzeczną, a jej oscylujące pola elektryczne i magnetyczne są prostopadłe do kierunku jej propagacji.

Płaskie fale elektromagnetyczne I

Istnienie połączonych pól elektrycznych i magnetycznych, które rozchodzą się w przestrzeni jako fale elektromagnetyczne (EM), jest najważniejszą prognozą ...

Education

JoVE Core

Fizyka

Unit 1

Jednostka 1

Electromagnetic Waves

Fale elektromagnetyczne

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

Tags

More videos by Standards