energy transport by waves; transverse waves; amplitude, frequency, wavelength, wavenumber, and angular frequency; equations for waves (Sections 11.1–11.5)
Ampère's and Faraday's laws (Sections 19.9 and 20.3)
dipoles (Sections 16.4 and 19.1)
rms values (Section 21.1)
thermal radiation (Section 14.8)
Doppler effect (Section 12.8)
relative velocity (Section 3.5)
Mastering the Concepts
EM waves consist of oscillating electric and magnetic fields that propagate away from their source. EM waves always have both electric and magnetic fields.
The Ampère-Maxwell law is Ampère's law modified by Maxwell so that a changing electric field generates a magnetic field.
The Ampère-Maxwell law, along with Gauss's law, Gauss's law for magnetism, and Faraday's law, are called Maxwell's equations. They describe completely the electric and magnetic fields. Maxwell's equations say that <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/299145/ch22_EandBfield.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> lines do not have to be tied to matter. Instead, they can break free and electromagnetic waves can travel far from their sources.
Radiation from a dipole antenna is weakest along the antenna's axis and strongest in directions perpendicular to the axis. Electric dipole antennas and magnetic dipole antennas can be used either as sources of EM waves or as receivers of EM waves.
The electromagnetic spectrum—the range of frequencies and wavelengths of EM waves—is traditionally divided into named regions. From lowest to highest frequency, they are: radio waves, microwaves, infrared, visible, ultraviolet, x-rays, and gamma rays.
EM waves of any frequency travel through vacuum at a speed <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/22_3.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a>
EM waves can travel through matter, but they do so at speeds less than c. The index of refraction for a material is defined as <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/22_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a> where u is the speed of EM waves through the material.
The speed of EM waves (and therefore also the index of refraction) in matter depends on the frequency of the wave.
When an EM wave passes from one medium to another, the wavelength changes; the frequency remains the same. The wave in the second medium is created by the oscillating charges at the boundary, so the fields in the second medium must oscillate at the same frequency as the fields in the first.
Properties of EM waves in vacuum:
The electric and magnetic fields oscillate at the same frequency and are in phase. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/22_7.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a> <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/E_arrow_B.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>and the direction of propagation are three mutually perpendicular directions. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/E_Cross_b.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>is always in the direction of propagation. The electric energy density is equal to the magnetic energy density.
Energy density (SI unit: J/m3) of an EM wave in vacuum:
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/22_13.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
Intensity is proportional to the squares of the electric and magnetic field amplitudes.
The average power incident on a surface of area A is
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/22_14.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
where q is 0o for normal incidence and 90o for grazing incidence.
The polarization of an EM wave is the direction of its electric field.
If unpolarized waves pass through a polarizer, the transmitted intensity is half the incident intensity:
If a linearly polarized wave is incident on a polarizer, the component of<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0073512141/663830/E.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>parallel to the transmission axis gets through. If q is the angle between the incident polarization and the transmission axis, then <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663830/22_16a.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>
Since intensity is proportional to the square of the amplitude, the transmitted intensity is
where urel is positive if the source and observer are approaching, and negative if receding. If the relative speed of source and observer is much less than c,
