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

היחס בין שדות חשמליים ומגנטיים מתקבל על ידי החלת חוק פאראדיי על חזית גל מישורית הנעה בכיוון +x במהירות קבועה.
חשבו על מלבן בגובה "a" בעל וקטור שטח בכיוון +z.
בעת שילוב סביב המלבן נגד כיוון השעון, נמצא שהשדה החשמלי הוא אפס לאורך "PQ", או בניצב ליסודות למעט אורך "RS". זה רק תורם לאינטגרל נותן ערך שאינו אפס.
כדי לקיים את חוק פאראדיי, חייב להיות רכיב שדה מגנטי בכיוון +z, שיכול לספק שטף מגנטי שאינו אפס דרך המלבן ומכאן נגזרת זמן שאינה אפס של שטף מגנטי.
בזמן "dt", הגל נע מרחק "c dt". תוך כדי תנועה, הוא גורף שטח השווה ל- "ac dt".
במהלך מרווח זמן זה, השטף המגנטי דרך המלבן גדל, נותן את קצב השינוי של שטף מגנטי.
ערך זה מוחלף בחוק פאראדיי, וכתוצאה מכך נוצר קשר בין E ל-B במונחים של מהירות התפשטות הגלים בריק.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון. סעיף 32.2; עמוד 1056.</li>
	<li>OpenStax. (2019). פיזיקה אוניברסיטאית כרך 2. [גרסת אינטרנט]. מקור: <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; סעיף 16.2; עמודים 710–711.</li>
</ol>

גלים אלקטרומגנטיים מישוריים ii

<div style="direction:rtl">חשבו על חזית גל מישורית הנוסעת במיקום x-במהירות קבועה. ניתן לנצל את חזית הגל הזו כדי להשיג את הקשר בין שדות חשמליים למגנטיים בעזרת חוק פאראדיי. <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;"> כדי להחיל את חוק פאראדיי, חשבו על מלבן ברוחב a, כפי שמוצג באיור.1, שווקטור השטח שלו נמצא בכיוון החיובי של z. כדי לפתור את אינטגרל הצד השמאלי בחוק פאראדיי, שלב נגד כיוון השעון לאורך המלבן. השדה החשמלי הוא אפס לאורך אחד מהאורכים השוכנים מחוץ לחזית הגל, בעוד השדה החשמלי מאונך לשני מרכיבי האורך האחרים. שלושת הצדדים הללו אינם נותנים תרומה לאינטגרל. רק לצד אחד, לשדה החשמלי יש ערך שאינו אפס, והוא מקביל לאורך. צד זה תורם לאינטגרל, נותן ערך שאינו אפס. <img alt="Equation2" src="/files/ftp_upload/13823/13823_Equation_PT_2.svg" style="text-align: center; height: 35px;"> מכיוון שהצד השמאלי של חוק פאראדיי אינו אפס, כדי לעמוד במשוואה חייב להיות רכיב שדה מגנטי בכיוון החיובי z, שיכול לספק שטף מגנטי שאינו אפס דרך המלבן ומכאן נגזרת זמן שאינה אפס של השטף המגנטי. כדי לקבל ערך זה, קחו בחשבון שבזמן dt, הגל נע למרחק c dt. תוך כדי תנועה, הוא מטאטא אזור השווה לac dt. במהלך מרווח זמן זה, השטף המגנטי דרך המלבן גדל, מה שנותן את קצב השינוי של השטף המגנטי. ערך זה מוחלף בחוק פאראדיי, וכתוצאה מכך נוצר קשר בין E ל-B במונחים של מהירות התפשטות הגלים בוואקום. <img alt="Equation3" src="/files/ftp_upload/13823/13823_Equation_PT_3.svg" style="text-align: center; height: 14px;"> ביטוי זה מראה שהגל תואם את חוק פאראדיי רק אם מהירות הגל וגדלות הווקטורים הניצבים קשורים, כמו במשוואה שלעיל.</div>

גלים אלקטרומגנטיים מישוריים II

חשבו על חזית גל של מטוס הנוסע בכיוון x במהירות קבועה. ניתן להשתמש בחזית גל זו כדי להשיג את הקשר בין ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Electromagnetic Waves

גלי אלקטרומגנטיים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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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key terms and concepts

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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