Name: how maxwell linked light to waves
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 24 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 Wave Equation

חשבו על הצורה הדיפרנציאלית של ארבע משוואות מקסוול בריק, המקשרות זו לזו את השדות החשמליים והמגנטיים.
ניתן למצוא משוואות נפרדות עבור השדות החשמליים והמגנטיים על ידי החלת התלתל על שני צידי המשוואה השלישית והרביעית, תוך שימוש בזהויות גיאומטריות, המשוואה הראשונה והשנייה, כלל הנגזרות החלקיות ומשוואות השלישית והרביעית.
פישוט מגלה שהשדות החשמליים והמגנטיים פועלים לפי אותה משוואה. זה מרמז שכל רכיב קרטזי מקיים את משוואת הגל. לכן, השדות האלקטרומגנטיים הם גלים תלת מימדיים.
הם מתפשטים בריק במהירות שנקבעת על ידי קבועים טבעיים.
נניח שהגל חוצה בכיוון z. הפתרונות הכלליים לשדות כתובים.
לפתרונות אלה מיושמות משוואות מקסוול הראשונה והשנייה. פישוט מגלה שרכיבי z של השדות הם אפס. לכן, גלים אלקטרומגנטיים הם גלים רוחביים.
המשוואה השלישית של מקסוול המיושמת על הפתרונות נותנת יחסים בין מרכיבי x ו-y שלהם, שיכולים להיות מיוצרים בצורה וקטורית. לכן, השדות החשמליים והמגנטיים הנעים הם מאונכים זה לזה.

<ol>
	<li>גריפיתס, דייוויד ג'יי (1999). מבוא לאלקטרודינמיקה (מהדורה שלישית). אפר סאדל ריבר, ניו ג'רזי 07458; סעיף 9.2; עמודים 375–379.</li>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון; סעיף 32.2; עמוד 1058.</li>
</ol>

משוואת גלים אלקטרומגנטיים

<div style="direction:rtl">המשוואות של מקסוול לשדות אלקטרומגנטיים קשורות למטענים מקוריים, סטטיים או נעים. שדות אלו פועלים על מטען בדיקה, אשר כך ניתן לקבוע את מסלולו באמצעות תנאי גבול מתאימים. מטרת האלקטרומגנטיות הושלמה אפוא מבחינה תיאורטית. עם זאת, למרות ששדות חשמליים ומגנטיים הוצגו לראשונה כמבנים מתמטיים כדי לפשט את התיאור של כוחות הדדיים בין מטענים, עולה שאלה טבעית מהמשוואות של מקסוול: מה קורה לשדות החשמליים והמגנטיים כאשר אין מטענים מקוריים? חשבו על צורות הדיפרנציאליות של ארבע משוואות מקסוול בחלל ריק. סימטריה טבעית נצפית במשוואות דיפרנציאליות חלקיות מסדר ראשון למעט הקבועים הטבעיים. מחקרים מתמטיים גילו שכל מרכיב של שדה חשמלי ומגנטי עוקב אחר אותה משוואת גל. המהירות נקבעת על ידי שילוב של הקבועים הטבעיים: היתריות של הוואקום וחדירותו של הוואקום. כשהחליף את המספרים שלהם, מקסוול גילה שמהירות זו קרובה מאוד לערך הניסוי של מהירות האור. התוצאה מפתיעה בהתחשב בעצמאותן של התצפיות: אחת מתורת האלקטרודינמיקה, שנוצרה מחקר מטענים וזרמים במעבדה, והשנייה קביעה ניסיונית של מהירות האור. בחיבור הנקודות, מקסוול שיער שאור אינו אלא גלים אלקטרומגנטיים. ההשערה אומתה מאוחר יותר בניסוי. מהלך ההיסטוריה הזה הוא שיעור חיוני על חשיבותה של המתמטיקה בהסבר הטבע. יתרה מכך, שדות חשמליים ומגנטיים אינם מבנים מתמטיים בלבד; הם יכולים לנסוע ללא נוכחות חומרית, מה שנותן להם משמעות פיזית. הפתרונות הכלליים למשוואות הגלים ידועים. מכיוון ששדות אלקטרומגנטיים פועלים לפי עקרון הסופרפוזיציה, ניתן לכתוב פתרונות כלליים יותר של משוואות הגלים כסופרפוזיציות ליניאריות של פתרונות אלו. משוואות מקסוול מיישמות אילוצים נוספים על הפתרונות הכלליים. הם חושפים עובדות יוצאות דופן אחרות: השדות החשמליים והמגנטיים נמצאים בפאזה זה עם זה, מאונכים זה לזה, ושניהם מאונכים לכיוון ההתפשטות של הגל. לפיכך, גלים אלקטרומגנטיים הם גלים רוחביים.</div>

משוואות מקסוול לשדות אלקטרומגנטיים קשורות למטעני מקור, סטטיים או נעים. שדות אלה פועלים על חיוב בדיקה, אשר ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Electromagnetic Waves

גלי אלקטרומגנטיים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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 equations have a clear symmetry, except for the natural constants. From this symmetry, mathematicians found that each component of the electric field and magnetic field satisfies the same wave equation.

The wave speed depends on two vacuum constants: permittivity and permeability. When Maxwell used their values, he found a speed very close to the measured speed of light. That was a striking match because the two results came from very different places: one from electrodynamics in the lab and the other from experiments on light.

Maxwell then proposed that light is an electromagnetic wave. Later experiments confirmed this idea. This story also shows why mathematics matters in science, because it can reveal links that are not obvious from experiments alone.

The fields are not just mathematical ideas. They can travel through space without any material medium, so they have real physical meaning. The general solutions of the wave equation are known, and because electromagnetic fields follow superposition, more complex waves can be built from linear combinations of those solutions.

Maxwell's equations add more rules to these solutions. They show that the electric and magnetic fields are in phase with each other, meaning their peaks and valleys line up. They are also perpendicular to each other and both are perpendicular to the direction the wave travels, so electromagnetic waves are transverse waves.

How Maxwell Linked Light to 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...

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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

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...

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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

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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

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momentum and radiation pressure

Radiation Pressure in Light and Comets

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radiation pressure: problem solving

Radiation Pressure in Light and Space

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standing electromagnetic waves

Electromagnetic Wave Reflection at Conductors

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Electromagnetic Modes in a Microwave Cavity

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key terms and concepts

Explore how Maxwell's equations lead to the electromagnetic wave equation, show the wave speed in vacuum, and explain why light is an electromagnetic wave.

How Maxwell Linked Light to 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

Louisiana Student Standards for Science

High School

Waves And Their Applications In Technologies For Information Transfer

HS-PS4-1

Tennessee Academic Standards

PHYS.PS4.5

Virginia  Standards of Learning

HIgh School

PS.7

PS.7.a

PH.5

PH.5.c

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

New Jersey Student Learning Standards for Science

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.10.18

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.

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 ...

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Velocity and Acceleration of a Wave

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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

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 ...

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 ...

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.

How Maxwell Linked Light to Waves

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