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

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Waves and Their Applications

PS.PSc.8.2

Electromagnetic Wave Equation

Rozważmy formę różniczkową czterech równań Maxwella w próżni, które wzajemnie wiążą pola elektryczne i magnetyczne.
Oddzielne równania dla pola elektrycznego i magnetycznego można znaleźć, stosując zawinięcie po obu stronach trzeciego i czwartego równania, używając tożsamości geometrycznych, pierwszego i drugiego równania, reguły pochodnych cząstkowych oraz trzeciego i czwartego równania.
Uproszczenie pokazuje, że pola elektryczne i magnetyczne podążają za tym samym równaniem. Oznacza to, że każdy składnik kartezjański spełnia równanie falowe. Tak więc pola elektromagnetyczne są falami trójwymiarowymi.
Rozchodzą się w próżni z prędkością określoną przez stałe naturalne.
Załóżmy, że fala przechodzi w kierunku z. Ogólne rozwiązania dla pól są napisane.
Do tych rozwiązań stosuje się pierwsze i drugie równanie Maxwella. Uproszczenie pokazuje, że składowe z pól są równe zero. Tak więc fale elektromagnetyczne są falami poprzecznymi.
Trzecie równanie Maxwella zastosowane do rozwiązań daje relacje między ich składowymi x i y, które można połączyć w postaci wektorowej. Tak więc poruszające się pola elektryczne i magnetyczne są wzajemnie prostopadłe.

<ol>
	<li>Griffiths, David J. (1999). Wprowadzenie do elektrodynamiki (wyd. 3). Górna rzeka Saddle, New Jersey 07458; ppkt 9.2; strony 375–379.</li>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson; sekcja 32.2; Strona 1058.</li>
</ol>

równanie fali elektromagnetycznej

Równania Maxwella dla pól elektromagnetycznych są powiązane z ładunkami źródłowymi, statycznymi lub ruchomymi. Pola te działają na ładunek próbny, którego trajektorię można w ten sposób wyznaczyć na podstawie odpowiednich warunków brzegowych. Cel elektromagnetyzmu jest zatem teoretycznie zakończony.

Chociaż pola elektryczne i magnetyczne zostały po raz pierwszy wprowadzone jako konstrukcje matematyczne w celu uproszczenia opisu wzajemnych sił między ładunkami, z równań Maxwella wyłania się naturalne pytanie: co dzieje się z polami elektrycznymi i magnetycznymi, gdy nie ma opłaty źródłowe?

Rozważ formy różniczkowe czterech równań Maxwella w próżni. W równaniach różniczkowych cząstkowych pierwszego rzędu obserwuje się naturalną symetrię, z wyjątkiem stałych naturalnych.

Badania matematyczne wykazały, że każda składowa pola elektrycznego i magnetycznego podlega temu samemu równaniu falowemu. Prędkość jest określana przez kombinację stałych naturalnych: przenikalności próżniowej i przepuszczalności próżni. Zastępując ich liczby, Maxwell odkrył, że prędkość ta jest bardzo bliska eksperymentalnej wartości prędkości światła.

Wynik jest zaskakujący, biorąc pod uwagę niezależność obserwacji: jednej z teorii elektrodynamiki, która wyłoniła się z badania ładunków i prądów w laboratorium, a drugiej eksperymentalnego określenia prędkości światła.

Łącząc kropki, Maxwell postawił hipotezę, że światło to nic innego jak fale elektromagnetyczne. Hipoteza została później zweryfikowana eksperymentalnie. Ten bieg historii jest istotną lekcją na temat znaczenia matematyki w wyjaśnianiu przyrody. Co więcej, pola elektryczne i magnetyczne nie są konstrukcjami czysto matematycznymi; mogą podróżować bez żadnego materiału, co nadaje im fizyczne znaczenie.

Znane są ogólne rozwiązania równań falowych. Ponieważ pola elektromagnetyczne działają zgodnie z zasadą superpozycji, bardziej ogólne rozwiązania równań falowych można zapisać jako liniowe superpozycje tych rozwiązań.

Równania Maxwella nakładają dodatkowe ograniczenia na rozwiązania ogólne. Ujawniają inne niezwykłe fakty: pola elektryczne i magnetyczne są ze sobą w fazie, są wzajemnie prostopadłe i oba są prostopadłe do kierunku propagacji fali. Zatem fale elektromagnetyczne są falami poprzecznymi.

Równanie fali elektromagnetycznej

Równania Maxwella dla pól elektromagnetycznych są związane z ładunkami źródłowymi, zarówno statycznymi, jak i ruchomymi. Pola te działają na ładunek testowy, którego ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Electromagnetic Waves

Fale elektromagnetyczne

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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How Maxwell Linked Light to Waves | JoVE K12

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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.

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How Maxwell Linked Light to Waves

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