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

ضع في اعتبارك الشكل التفاضلي لمعادلات ماكسويل الأربع في الفراغ ، والتي تربط بشكل متبادل بين المجالين الكهربائي والمغناطيسي.
يمكن العثور على معادلات منفصلة للمجال الكهربائي والمغناطيسي من خلال تطبيق الضفيرة على جانبي المعادلتين الثالثة والرابعة ، باستخدام الهويات الهندسية ، والمعادلتين الأولى والثانية ، وقاعدة المشتقات الجزئية ، والمعادلتين الثالثة والرابعة.
يكشف التبسيط أن المجالين الكهربائي والمغناطيسي يتبعون نفس المعادلة. هذا يعني أن كل مكون ديكارتي يفي بمعادلة الموجة. إذن ، فإن المجالات الكهرومغناطيسية هي موجات ثلاثية الأبعاد.
تنتشر في فراغ بسرعة تحددها الثوابت الطبيعية.
افترض أن الموجة تعبر في الاتجاه z. تمت كتابة الحلول العامة للحقول.
على هذه الحلول ، يتم تطبيق معادلتي ماكسويل الأولى والثانية. يكشف التبسيط أن مكونات الحقول z تساوي صفرا. إذن ، الموجات الكهرومغناطيسية هي موجات عرضية.
تعطي معادلة ماكسويل الثالثة المطبقة على الحلول علاقات بين مكوني x و y ، والتي يمكن تجميعها في شكل متجه. لذا ، فإن المجالات الكهربائية والمغناطيسية المتنقلة متعامدة بشكل متبادل.

<ol>
	<li>جريفيث ، ديفيد ج. (1999). مقدمة في الديناميكا الكهربائية (الطبعة الثالثة). نهر السرج العلوي ، نيو جيرسي 07458 ؛ القسم 9.2 ؛ الصفحات 375-379.</li>
	<li>يونغ ، إتش دي وفريدمان ، ر. (2012). الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون. القسم 32.2 ؛ صفحة 1058.</li>
</ol>

معادلة الموجات الكهرومغناطيسية

<div style="direction:rtl">ترتبط معادلات ماكسويل للمجالات الكهرومغناطيسية بشحنات المصدر، سواء كانت ثابتة أو متحركة. تعمل هذه الحقول على شحنة اختبار، وبالتالي يمكن تحديد مسارها باستخدام شروط حدودية مناسبة. وبذلك يكون هدف الكهرومغناطيسية مكتملًا من الناحية النظرية. ومع ذلك، على الرغم من أن المجالات الكهربائية والمغناطيسية تم تقديمها لأول مرة كتركيبات رياضية لتبسيط وصف القوى المتبادلة بين الشحنات، إلا أن سؤالًا طبيعيًا يبرز من معادلات ماكسويل: ماذا يحدث للمجالات الكهربائية والمغناطيسية عندما لا يكون هناك رسوم المصدر؟ تأمل الأشكال التفاضلية لمعادلات ماكسويل الأربع في الفراغ. ويلاحظ وجود تماثل طبيعي في المعادلات التفاضلية الجزئية من الدرجة الأولى باستثناء الثوابت الطبيعية. كشفت الاستكشافات الرياضية أن كل مكون من مكونات المجال الكهربائي والمغناطيسي يتبع نفس المعادلة الموجية. يتم تحديد السرعة المتجهة المتجهة المتجهة المتجهة من خلال مجموعة من الثوابت الطبيعية: سماحية الفراغ ونفاذية الفراغ. وباستبدال أرقامها، اكتشف ماكسويل أن هذه السرعة المتجهة المتجهة المتجهة المتجهة قريبة جدًا من القيمة التجريبية لسرعة الضوء. النتيجة مذهلة نظرًا لاستقلال الملاحظات: إحداهما عن نظرية الديناميكا الكهربائية، التي انبثقت من دراسة الشحنات والتيارات في المختبر، والأخرى تحديد تجريبي لسرعة الضوء. من خلال ربط النقاط، افترض ماكسويل أن الضوء ليس سوى موجات كهرومغناطيسية. تم التحقق من الفرضية في وقت لاحق تجريبيا. تعتبر دورة التاريخ هذه درسًا أساسيًا عن أهمية الرياضيات في تفسير الطبيعة. علاوة على ذلك، فإن المجالات الكهربائية والمغناطيسية ليست بناءات رياضية بحتة؛ يمكنهم السفر دون أي هدية مادية، مما يمنحهم معنى ماديًا. الحلول العامة للمعادلات الموجية معروفة. بما أن المجالات الكهرومغناطيسية تتبع مبدأ التراكب، فيمكن كتابة حلول أكثر عمومية للمعادلات الموجية على شكل تراكبات خطية لهذه الحلول. تطبق معادلات ماكسويل قيودًا إضافية على الحلول العامة. إنها تكشف عن حقائق ملحوظة أخرى: المجالان الكهربائي والمغناطيسي متفقان في الطور مع بعضهما البعض، ومتعامدان بشكل متبادل، وكلاهما متعامدان مع اتجاه انتشار الموجة. وبالتالي فإن الموجات الكهرومغناطيسية هي موجات مستعرضة.</div>

ترتبط معادلات ماكسويل للمجالات الكهرومغناطيسية بشحنات المصدر ، سواء كانت ثابتة أو متحركة. تعمل هذه الحقول على شحنة اختبار ، والتي ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Electromagnetic Waves

الموجات الكهرومغناطيسية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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...

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

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 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

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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

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Problem-Solving: Tuning of a Guitar String

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Kinetic and Potential Energy of a Wave

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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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