Name: maxwell’s equations and light speed
Uploaded: 2023-04-30T12:46:19.000Z
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

propagation-speed-of-electromagnetic-waves

Propagation Speed of Electromagnetic Waves

Электромагнитные волны согласуются с законом Ампера.
Рассмотрим плоский волновой фронт, движущийся в направлении +x. Над ним рассмотрим прямоугольник в плоскости xz, с вектором площади в направлении +y.
Интегрирование выполняется против часовой стрелки вокруг прямоугольника.
Магнитное поле либо равно нулю, либо перпендикулярно элементам длины, за исключением длины "RS", где поле параллельно и вносит свой вклад в интеграл.
Из этого следует, что правая часть закона Ампера также должна быть ненулевой. Следовательно, электрическое поле должно иметь y-компоненту, которая может обеспечить ненулевую производную электрического потока по времени.
Он также устанавливает, что электрическое и магнитное поля должны быть взаимно перпендикулярны.
Электрический поток увеличивается до положительного значения во времени "dt. Скорость изменения электрического потока может быть подставлена в закон Ампера.
Поскольку электромагнитные волны согласуются со всеми уравнениями Максвелла, полученное выражение сравнивают с выражением, выведенным с помощью закона Фарадея, который дает скорость распространения волны в вакууме.
Если подставить значения проницаемости и диэлектрической проницаемости, то скорость распространения будет равна скорости света.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. Статья 32.2; стр. 1057.</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. 707–709.</li>
</ol>

Скорость распространения электромагнитных волн

Электромагнитные волны соответствуют закону Ампера. При отсутствии проводимого тока закон Ампера имеет вид:

<img alt="Equation1" src="/files/ftp_upload/13824/13824_Equation_PT_1.svg" style="text-align: center; height: 38px;" />

<img alt="Figure1" src="/files/ftp_upload/13824/13824_Figure_PT_1.svg" style="text-align: center; height: 220px;" />

Предположим, что волна распространяется в положительном направлении оси x, как показано на рисунке. Рассмотрим прямоугольник на плоской волне в плоскости xz, с вектором площади, направленным в положительном направлении оси y. Интегрирование выполняется против часовой стрелки вокруг прямоугольника для решения левой части закона Ампера. Магнитное поле либо равно нулю, либо перпендикулярно элементам длины, за исключением одной длины, где поле параллельно. Эта длина вносит вклад в интеграл, давая ненулевое значение.

Для удовлетворения закону Ампера правая часть закона также должна быть ненулевой. Следовательно, электрическое поле должно иметь компоненту по оси y, которая может обеспечивать ненулевую временную производную электрического потока. Это также подтверждает, что электрические и магнитные поля должны быть взаимно перпендикулярными. Электрический поток увеличивается до положительного значения во времени dt. Скорость изменения электрического потока может быть подставлена в закон Ампера.

<img alt="Equation2" src="/files/ftp_upload/13824/13824_Equation_PT_2.svg" style="text-align: center; height: 17px;" />

Поскольку электромагнитные волны соответствуют всем уравнениям Максвелла, полученное выражение сравнивается с выражением, полученным с использованием закона Фарадея, которое даёт скорость распространения волны в вакууме.

<img alt="Equation3" src="/files/ftp_upload/13824/13824_Equation_PT_3.svg" style="text-align: center; height: 45px;" />

Когда заменяются числовые значения проницаемости и диэлектрической проницаемости, полученная скорость распространения равна скорости света.

<img alt="Equation4" src="/files/ftp_upload/13824/13824_Equation_PT_4.svg" style="text-align: center; height: 17px;" />

Это означает, что предполагаемая волна соответствует всем уравнениям Максвелла, при условии, что фронт волны движется со скоростью, указанной выше, которая признана скоростью света. Обратите внимание, что точное значение скорости света определено как 299 792 458 м/с.

Электромагнитные волны согласуются с законом Ампера. Предполагая, что ток проводимости отсутствует, закон Ампера задается как:

Рассмотрим самолет...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Electromagnetic Waves

Электромагнитные волны

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 Ampere’s law is non-zero, the right side must also be non-zero. That means the electric field needs a y-component. This component creates a changing electric flux, and it also shows that the electric and magnetic fields are mutually perpendicular.

The increase in electric flux over time dt is placed into Ampere’s law as a time derivative. The result is then compared with the expression from Faraday’s law. From this comparison, the wave speed in vacuum is obtained.

When the permeability and permittivity values are substituted, the calculated speed matches the speed of light. This shows that the assumed wavefront is consistent with Maxwell’s equations if it moves at that speed. The exact speed of light is defined as 299,792,458 m/s.

Maxwell’s Equations and Light Speed

electromagnetic waves

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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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the electromagnetic spectrum

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plane electromagnetic waves ii

Faraday’s Law in a Plane Wave

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intensity of electromagnetic waves

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key terms and concepts

See how Ampere’s law and Faraday’s law lead to the vacuum speed of electromagnetic waves and show why it matches the speed of light.

Maxwell’s Equations and Light Speed | 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.

Pennsylvania State Academic Standards

Waves and Electromagnetic Radiation

3.2.9-12.V

Louisiana Student Standards for Science

High School

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

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

Tennessee Academic Standards

Waves and Their Applications in Technologies for Information Transfer

PHYS.PS4.2

Virginia  Standards of Learning

HIgh School

PS.7

PS.7.a

PH.5

PH.5.c

PH.6

PH.6.b

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

HS-PS4-5

Arizona Science Standards

HS.P4

HS.P4U1.10

Alabama Course of Study Science

9-12.PS.2.2

9-12.PS.2.2.c

Earth and Space Science

Earth's Place in the Universe

9-12.ESS.1.2.b

9-12.P.3.7.c

Next Generation Science Standards

HS-PS4-3

HS-PS4-4

Florida Department of Education

SC.912.P.10

SC.912.P.10.18

SC.912.P.12

SC.912.P.12.7

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.B

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-PS4-1

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.

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

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Wave Parameters

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Equations of Wave Motion

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Graphing the Wave Function

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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

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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 ...

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 ...

Sound Waves: Interference

Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure ...

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two ...

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

PS.PSc.8.3

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a ...

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Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. ...

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Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions ...

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Obtain, evaluate, and communicate information to explain how instruments that transmit and detect waves are used in everyday life.

PS.PSc.8.4

Analyze the nature of waves and their applications.

Maxwell’s Equations and Light Speed

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