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Physics LibreTexts

15.9: Electromagnetic Waves

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Maxwell predicted the existence of electromagnetic waves, and these were generated experimentally by Hertz shortly afterwards. In addition, the predicted speed of the waves was 3×108m s1, the same as the measured speed of light, showing that light is an electromagnetic wave.

In an isotropic, homogeneous, nonconducting, uncharged medium, where the permittivity and permeability are scalar quantities, Maxwell's equations can be written

E=ρ.

H=0.

×H=ϵ˙E.

×E=μ˙H.

These equations involve E, H, and t. Let us see if we can eliminate E and hence find an equation in just H and t.

Take the curl of equation 15.9.3, and make use of equation 15.6.4:

graddivH2H=ϵtcurlE

Substitute for div H and curlE from equations 15.9.2 and 15.9.4 to obtain

2H=ϵμ¨H

This is the equation in terms of just H and t that we sought.

Comparison with equation 15.1.2 shows that this is a wave of speed 1/ϵμ (Verify that this has the dimensions of speed.)

In a similar manner the reader should easily be able to eliminate B to derive the equation

2E=ϵμ¨E

In a vacuum, the speed is 1/ϵoμo. With μo=4π×107H m1 and ϵo=8.854×1012F m1, this comes to 2.998×108m s1.

Can we eliminate t from the equations, and hence obtain a relation between just E and H? If you do, you will obtain

EH=μϵ,

which, in a vacuum, or free space, becomes

EH=μoϵo=377Ω,

which is the impedance of a vacuum, or of free space. Since the SI units of E and H are, respectively V m-1 and A m-1, it is easy to verify that the units of impedance are V A-1, or Ω.


This page titled 15.9: Electromagnetic Waves is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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