Name: transverse fields in electromagnetic waves
Uploaded: 2023-04-30T12:46:03.000Z
Duration: 1 min 30 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physics

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Waves and Their Applications in Technologies for Information Transfer

PS.Phy.7.1

Plane Electromagnetic Waves I

ضع في اعتبارك إحداثيات xyz مقسمة إلى منطقتين متميزتين بواسطة مستوى مواز للمستوى yz.
يوجد مجال كهربائي ومغناطيسي موحد في اتجاهين + y و + z على الجانب الأيسر ، بينما الجانب الأيمن خال من المجال.
يتحرك هذا المستوى الحدودي ، المسمى جبهة الموجة ، في اتجاه + x بسرعة ثابتة.
تسمى هذه الموجات التي تكون فيها الحقول ، في أي لحظة ، موحدة فوق أي مستوى عمودي على اتجاه الانتشار الموجات المستوية.
ترضي هذه الموجات معادلات ماكسويل. ضع في اعتبارك صندوقا غاوسي مستطيل.
نظرا لأن المجال الكهربائي على طول الاتجاه y ، فإن التدفقات الكهربائية للسطح على طول الاتجاه x والاتجاه z تساوي صفرا.
بالنسبة للسطح العلوي ، يكون التدفق معاكسا للسطح السفلي ، مما يعطي صفر صافي تدفق.
نظرا لأن الصندوق لا يحتوي على شحنة كهربائية ، فإن التدفق الكهربائي والمغناطيسي يساوي صفرا.
وهكذا ، فإن قانون جاوس ينطبق على الإشعاع الكهرومغناطيسي.
لذلك ، فإن متجهات المجال الكهربائي والمغناطيسي متعامدة مع بعضها البعض وعلى اتجاه الانتشار ، مما يظهر طبيعة عرضية.

<ol>
	<li>يونغ ، إتش دي وفريدمان ، ر. (2012). الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون. القسم 32.2; الصفحات 1055-1056.</li>
	<li>OpenStax. (2019). جامعة الفيزياء المجلد 2. [نسخة الويب]. تم الاسترجاع من <a href = "https://openstax.org/details/books/university-physics-volume-2" >https://openstax.org/details/books/university-physics-volume-2</a> ؛ القسم 16.2 ؛ الصفحات 706-707.</li>
</ol>

الموجات الكهرومغناطيسية الطائرة i

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 إن وجود مجالات كهربائية ومغناطيسية مجتمعة تنتشر عبر الفضاء على شكل موجات كهرومغناطيسية (EM) هو التنبؤ الأكثر أهمية لمعادلات ماكسويل. وبما أن معادلات ماكسويل تنطبق على الفضاء الحر، فإن الموجات الكهرومغناطيسية المتوقعة لا تحتاج إلى وسط لانتشارها. تتكون الموجة الكهرومغناطيسية من مجال كهربائي، يُعرف بالقوة المؤثرة على شحنة ثابتة، ومجال مغناطيسي، وهو القوة المؤثرة على شحنة متحركة.

 من المفترض أن يكون حقل EM دالة للإحداثيات x والوقت فقط. وبالتالي، تتم كتابة المكون y للمجال الكهربائي بالشكل Ey(x, t)، ويتم كتابة مكون المجال المغناطيسي z بالشكل Bz(x، ر). ونظرًا لافتراض وجود مساحة حرة، لا توجد شحنات أو تيارات حرة، وبالتالي فإن الشحنة المحصورة والتيار في معادلة ماكسويل مضبوطة على صفر.

 يتم فحص قابلية تطبيق قانون غاوس على المجالات الكهربائية من خلال افتراض سطح غوسي مستطيل مع مقطع عرضي مربع من الجانب l وطول ضلعه الثالث Δ< م>س</م>. المكون y للمجال الكهربائي هو نفسه الموجود على الجانبين العلوي والسفلي للصندوق. ولذلك، فإن التدفقات على كلا الجانبين تلغي بعضها البعض. وبالمثل، يتم أيضًا إلغاء التدفق الصافي من المكون z للمجال الكهربائي عبر الجانبين الجانبيين. وبالتالي فإن أي تدفق صافي عبر السطح يأتي بالكامل من المكون x للمجال الكهربائي. بما أن المجال الكهربائي لا يعتمد على y- أو z، Ex(x em>, t) ثابت على وجه مربع بمساحة A وله قيمة مختلفة محتملة Ex(x + Δx, t) ثابت على الوجه المقابل للمربع. يؤدي تطبيق قانون غاوس إلى الحصول على التدفق الصافي للمكون x.


 <img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;">

 بما أن qenc، فإن الشحنة المحيطة تساوي صفرًا، وصافي التدفق للمكون هو أيضًا صفر، والمعادلة أعلاه تشير إلى E x(x, t) = Ex(x + Δx, t) لأي Δx. مثل هذا المكون Ex(x, t) لن يكون جزءًا من موجة كهرومغناطيسية تنتشر على طول < محور em>x، لذا Ex(x, t) = 0 لهذا موجة. ولذلك، فإن المكونات الوحيدة غير الصفرية للمجال الكهربائي هي Ey(x, t) وEz(x, t)، عموديًا على اتجاه انتشار الموجة.


 توجد حجة مماثلة عن طريق استبدال E بـ B واستخدام قانون غاوس للمغناطيسية بدلاً من قانون غاوس للمجالات الكهربائية. يوضح هذا أن المجال B متعامد أيضًا مع اتجاه انتشار الموجة. وبالتالي فإن الموجة الكهرومغناطيسية هي موجة مستعرضة، بمجالاتها الكهربائية والمغناطيسية المتذبذبة متعامدة مع اتجاه انتشارها.

</div>

الموجات الكهرومغناطيسية الطائرة I

يعد وجود المجالات الكهربائية والمغناطيسية مجتمعة التي تنتشر عبر الفضاء كموجات كهرومغناطيسية (EM) أهم تنبؤ ...

Education

JoVE Core

الفيزياء

Unit 1

الوحدة الأولى

Electromagnetic Waves

الموجات الكهرومغناطيسية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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 set to zero. This lets us test which field components can remain in the wave.

To apply Gauss's law for electric fields, a rectangular Gaussian surface with a square cross-section of side l and a third side of length Δx is used. The y-component of the electric field is the same on the top and bottom sides, so those fluxes cancel. The z-component through the two lateral sides also cancels, so any net flux comes only from Ex.

Because Ex depends only on x and time, it is constant over one face of the box and may have a different value on the opposite face. Gauss's law gives zero net flux because the enclosed charge is zero. That means Ex(x, t) = Ex(x + Δx, t) for any Δx, so Ex(x, t) is not part of the wave and must be zero. The electric field components left in the wave are Ey(x, t) and Ez(x, t), both perpendicular to the direction of travel.

A similar argument applies to the magnetic field by using Gauss's law for magnetism instead of Gauss's law for electric fields. This shows that the magnetic field is also perpendicular to the direction of propagation. An electromagnetic wave is therefore a transverse wave, with oscillating electric and magnetic fields at right angles to the wave's motion.

Transverse Fields in Electromagnetic Waves

transverse-fields-in-electromagnetic-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...

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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

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

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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

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standing waves in a cavity

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key terms and concepts

See why electromagnetic waves are transverse. Learn how Maxwell’s equations show that electric and magnetic fields stay perpendicular to the direction of travel.

Transverse Fields in Electromagnetic 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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PS.7.a

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Transverse Fields in Electromagnetic Waves

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