Name: electromagnetic wave reflection at conductors
Uploaded: 2023-09-18T17:11:17.000Z
Duration: 1 min 15 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.7

PS.7.a

Standing Electromagnetic Waves

Rappelez-vous les ondes stationnaires formées en une corde serrée. 
Les ondes stationnaires sont la combinaison de deux ondes qui se déplacent dans la direction opposée mais qui ont la même amplitude et la même fréquence.
Considérons une feuille conductrice parfaite placée dans le plan y-z. Une onde électromagnétique polarisée linéairement frappe la feuille, tout en se déplaçant dans la direction négative de l’x.
L’onde incidente induit le courant à la surface du conducteur, ce qui entraîne des champs électriques supplémentaires, produisant une onde réfléchie de même fréquence et de même amplitude que l’onde incidente.
La superposition de ces deux ondes génère l’onde stationnaire. En simplifiant ces expressions, on obtient les points sur l’onde où les intensités du champ électrique et du champ magnétique sont nulles. C’est ce qu’on appelle les nœuds ou les plans nodaux.
Un antinœud est un point dont l’amplitude va du déplacement positif maximal au déplacement négatif maximal.
Les nœuds du champ électrique coïncident avec les antinœuds des champs magnétiques, et vice versa. Par conséquent, ils sont déphasés de 90 degrés en chaque point.

<ol>
	<li>Young, H.D. et Freedman, R.A. (2012). La physique universitaire avec la physique moderne. San Francisco, Californie : Pearson. l’article 32.5 ; Pages 1069 et 1070.</li>
</ol>

ondes électromagnétiques stationnaires

Les ondes électromagnétiques peuvent être réfléchies ; la surface d'un conducteur ou d'un diélectrique peut agir comme un réflecteur. Comme les champs électriques et magnétiques obéissent au principe de superposition, les ondes électromagnétiques aussi. La superposition d'une onde incidente et d'une onde électromagnétique réfléchie produit une onde stationnaire analogue aux ondes stationnaires créées sur une corde tendue.

Supposons qu'une feuille d'un conducteur parfait soit placée dans le plan yz, et qu'une onde électromagnétique polarisée linéairement voyageant dans la direction x négative la frappe. Puisque le champ électrique ne peut pas avoir une composante parallèle à la surface d'un conducteur parfait, le champ électrique doit être nul partout dans le plan yz. Le champ électrique de l'onde électromagnétique incidente n'est pas nul à tout moment dans le plan yz, mais cette onde incidente induit des courants oscillants à la surface du conducteur, donnant lieu à un champ électrique supplémentaire. Le champ électrique net, qui est la somme vectorielle de ce champ et du champ incident, est nul partout à l'intérieur et sur la surface du conducteur. Les courants induits à la surface du conducteur produisent également une onde réfléchie qui se propage hors du plan. Le principe de superposition stipule que le champ total en tout point est la somme vectorielle des champs électriques des ondes incidentes et réfléchies, similairement au champ magnétique. La superposition des ondes incidentes et réfléchies génère des ondes stationnaires.

<img alt="Equation1" src="/files/ftp_upload/13829/13829_Equation_1.png" style="text-align: center; height: 24px;" />
<img alt="Equation2" src="/files/ftp_upload/13829/13829_Equation_2.png" style="text-align: center; height: 22px;" />

Simplifier ces expressions fournit les points sur l'onde où les magnitudes du champ électrique et du champ magnétique sont nulles. Ceux-ci sont appelés les nœuds ou les plans nodaux. À mi-chemin entre deux plans nodaux adjacents se trouvent les plans d'amplitude maximale ; ce sont les plans anti-nodaux.

Le champ électrique total est une fonction sinusoïdale, et le champ magnétique total est une fonction cosinus. Par conséquent, les variations sinusoïdales des deux champs sont déphasées à chaque point. Les nœuds du champ électrique coïncident avec les antinœuds des champs magnétiques et vice versa. Par conséquent, ils sont déphasés de 90° à chaque point. Ceci est en contraste avec une onde se déplaçant dans une direction, pour laquelle les variations sinusoïdales des champs électrique et magnétique sont en phase à tout point particulier.

Ondes électromagnétiques stationnaires

Les ondes électromagnétiques peuvent être réfléchies ; La surface d’un conducteur ou d’un diélectrique peut agir comme un réflecteur. Comme les champs électriques et magnétiques obéissent à la ...

Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

Electromagnetic Waves

Ondes électromagnétiques

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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 conductor, so the electric field must be zero everywhere in the yz-plane.

The incident wave is not zero at the surface, but it induces oscillating currents on the conductor. These currents create an additional electric field. The net electric field is the vector sum of the incident and induced fields, and it is zero everywhere inside and on the conductor's surface. The same surface currents also produce a reflected wave that moves away from the plane.

The total field at any point is the vector sum of the incident and reflected electric fields, and the same idea applies to the magnetic field. This superposition creates standing waves. The places where the electric or magnetic field magnitude is zero are called nodes, or nodal planes. The planes halfway between adjacent nodes have maximum amplitude and are called antinodal planes.

For these standing waves, the total electric field follows a sine function, while the total magnetic field follows a cosine function. The two fields are therefore 90° out of phase at each point. Electric field nodes line up with magnetic field antinodes, and magnetic field nodes line up with electric field antinodes. This is different from a wave traveling in one direction, where the electric and magnetic fields are in phase at a given point.

Electromagnetic Wave Reflection at Conductors

electromagnetic-wave-reflection-at-conductors

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 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

Explore how reflected electromagnetic waves form standing patterns at conductors, with nodes, antinodes, and electric and magnetic fields out of phase.

Electromagnetic Wave Reflection at Conductors | JoVE K12

physics

JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

Minnesota Academic Standards in Science

9-12

4.2.1 9P.3.2.2.1

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.PS.2.2.e

9-12.P.3.7.c

Florida Department of Education

SC.912.P.10

SC.912.P.10.17

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 ...

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 ...

Standing Waves in a Cavity

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 Wave Reflection at Conductors

Description

Transcript

Tags

More videos by Standards