Name: maxwell’s equations behind em waves
Uploaded: 2023-04-30T12:45:48.000Z
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

Physical Science

Waves and Their Applications

PS.PSc.8.2

Electromagnetic Waves

Рассмотрим статический электрический заряд. Он создает вокруг себя стационарное электрическое поле. Когда заряд начинает двигаться, дополнительно создается магнитное поле, перпендикулярное направлению движущегося заряда.
Если движущийся заряд ускоряется, колеблясь вокруг точки, электрическое поле вокруг него также начинает колебаться.
Согласно закону Ампера-Максвелла, это изменяющееся во времени электрическое поле производит ток смещения, который индуцирует другое изменяющееся во времени магнитное поле, перпендикулярное электрическому полю.
Согласно закону Фарадея, изменяющееся во времени магнитное поле, в свою очередь, создает электрическое поле, и этот процесс продолжается.
Последовательная индукция обоих полей приводит к самоподдерживающимся электрическим и магнитным полям в областях, удаленных от места их возникновения.
Эти поля распространяются в пространстве, создавая электромагнитные волны, которые не требуют среды для поддержания этого движения.
Производимые электромагнитные волны имеют ту же частоту, что и частота колебаний ускоренного электрического заряда.
Эти волны поперечны, так как составляющие их электрические и магнитные поля колеблются перпендикулярно друг другу и в фазе друг с другом, а также перпендикулярны направлению распространения.

<ol>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Получено из <a href="https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves">16.1 Уравнения Максвелла и электромагнитные волны - Университетская физика Том 2 | OpenStax</a></li>
</ol>

Электромагнитные волны

Джеймс Клерк Максвелл сформулировал единую теорию, объединяющую все электрические и магнитные эффекты, о которых знали учёные в то время, назвав явления, которые предсказывает его теория, "электромагнитными волнами". Он объединил все результаты работ, выполненных такими блестящими физиками, как Эрстед, Кулонб, Гаусс и Фарадей, и добавил свои собственные идеи для разработки всесторонней теории электромагнетизма. Уравнения Максвелла, совместно с законом силы Лоренца, охватывают все законы электричества и магнетизма. Однако симметрия, которую Максвелл внёс в свою математическую систему, может не быть сразу очевидной; закон Фарадея описывает то, как изменяющиеся магнитные поля создают электрические поля. Вместо этого введённый Максвеллом ток смещения возникает из меняющегося электрического поля и объясняет, как изменение электрического поля порождает магнитное поле. Уравнения эффектов как изменяющихся электрических, так и изменяющихся магнитных полей отличаются формой только там, где отсутствие магнитных монополей приводит к отсутствию некоторых членов. Эта симметрия между эффектами изменяющихся магнитных и электрических полей необходима для объяснения природы электромагнитных волн.

Чтобы увидеть, как симметрия, введённая Максвеллом, объясняет существование комбинированных электрических и магнитных волн, распространяющихся через пространство, представьте себе изменяющееся во времени магнитное поле, создаваемое высокочастотным переменным током. Согласно закону Фарадея, изменяющееся магнитное поле через поверхность порождает изменяющееся электрическое поле на границе этой поверхности. Источником смещения тока для электрического поля, подобно источнику закона Фарадея для магнитного поля, являются только замкнутые циклы линий поля, из-за математической симметрии, заключённой в уравнениях для индуцированных электрических и индуцированных магнитных полей. В свою очередь, изменяющееся электрическое поле создаёт магнитное поле в соответствии с модифицированным законом Ампера. Это изменяющееся поле порождает ещё одно электрическое поле, которое, в свою очередь, порождает ещё одно магнитное поле, и так далее. Таким образом, у нас имеется самоподдерживающийся процесс, приводящий к созданию изменяющихся электрических и магнитных полей в областях, всё дальше и дальше от точки, где они изначально возникли. Этот процесс можно представить как распространение электромагнитной волны через пространство.

Джеймс Клерк Максвелл сформулировал единую теорию, объединив все электрические и магнитные эффекты, известные ученым того времени, назвав эти явления своими...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 the displacement current, which comes from a changing electric field and produces a magnetic field.

The two equations are similar in form, except for the missing terms caused by the absence of magnetic monopoles. This symmetry between changing magnetic fields and changing electric fields is what makes electromagnetic waves possible. It helps explain how combined electric and magnetic waves can move through space.

One way to picture this process is to imagine a high-frequency alternating current that creates a time-varying magnetic field. Faraday’s law says that this changing magnetic field induces a time-varying electric field around the edge of the surface. The displacement current source for the electric field, like the source in Faraday’s law for the magnetic field, produces only closed loops of field lines.

The changing electric field then creates a magnetic field by the modified Ampère’s law. That changing magnetic field induces another electric field, which then induces another magnetic field. This repeating process continues outward from where it started and creates time-varying electric and magnetic fields farther and farther away. This is the propagation of an electromagnetic wave through space.

Maxwell’s Equations Behind EM Waves

electromagnetic 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

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...

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

Explore how Maxwell’s equations and the displacement current explain the linked electric and magnetic fields that propagate as electromagnetic waves through space.

Maxwell’s Equations Behind EM 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.

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

Waves and Their Applications in Technologies for Information Transfer

PS.Phy.7.1

Pennsylvania State Academic Standards

Waves and Electromagnetic Radiation

3.2.9-12.V

3.2.9-12.W

Louisiana Student Standards for Science

High School

Waves And Their Applications

HS-PS4-4

Waves And Their Applications In Technologies For Information Transfer

HS-PS4-1

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Energy And Waves

Waves

Light phenomena

Tennessee Academic Standards

Energy

PHYS.PS3.15

PHYS.PS4.5

PHYS.PS4.6

Virginia  Standards of Learning

HIgh School

PS.7

PS.7.a

PH.5

PH.5.c

PH.6

PH.6.a

PH.6.b

Minnesota Academic Standards in Science

Earth and Space Science

3.1.1 9E.3.1.1.1

3.2.2 9P.3.1.1.2

4.2.1 9P.3.2.2.1

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

New Jersey Student Learning Standards for Science

HS-PS4-3

Arizona Science Standards

HS.P4

HS.P4U1.10

Alabama Course of Study Science

9-12.PS.2.2

9-12.PS.2.2.c

9-12.P.3.7.c

Next Generation Science Standards

HS-PS4-2

HS-PS4-5

Earth’s Systems

HS-ESS2-4

Florida Department of Education

SC.912.P.10

SC.912.P.10.16

SC.912.P.10.17

SC.912.P.10.18

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.B

PHYS.8.E

Chemistry and Physics

IPC.6

IPC.6.E

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

South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-3

P-PS4-5

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-1.

E-ESS1-2.

E-ESS2-2.

E-ESS2-4.

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-4.

Georgia Standards of Excellence

SPS9.

electromagnetic-waves-and-mechanical-waves

Electromagnetic Waves and Mechanical Waves

SP4.

mechanical-and-electromagnetic-waves-properties

Mechanical and Electromagnetic Waves Properties

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 ...

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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 ...

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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 ...

Carry out investigations to explain the quantitative and qualitative relationships among wave frequency, wave velocity, wavelength, and wave energy.

PS.PSc.8.1

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 ...

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


Consider a plane ...

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 ...

Use models to compare the characteristics of mechanical and electromagnetic waves.

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect ...

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at ...

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second ...

Use models to explain the wave interactions of reflection, refraction, diffraction, and interference.

PS.PSc.8.3

Analyze the nature of waves and their applications.

Maxwell’s Equations Behind EM Waves

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