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

Recall the standing waves formed in a tight string. 
Standing waves are the combination of two waves that move in the opposite direction but have the same amplitude and frequency.
Consider a perfect conducting sheet placed in the y-z plane. A linearly polarized electromagnetic wave strikes the sheet, while traveling in the negative x-direction.
The incident wave induces the current on the surface of the conductor, resulting in additional electric fields, producing a reflected wave with the same frequency and amplitude as the incident wave.
The superposition of these two waves generates the standing wave. Simplifying these expressions provide the points on the wave where the magnitudes of the electric field and the magnetic field are zero. These are called the nodes or nodal planes.
An antinode is a point where the amplitude goes from the maximum positive to the maximum negative displacement.
The nodes of the electric field coincide with the antinodes of the magnetic fields, and vice versa. Hence, they are 90-degrees out of phase at each point.

staande elektromagnetische golven

Elektromagnetische golven kunnen worden gereflecteerd; het oppervlak van een geleider of een diëlektricum kan als reflector fungeren. Zoals elektrische en magnetische velden het superpositieprincipe gehoorzamen, zo doen elektromagnetische golven dat ook. De superpositie van een invallende golf en een gereflecteerde elektromagnetische golf produceert een staande golf die analoog is aan de staande golven die op een uitgerekte snaar worden gecreëerd. 

Stel dat een vel van een perfecte geleider in het yz-vlak wordt geplaatst, en een lineair gepolariseerde elektromagnetische golf die zich in de negatieve x-richting voortbeweegt, treft het. Omdat het elektrische veld geen component kan hebben die evenwijdig is aan het oppervlak van een perfecte geleider, moet het elektrische veld overal in het yz-vlak nul zijn. Het elektrische veld van de invallende elektromagnetische golf is niet altijd nul in het yz-vlak, maar deze invallende golf induceert oscillerende stromen op het oppervlak van de geleider, waardoor een extra elektrisch veld ontstaat. . Het netto elektrische veld, dat de vectorsom is van dit veld en het invallende veld, is overal binnen en op het oppervlak van de geleider nul. De stromen die op het oppervlak van de geleider worden geïnduceerd, produceren ook een gereflecteerde golf die zich vanuit het vlak voortplant. Het superpositieprincipe stelt dat het totale veld op elk punt de vectorsom is van de elektrische velden van de invallende en gereflecteerde golven, vergelijkbaar met het magnetische veld. De superpositie van invallende en gereflecteerde golven genereert staande golven.
 <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;"> 

 Het vereenvoudigen van deze uitdrukkingen levert de punten op de golf op waar de magnitudes van het elektrische veld en het magnetische veld nul zijn. Dit worden de knooppunten of knooppuntvlakken genoemd. Halverwege tussen twee aangrenzende knoopvlakken bevinden zich de vlakken met maximale amplitude; dit zijn de antinodale vlakken. 

 Het totale elektrische veld is een sinusfunctie en het totale magnetische veld is een cosinusfunctie. Daarom zijn de sinusoïdale variaties van de twee velden op elk punt uit fase. De elektrische veldknooppunten vallen samen met de antinodes van de magnetische velden en omgekeerd. Daarom zijn ze 90° op elk punt uit fase. Dit is in tegenstelling tot een golf die zich in één richting voortbeweegt, waarbij de sinusoïdale variaties van de elektrische en magnetische velden op een bepaald punt in fase zijn.

Staande elektromagnetische golven

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 ...

Education

JoVE Core

Physics

Natuurkunde

Unit 1

Onderdeel 1

Electromagnetic Waves

Elektromagnetische golven

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

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

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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

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Minnesota Academic Standards in Science

9-12

4.2.1 9P.3.2.2.1

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HS-PS4-5

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Florida Department of Education

SC.912.P.10

SC.912.P.10.17

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South Carolina College and Career Ready Science Standards

P-PS4-2

P-PS4-4

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PS.7.b

Electromagnetic Wave Reflection at Conductors

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