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

Микроволновые печи используют электромагнитные волны для разогрева пищи.
Большинство продуктов питания содержат полярные молекулы, такие как вода, которые переворачиваются вперед и назад под действием переменного электрического поля. При переворачивании молекулы подвергаются трению с другими молекулами, в результате чего выделяется тепло.
Микроволновая камера действует как резонирующая полость, в которой при отражении от металлической поверхности образуются стоячие электромагнитные волны. Две металлические поверхности расположены в узловых плоскостях.
Таким образом, расстояние между плоскостями должно быть целым кратным половине длины волны.
Длины волн, удовлетворяющие этому условию, называются характеристическими длинами волн, а соответствующие частоты — характеристическими.
Каждая характеристическая частота, форма волны и паттерн узла представляют собой набор нормальных мод.
Например, типичная бытовая микроволновая печь работает на частоте 2,4 гигагерца, что соответствует длине волны, легко поглощаемой молекулами воды.
Эта длина волны имеет узлы на расстоянии 6,1 сантиметра друг от друга, что означает, что пища будет холодной в этих точках и максимально нагретой в пучных узлах.
Таким образом, поворотный стол микроволновой печи вращается для равномерного распределения тепла.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. Статья 32.5; стр. 1071.</li>
</ol>

Стоячие волны в полости

Микроволновая печь и лазеры в домашних условиях являются примерами стоячих электромагнитных волн в полости. Когда две проводящие металлические плиты располагаются параллельно на узловых плоскостях, образуется полость, в которой образуются стоячие волны. Полость между двумя плитами аналогична натянутой струне, удерживаемой в точках x = 0 и x = L. Здесь расстояние 'L' между двумя плитами должно быть целым и кратным половине длины волны. Длины волн, удовлетворяющие этому условию, задаются следующим образом:

<img alt="Equation1" src="/files/ftp_upload/14213/14213_Equation_1.png" style="text-align: center; height: 40px;" />

Соответствующие частоты:

<img alt="Equation2" src="/files/ftp_upload/14213/14213_Equation_2.png" style="text-align: center; height: 40px;" />

Каждая характеристическая частота, форма волны и узор узлов составляют набор нормальных мод. Длину волны можно определить, измерив положение узлов, и если известна частота, можно также определить скорость волны.

Помимо проводящих поверхностей, отражение электромагнитных волн также может происходить на границе между двумя изоляционными материалами с разными диэлектрическими или магнитными свойствами. Механический аналог - это соединение двух струн с одинаковым натяжением, но разной линейной плотностью массы. Обычно волна, падающая на такую граничную поверхность, частично проникает во второй материал и частично отражается обратно в первый. Например, свет проникает через стеклянное окно, но его поверхности также отражают свет.

Бытовая микроволновка и лазеры являются примерами стоячих электромагнитных волн в резонаторе. Когда две проводящие металлические пластины размещаются параллельно в ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Electromagnetic Waves

Электромагнитные волны

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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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

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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

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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.

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

New Jersey Student Learning Standards for Science

High School

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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

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PHYS.8

PHYS.8.E

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South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-4

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Standing Electromagnetic Waves

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The Electromagnetic Spectrum

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Infrared (IR) Spectroscopy: Overview

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PS.7.b

Electromagnetic Modes in a Microwave Cavity

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