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

Kuchenki mikrofalowe wykorzystują fale elektromagnetyczne do podgrzewania żywności.
Większość produktów spożywczych zawiera cząsteczki polarne, takie jak woda, które przeskakują tam iz powrotem wraz ze zmiennym polem elektrycznym. Podczas odwracania cząsteczki ulegają tarciu o inne cząsteczki, w wyniku czego generowane jest ciepło.
Komora mikrofalowa działa jak wnęka rezonansowa, w której stojące fale elektromagnetyczne są tworzone przez odbicie od powierzchni metalu. Dwie metalowe powierzchnie są umieszczone w płaszczyznach węzłowych.
Tak więc odległość między płaszczyznami musi być całkowitą wielokrotnością połowy długości fali.
Długości fal, które spełniają ten warunek, nazywane są długościami fal charakterystycznych, a odpowiadające im częstotliwości nazywane są częstotliwościami charakterystycznymi.
Każda charakterystyczna częstotliwość, kształt fali i wzór węzła stanowi zestaw modów normalnych.
Na przykład typowa domowa kuchenka mikrofalowa działa z częstotliwością 2,4 gigaherca, co odpowiada długości fali łatwo absorbowanej przez cząsteczki wody.
Ta długość fali ma węzły oddalone od siebie o 6,1 centymetra, co oznacza, że żywność będzie zimna w tych punktach i podgrzana do maksimum w antywęzłach.
Tak więc talerz obrotowy kuchenki mikrofalowej jest obracany, aby zapewnić równomierny rozkład ciepła.

<ol>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson. Sekcja 32.5; Strona 1071.</li>
</ol>

fale stojące w jamie

Przykładami stojących fal elektromagnetycznych we wnęce są kuchenki mikrofalowe i lasery do użytku domowego. Kiedy dwie przewodzące metalowe płytki są umieszczone równolegle w płaszczyznach węzłowych, tworzy się wnęka, w której tworzą się fale stojące. Wnęka pomiędzy dwiema płaszczyznami jest analogiczna do rozciągniętej struny utrzymywanej w punktach x = 0 i x = L. Tutaj odległość `L` między dwiema płaszczyznami musi być całkowitą wielokrotnością połowy długości fali. Długości fal spełniające ten warunek są określone wzorem:

<img alt="Równanie1" src="/files/ftp_upload/14213/14213_Equation_1.png" style="text-align: center; height: 40px;" />

Odpowiadające częstotliwości to:

<img alt="Równanie2" src="/files/ftp_upload/14213/14213_Equation_2.png" style="text-align: center; height: 40px;" />

Każda charakterystyczna częstotliwość, kształt fali i wzór węzłów stanowi zbiór modów normalnych. Długość fali można oszacować, mierząc położenie węzłów, a jeśli znana jest częstotliwość, można również określić prędkość fali.

Oprócz powierzchni przewodzących odbicie fal elektromagnetycznych może również wystąpić na styku dwóch materiałów izolacyjnych o różnych właściwościach dielektrycznych lub magnetycznych. Mechaniczny analog to połączenie dwóch strun o równym napięciu, ale różnej liniowej gęstości masy. Zwykle fala padająca na taką powierzchnię graniczną jest częściowo przekazywana do drugiego materiału, a częściowo odbijana z powrotem do pierwszego. Na przykład światło przechodzi przez szklane okno, ale jego powierzchnie również odbijają światło.

Fale stojące w jamie

Domowa kuchenka mikrofalowa i lasery są przykładami stojących fal elektromagnetycznych we wnęce. Gdy dwie przewodzące metalowe płytki są umieszczone równolegle na ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Electromagnetic Waves

Fale elektromagnetyczne

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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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the electromagnetic spectrum

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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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propagation speed of electromagnetic waves

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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...

electromagnetic waves in matter

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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

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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.

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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

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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.

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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 ...

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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

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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 ...

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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

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

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PS.7.b

Electromagnetic Modes in a Microwave Cavity

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