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

تستخدم أفران الميكروويف الموجات الكهرومغناطيسية لتسخين الطعام.
تحتوي معظم المواد الغذائية على جزيئات قطبية مثل الماء ، والتي تنقلب ذهابا وإيابا مع المجال الكهربائي المتناوب. أثناء التقليب ، تخضع الجزيئات للاحتكاك مع الجزيئات الأخرى ، ونتيجة لذلك ، تتولد الحرارة.
تعمل غرفة الميكروويف كتجويف رنين حيث تتشكل الموجات الكهرومغناطيسية الدائمة عن طريق الانعكاس من السطح المعدني. يتم وضع السطحين المعدنيين في المستويات العقدية.
لذلك ، يجب أن تكون المسافة بين الطائرات مضاعفا متكاملا لنصف الطول الموجي.
تسمى الأطوال الموجية التي تفي بهذا الشرط الأطوال الموجية المميزة ، وتسمى الترددات المقابلة بالترددات المميزة.
يشكل كل تردد مميز وشكل موجة ونمط عقدة مجموعة من الأوضاع العادية.
على سبيل المثال ، يعمل الميكروويف المحلي النموذجي عند 2.4 جيجا هرتز ، وهو ما يتوافق مع طول موجي تمتصه جزيئات الماء بسهولة.
يحتوي هذا الطول الموجي على عقد تفصل بينها 6.1 سم ، مما يعني أن الطعام سيكون باردا في هذه النقاط ويسخن إلى الحد الأقصى عند العقد المضادة.
لذلك ، يتم تدوير القرص الدوار للميكروويف للحصول على توزيع موحد للحرارة.

<ol>
	<li>يونغ ، إتش دي وفريدمان ، ر. (2012). الفيزياء الجامعية مع الفيزياء الحديثة. سان فرانسيسكو ، كاليفورنيا: بيرسون. القسم 32.5; صفحة 1071.</li>
</ol>

موجات واقفة في تجويف

<div style="direction:rtl">يعد الميكروويف المنزلي وأشعة الليزر أمثلة على الموجات الكهرومغناطيسية الموجودة في التجويف. عندما يتم وضع لوحتين معدنيتين موصلتين بشكل متوازي على المستويات العقدية، فإن ذلك يخلق تجويفًا تتشكل فيه الموجات المستقرة. يشبه التجويف بين المستويين خيطًا ممتدًا مثبتًا عند النقطتين x = 0 وx = L. هنا المسافة 'L' يجب أن يكون بين المستويين عددًا صحيحًا مضاعفًا لنصف الطول الموجي. يتم إعطاء الأطوال الموجية التي تحقق هذا الشرط بواسطة: <img alt="Equation1" src="/files/ftp_upload/14213/14213_Equation_1.png" style="text-align: center; height: 40px;"> الترددات المقابلة هي: <img alt="Equation2" src="/files/ftp_upload/14213/14213_Equation_2.png" style="text-align: center; height: 40px;"> يشكل كل تردد مميز وشكل موجة ونمط عقدة مجموعة من الأوضاع العادية. ويمكن تقدير الطول الموجي عن طريق قياس مواضع العقد، وإذا كان التردد معروفاً فيمكن تحديد سرعة الموجة أيضاً. بصرف النظر عن الأسطح الموصلة، يمكن أن يحدث انعكاس الموجات الكهرومغناطيسية أيضًا عند السطح البيني بين مادتين عازلتين لهما خصائص عازلة أو مغناطيسية مختلفة. التناظرية الميكانيكية عبارة عن تقاطع بين سلسلتين متساويتين في التوتر ولكنهما مختلفان في كثافة الكتلة الخطية. عادةً، تنتقل الموجة الساقطة على هذا السطح الحدودي جزئيًا إلى المادة الثانية وتنعكس جزئيًا مرة أخرى إلى المادة الأولى. على سبيل المثال، ينتقل الضوء عبر نافذة زجاجية، ولكن أسطحها تعكس الضوء أيضًا.</div>

يعد الميكروويف المنزلي والليزر أمثلة على الموجات الكهرومغناطيسية الدائمة في التجويف. عندما يتم وضع لوحين معدنيين موصلين بالتوازي عند ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Electromagnetic Waves

الموجات الكهرومغناطيسية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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...

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...

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

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...

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 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.

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

HS-PS4-5

Alabama Course of Study Science

9-12

9-12.PS.2.2.e

9-12.P.3.7.c

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.E

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-4

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-2.

James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his ...

Electromagnetic Wave Equation

Maxwell&#39;s equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose ...

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of ...

Plane Electromagnetic Waves II

Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between ...

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


Consider a plane ...

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a ...

Momentum And Radiation Pressure

An object absorbing an electromagnetic wave would experience a force in the direction of propagation of the wave. This force occurs because ...

Radiation Pressure: Problem Solving

The radiation pressure applied by an electromagnetic wave on a perfectly absorbing surface equals the energy density of the wave. The wave&#39;s momentum ...

Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the ...

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the ...

The student will investigate and understand that electromagnetic radiation has characteristics. Key ideas include electromagnetic radiation, including visible light, has wave characteristics and behavior; and

The Electromagnetic Spectrum

Electromagnetic waves are categorized according to their wavelengths and frequencies, giving the electromagnetic spectrum. These waves are classified as ...

Infrared (IR) Spectroscopy: Overview

When electromagnetic radiation passes through a material, atoms or molecules transition from a lower to a higher energy state by absorbing radiation ...

ultraviolet-and-visible-uvvis-spectroscopy-overview

Ultraviolet and Visible (UV&ndash;Vis) Spectroscopy: Overview

Ultraviolet&#8211;visible (UV&#8211;visible or UV&#8211;Vis) spectroscopy is an analytical technique that investigates the interaction between matter and ...

X-ray Imaging

German physicist Wilhelm R&#246;ntgen (1845&#8211;1923) was experimenting with electrical current when he discovered that a mysterious and invisible ...

Radiation: Applications

The average temperature of Earth is the subject of much current discussion. Earth is in radiative contact with both the Sun and dark space; it receives ...

Absorption of Radiation

The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:

where &#963; is the Stefan-Boltzmann constant, a ...

The student will investigate and understand that electromagnetic radiation has characteristics. Key ideas include regions of the electromagnetic spectrum have specific characteristics and uses.

PS.7.b

Electromagnetic Modes in a Microwave Cavity

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