Name: faraday’s law in a plane wave
Uploaded: 2023-04-30T12:46:11.000Z
Duration: 1 min 29 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.7

PS.7.a

Plane Electromagnetic Waves II

يتم الحصول على العلاقة بين المجالين الكهربائي والمغناطيسي من خلال تطبيق قانون فاراداي على واجهة موجة مستوية تتحرك في اتجاه + x بسرعة ثابتة.
ضع في اعتبارك مستطيلا بارتفاع "a" له متجه مساحة في اتجاه + z.
أثناء التكامل حول المستطيل عكس اتجاه عقارب الساعة ، وجد أن المجال الكهربائي يكون صفرا على طول "PQ" ، أو عموديا على العناصر باستثناء الطول "RS". إنه يساهم فقط في إعطاء التكامل قيمة غير صفرية.
لتلبية قانون فاراداي ، يجب أن يكون هناك مكون مجال مغناطيسي في اتجاه + z ، والذي يمكن أن يوفر تدفقا مغناطيسيا غير صفري عبر المستطيل وبالتالي مشتق زمني غير صفري للتدفق المغناطيسي.
في الوقت "dt" ، تتحرك الموجة مسافة "c dt". أثناء الحركة ، يكتسح مساحة تساوي "ac dt".
خلال هذه الفترة الزمنية ، يزداد التدفق المغناطيسي عبر المستطيل ، مما يعطي معدل تغير التدفق المغناطيسي.
يتم استبدال هذه القيمة في قانون فاراداي ، مما يؤدي إلى وجود علاقة بين E و B من حيث سرعة انتشار الموجة في الفراغ.

<ol>
	<li>يونغ ، إتش دي وفريدمان ، ر. (2012). الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون. القسم 32.2; صفحة 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 710-711.</li>
</ol>

الموجات الكهرومغناطيسية الطائرة ii

<div style="direction:rtl">لنفترض أن واجهة موجة مستوية تتحرك في الاتجاه x وبسرعة ثابتة. يمكن استخدام واجهة الموجة هذه للحصول على العلاقة بين المجالات الكهربائية والمغناطيسية بمساعدة قانون فاراداي. <img alt="Equation1" src="/files/ftp_upload/13823/13823_Equation_PT_1.svg" style="text-align: center; height: 35px;"> <img alt="Figure1" src="/files/ftp_upload/13823/13823_PT _Figure_1.svg" style="text-align: center; height: 175px;"> لتطبيق قانون فاراداي، فكر في مستطيل بعرض a، كما هو موضح في الشكل 1، ومتجه مساحته في الاتجاه الموجب z. لحل تكامل الجانب الأيسر في قانون فاراداي، قم بالتكامل عكس اتجاه عقارب الساعة على طول المستطيل. يكون المجال الكهربائي صفرًا على طول أحد الأطوال الواقعة خارج جبهة الموجة، بينما يكون المجال الكهربائي متعامدًا مع عنصري الطول الآخرين. هذه الجوانب الثلاثة لا تقدم أي مساهمة في التكامل. على طول جانب واحد فقط، يكون للمجال الكهربائي قيمة غير صفرية، وهو موازٍ للطول. يساهم هذا الجانب في التكامل، مما يعطي قيمة غير الصفر. <img alt="Equation2" src="/files/ftp_upload/13823/13823_Equation_PT_2.svg" style="text-align: center; height: 35px;"> بما أن الجانب الأيسر من قانون فاراداي ليس صفرًا، لتحقيق المعادلة يجب أن يكون هناك عنصر مجال مغناطيسي في الاتجاه الموجب z، والذي يمكن أن يوفر عدم - التدفق المغناطيسي صفر عبر المستطيل وبالتالي مشتق زمني غير صفري للتدفق المغناطيسي. للحصول على هذه القيمة، ضع في اعتبارك أنه في الزمن dt، تتحرك الموجة مسافة c dt. أثناء التحرك، فإنه يمسح مساحة تساوي ac dt. خلال هذه الفترة الزمنية، يزداد التدفق المغناطيسي عبر المستطيل، مما يعطي معدل تغير التدفق المغناطيسي. تم استبدال هذه القيمة في قانون فاراداي، مما أدى إلى وجود علاقة بين E وB بدلالة سرعة انتشار الموجة في الفراغ. <img alt="Equation3" src="/files/ftp_upload/13823/13823_Equation_PT_3.svg" style="text-align: center; height: 14px;"> يوضح هذا التعبير أن الموجة تتوافق مع قانون فاراداي فقط إذا كانت سرعة الموجة ومقادير المتجهات المتعامدة مرتبطة ببعضها البعض، كما في المعادلة أعلاه.</div>

الموجات الكهرومغناطيسية الطائرة II

ضع في اعتبارك جبهة موجية مستوية تتحرك في الاتجاه x بسرعة ثابتة. يمكن استخدام هذه الجبهة الموجية للحصول على العلاقة بين ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Electromagnetic Waves

الموجات الكهرومغناطيسية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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 field there is zero. On the other two length elements, the electric field is perpendicular to the path, so they also give no contribution. Only one side has a non-zero electric field that is parallel to the length, so that side makes the integral non-zero.

Because the left side of Faraday’s law is non-zero, the magnetic side must also be non-zero. That means there must be a magnetic field component in the positive z-direction. This component gives magnetic flux through the rectangle, and its change in time must match the electric field term.

To find the flux change, consider the time interval dt. In that time, the wavefront moves a distance c dt, where c is the wave speed in vacuum. As it moves, it sweeps out an area equal to ac dt. That growing area increases the magnetic flux through the rectangle and gives the rate of change of flux.

Substituting this result into Faraday’s law gives a relationship between E and B in terms of the wave speed in vacuum. The expression shows that the plane wave satisfies Faraday’s law only when the wave speed and the magnitudes of the perpendicular electric and magnetic fields are related in this way.

Faraday’s Law in a Plane Wave

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Use Faraday’s law to relate electric and magnetic fields in a plane wave, and see how a moving wavefront sets the link with wave speed in vacuum.

Faraday’s Law in a Plane Wave | JoVE K12

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PS.7.b

Faraday’s Law in a Plane Wave

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