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

חשבו על קואורדינטת xyz המחולקת לשני אזורים נפרדים על ידי מישור מקביל למישור yz.
שדה חשמלי ומגנטי אחיד בכיוון +y ו- +z קיים בצד שמאל, בעוד שהצד הימני הוא ללא שדה.
מישור גבול זה, הנקרא חזית גל, נע בכיוון +x במהירות קבועה.
גלים כאלה שבם, בכל רגע, השדות אחידים מעל כל מישור המאונך לכיוון ההתפשטות, נקראים גלי מישור.
גלים אלה מספקים את משוואות מקסוול. חשבו על תיבה גאוסית מלבנית.
מכיוון שהשדה החשמלי נמצא בכיוון y, השטפים החשמליים של פני השטח בכיוון x ובכיוון z הם אפס.
עבור המשטח העליון, השטף הפוך למשטח התחתון, מה שנותן אפס שטף נטו.
מכיוון שהקופסה אינה סוגרת מטען חשמלי, השטף החשמלי כמו גם המגנטי הוא אפס.
לפיכך, חוק גאוס תקף לגבי קרינה אלקטרומגנטית.
לכן, וקטורי השדה החשמלי והמגנטי מאונכים זה לזה ולכיוון ההתפשטות, ומראים טבע רוחבי.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון. סעיף 32.2; עמודים 1055–1056.</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 706–707.</li>
</ol>

גלים אלקטרומגנטיים מישוריים i

<div style="direction:rtl">
	קיומם של שדות חשמליים ומגנטיים משולבים המתפשטים בחלל כגלים אלקטרומגנטיים (EM) הוא החיזוי המשמעותי ביותר של משוואות מקסוול. מכיוון שמשוואות מקסוול מתקיימות בחלל הפנוי, הגלים האלקטרומגנטיים החזויים אינם דורשים מדיום להתפשטותם. גל EM מורכב משדה חשמלי, המוגדר ככוח למטען על מטען נייח, ושדה מגנטי, שהוא הכוח למטען על מטען נע. 

	מניחים ששדה EM הוא פונקציה של קואורדינטה x בלבד והזמן. לפיכך, הרכיב y של השדה החשמלי נכתב כEy(x, t), והרכיב z- של השדה המגנטי נכתב כBz(x, t). בשל ההנחה של מקום פנוי, אין מטענים או זרמים פנויים, ולפיכך, המטען המוקף והזרם במשוואת מקסוול מוגדרים לאפס. 

	הישימות של חוק גאוס עבור שדות חשמליים נבדקת על ידי הנחה של משטח גאוס מלבני עם חתך מרובע של הצלע l ושלצלע השלישית שלו יש אורך Δx. הרכיב y של השדה החשמלי זהה בצד העליון והתחתון של הקופסה. לכן, השטפים משני הצדדים מבטלים זה את זה. באופן דומה, השטף הנקי ממרכיב ה-z של השדה החשמלי דרך שני הצדדים הרוחביים מתבטל גם הוא. לכן כל שטף נטו דרך פני השטח מגיע כולו ממרכיב הx של השדה החשמלי. מכיוון שלשדה החשמל אין תלות y- או z, Ex(x , t) קבוע על פני תיבה עם אזור A ויש לו ערך שונה אולי של Ex(x + Δx, t) שהוא קבוע מעל הצד הנגדי של התיבה. יישום חוק גאוס נותן את השטף הנקי של רכיב x. 
	<img alt="Equation1" src="/files/ftp_upload/13822/13822_Equation_PT_1.svg" style="text-align: center; height: 30px;"> 

	מכיוון שqenc, המטען המוקף, הוא אפס, גם השטף הנקי של הרכיב הוא אפס, והמשוואה לעיל מרמזת על E x(x, t) = Ex(x + Δx, t) עבור כל Δx. רכיב כזה Ex(x, t) לא יהיה חלק מגל אלקטרומגנטי המתפשט לאורך הx-axis, אז Ex(x, t) = 0 עבור גל זה. לכן, הרכיבים היחידים שאינם אפס של השדה החשמלי הם Ey(x, t) ו-Ez(x, t), בניצב לכיוון ההתפשטות של הגל. 

	טיעון דומה מתקיים על ידי החלפת E בB ושימוש בחוק גאוס למגנטיות במקום חוק גאוס לשדות חשמליים. זה מראה שהשדה B גם מאונך לכיוון ההתפשטות של הגל. הגל האלקטרומגנטי הוא, אם כן, גל רוחבי, כאשר השדות החשמליים והמגנטיים המתנודדים שלו מאונכים לכיוון ההתפשטות שלו.
 </div>

גלים אלקטרומגנטיים מישוריים I

קיומם של שדות חשמליים ומגנטיים משולבים המתפשטים בחלל כגלים אלקטרומגנטיים (EM) הוא החיזוי המשמעותי ביותר של ...

Education

JoVE Core

פיזיקה

Unit 1

יחידה 1

Electromagnetic Waves

גלי אלקטרומגנטיים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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...

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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

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

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

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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HIgh School

Physical Science

PS.7

PS.7.a

Minnesota Academic Standards in Science

3.2.2 9P.3.1.1.2

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SC.912.P.10.17

SC.912.P.10.18

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South Carolina College and Career Ready Science Standards

P-PS4-3

Earth and Space Science (ESS)

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E-ESS1-2.

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New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-4.

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Transverse Fields in Electromagnetic Waves

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