Name: electromagnetic modes in a microwave cavity
Uploaded: 2023-09-18T17:11:21.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.7

PS.7.a

Standing Waves in a Cavity

תנורי מיקרוגל משתמשים בגלים אלקטרומגנטיים כדי לחמם מזון.
רוב פריטי המזון מכילים מולקולות קוטביות כמו מים, שמתהפכות קדימה ואחורה עם השדה החשמלי לסירוגין. תוך כדי היפוך עוברות המולקולות חיכוך עם מולקולות אחרות, וכתוצאה מכך נוצר חום.
תא המיקרוגל פועל כחלל מהדהד שבו גלים אלקטרומגנטיים עומדים נוצרים על ידי השתקפות מפני השטח של המתכת. שני המשטחים המתכתיים ממוקמים במישורי צומת.
לכן, המרחק בין המישורים חייב להיות כפולה אינטגרלית של מחצית אורך הגל.
אורכי הגל המקיימים תנאי זה נקראים אורכי הגל האופייניים, והתדרים המתאימים נקראים התדרים האופייניים.
כל תדר אופייני, צורת גל ותבנית צומת מהווים קבוצה של מצבים נורמליים.
לדוגמה, מיקרוגל ביתי טיפוסי פועל במהירות של 2.4 ג'יגה-הרץ, המקבילה לאורך גל הנבלע בקלות על ידי מולקולות המים.
אורך גל זה כולל צמתים במרחק של 6.1 סנטימטרים זה מזה, מה שאומר שהמזון יהיה קר בנקודות אלה ומחומם למקסימום באנטי-צמתים.
לכן, מסתובבים את פטיפון המיקרוגל כדי לקבל פיזור חום אחיד.

<ol>
	<li>יאנג, ה.ד. ופרידמן, ר. (2012). פיזיקה אוניברסיטאית עם פיזיקה מודרנית. סן פרנסיסקו, קליפורניה: פירסון. סעיף 32.5; עמוד 1071.</li>
</ol>

גלים עומדים בחלל

<div style="direction:rtl">

 מיקרוגל ביתי ולייזרים הם דוגמאות לגלים אלקטרומגנטיים עומדים בחלל. כאשר שני לוחות מתכת מוליכים ממוקמים במקביל במישורי הצמתים, זה יוצר חלל שבו נוצרים גלים עומדים. החלל בין שני המישורים מקביל למיתר מתוח המוחזק בנקודות x = 0 ו-x = L. כאן, המרחק 'L' בין שני המישורים חייב להיות כפולה שלמה של מחצית מאורך הגל. אורכי הגל העונים על תנאי זה ניתנים על ידי: 

 <img alt="Equation1" src="/files/ftp_upload/14213/14213_Equation_1.png" style="text-align: center; height: 40px;"> 

 התדרים המתאימים הם: <img alt="Equation2" src="/files/ftp_upload/14213/14213_Equation_2.png" style="text-align: center; height: 40px;"> 
 
 כל תדר אופייני, צורת גל ותבנית צומת מהווים קבוצה של מצבים רגילים. ניתן להעריך את אורך הגל על ידי מדידת מיקומי הצומת, ואם התדר ידוע, ניתן גם לקבוע את מהירות הגל. 
 
 מלבד משטחים מוליכים, השתקפות גלים אלקטרומגנטיים יכולה להתרחש גם בממשק בין שני חומרים מבודדים בעלי תכונות דיאלקטריות או מגנטיות שונות. האנלוגי המכני הוא צומת של שני מיתרים בעלי מתח שווה אך בצפיפות מסה ליניארית שונה. בדרך כלל, תקרית גל על משטח גבול כזה מועברת בחלקה לחומר השני ובחלקה מוחזרת לחומר הראשון. לדוגמה, האור מועבר דרך חלון זכוכית, אבל המשטחים שלו גם משקפים את האור.
 </div>

מיקרוגל ביתי ולייזרים הם דוגמאות לגלים אלקטרומגנטיים עומדים בחלל. כאשר שני לוחות מתכת מוליכים ממוקמים במקביל ב ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Electromagnetic Waves

גלי אלקטרומגנטיים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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, wave shape, and node pattern is a normal mode.

Node positions can be measured to estimate the wavelength. If the frequency is known, the wave speed can also be found. Electromagnetic waves can also reflect at the boundary between two insulating materials with different dielectric or magnetic properties.

This kind of boundary acts like a junction between two strings with the same tension but different linear mass density. A wave that reaches the boundary is partly transmitted into the second material and partly reflected back. Light passing through a glass window is one example, since the surfaces transmit some light and also reflect some of it.

Electromagnetic Modes in a Microwave Cavity

electromagnetic-modes-in-a-microwave-cavity

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...

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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...

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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...

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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...

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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...

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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...

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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...

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standing waves in a 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

Learn how standing electromagnetic waves form in a cavity, why only certain wavelengths fit, and how reflections create partial transmission at boundaries.

Electromagnetic Modes in a Microwave Cavity | 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.

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PS.7.b

Electromagnetic Modes in a Microwave Cavity

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