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

גלים אלקטרומגנטיים עולים בקנה אחד עם חוק אמפר.
חשבו על חזית גל של מטוס שנע בכיוון +x. מעליו, שקול מלבן במישור xz, עם וקטור שטח בכיוון +y.
האינטגרציה מתבצעת נגד כיוון השעון סביב המלבן.
השדה המגנטי הוא אפס או מאונך לרכיבי האורך למעט אורך "RS", שבו השדה מקביל ותורם לאינטגרל.
זה מרמז כי הצד הימני של חוק אמפר חייב להיות גם לא אפס. לכן, לשדה החשמלי חייב להיות רכיב y שיכול לספק נגזרת זמן שאינה אפס של שטף חשמלי.
הוא גם קובע כי השדות החשמליים והמגנטיים חייבים להיות מאונכים זה לזה.
השטף החשמלי עולה לערך חיובי בזמן "dt". ניתן להחליף את קצב השינוי של השטף החשמלי בחוק אמפר.
מכיוון שגלים אלקטרומגנטיים עקביים עם כל משוואות מקסוול, הביטוי המתקבל מושווה לביטוי הנגזר באמצעות חוק פאראדיי, הנותן את מהירות התפשטות הגל בריק.
החלפת ערכי החדירות וההיתריות, מהירות ההתפשטות שווה למהירות האור.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון. סעיף 32.2; עמוד 1057.</li>
	<li>OpenStax. (2019). פיזיקה אוניברסיטאית כרך 2. [גרסת אינטרנט]. מקור: <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; סעיף 16.2; עמודים 707–709.</li>
</ol>

מהירות התפשטות של גלים אלקטרומגנטיים

<div style="direction:rtl">

	גלים אלקטרומגנטיים תואמים לחוק אמפר. בהנחה שאין זרם הולכה חוק אמפר ניתן כ: 
	<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;"> 

	חשבו על חזית גל מישורית הנעה בכיוון x החיובי, כפי שמוצג באיור. מעליו, חשבו מלבן במישור xz, עם וקטור שטח בכיוון החיובי של y. האינטגרציה מתבצעת נגד כיוון השעון סביב המלבן כדי לפתור את הצד השמאלי של חוק אמפר. השדה המגנטי הוא אפס או מאונך ליסודות האורך למעט אורך אחד, שבו השדה מקביל. אורך זה תורם לאינטגרל, נותן ערך שאינו אפס.

	כדי לעמוד בחוק אמפר, הצד הימני של חוק אמפר חייב להיות גם לא אפס. לכן, לשדה החשמלי חייב להיות רכיב y שיכול לספק נגזרת זמן שאינה אפס של שטף חשמלי. זה גם קובע שהשדות החשמליים והמגנטיים חייבים להיות בניצב זה לזה. השטף החשמלי עולה לערך חיובי בזמן, dt. ניתן להחליף את קצב השינוי של השטף החשמלי בחוק אמפר. 
	<img alt="Equation2" src="/files/ftp_upload/13824/13824_Equation_PT_2.svg" style="text-align: center; height: 17px;"> 

	מכיוון שגלים אלקטרומגנטיים תואמים לכל המשוואות של מקסוול, הביטוי המתקבל מושווה לביטוי הנגזר באמצעות חוק פאראדיי, המעניק מהירות התפשטות גל בוואקום. 
	<img alt="Equation3" src="/files/ftp_upload/13824/13824_Equation_PT_3.svg" style="text-align: center; height: 45px;"> 

	כאשר מחליפים את הערכים המספריים של חדירות ופריטיטיביות, מהירות ההתפשטות המתקבלת שווה למהירות האור. 
	<img alt="Equation4" src="/files/ftp_upload/13824/13824_Equation_PT_4.svg" style="text-align: center; height: 17px;"> 

	זה מרמז שהגל המשוער תואם את כל המשוואות של מקסוול, בתנאי שחזית הגל נעה במהירות המפורטת לעיל, המוכרת כמהירות האור. שים לב שהערך המדויק של מהירות האור מוגדר להיות 299,792,458 מ"ש.
 </div>

גלים אלקטרומגנטיים עולים בקנה אחד עם חוק אמפר. בהנחה שאין זרם הולכה חוק אמפר ניתן כך:

חשבו על מטוס...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Electromagnetic Waves

גלי אלקטרומגנטיים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

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

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

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 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

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 ...

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 ...

/files/media/science-education/science-education-thumbs/14727.jpg

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 ...

/files/media/science-education/science-education-thumbs/12783.jpg

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. ...

/files/media/science-education/science-education-thumbs/12784.jpg

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 ...

/files/media/science-education/science-education-thumbs/14723.jpg

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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