Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
College Physics for AP® Courses

Section Summary

College Physics for AP® CoursesSection Summary

24.1 Maxwell’s Equations: Electromagnetic Waves Predicted and Observed

  • Electromagnetic waves consist of oscillating electric and magnetic fields and propagate at the speed of light c c . They were predicted by Maxwell, who also showed that
    c =1μ0ε0,c =1μ0ε0, size 12{"c "= { {1} over { sqrt {μ rSub { size 8{0} } ε rSub { size 8{0} } } } } } {}

    where μ0μ0 size 12{μ rSub { size 8{0} } } {} is the permeability of free space and ε0ε0 size 12{ε rSub { size 8{0} } } {} is the permittivity of free space.

  • Maxwell’s prediction of electromagnetic waves resulted from his formulation of a complete and symmetric theory of electricity and magnetism, known as Maxwell’s equations.
  • These four equations are paraphrased in this text, rather than presented numerically, and encompass the major laws of electricity and magnetism. First is Gauss’s law for electricity, second is Gauss’s law for magnetism, third is Faraday’s law of induction, including Lenz’s law, and fourth is Ampere’s law in a symmetric formulation that adds another source of magnetism—changing electric fields.

24.2 Production of Electromagnetic Waves

  • Electromagnetic waves are created by oscillating charges (which radiate whenever accelerated) and have the same frequency as the oscillation.
  • Since the electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.
  • The strengths of the electric and magnetic parts of the wave are related by
    EB= c,EB= c, size 12{ { {E} over {B} } = ital " c"} {}

    which implies that the magnetic field BB size 12{B} {} is very weak relative to the electric field EE size 12{E} {}.

24.3 The Electromagnetic Spectrum

  • The relationship among the speed of propagation, wavelength, and frequency for any wave is given by vW=fλvW=fλ size 12{v rSub { size 8{W} } =fλ} {}, so that for electromagnetic waves,
    c=fλ,c=fλ, size 12{c = fλ} {}
    where ff size 12{f} {} is the frequency, λλ size 12{λ} {} is the wavelength, and cc size 12{c} {} is the speed of light.
  • The electromagnetic spectrum is separated into many categories and subcategories, based on the frequency and wavelength, source, and uses of the electromagnetic waves.
  • Any electromagnetic wave produced by currents in wires is classified as a radio wave, the lowest frequency electromagnetic waves. Radio waves are divided into many types, depending on their applications, ranging up to microwaves at their highest frequencies.
  • Infrared radiation lies below visible light in frequency and is produced by thermal motion and the vibration and rotation of atoms and molecules. Infrared’s lower frequencies overlap with the highest-frequency microwaves.
  • Visible light is largely produced by electronic transitions in atoms and molecules, and is defined as being detectable by the human eye. Its colors vary with frequency, from red at the lowest to violet at the highest.
  • Ultraviolet radiation starts with frequencies just above violet in the visible range and is produced primarily by electronic transitions in atoms and molecules.
  • X-rays are created in high-voltage discharges and by electron bombardment of metal targets. Their lowest frequencies overlap the ultraviolet range but extend to much higher values, overlapping at the high end with gamma rays.
  • Gamma rays are nuclear in origin and are defined to include the highest-frequency electromagnetic radiation of any type.

24.4 Energy in Electromagnetic Waves

  • The energy carried by any wave is proportional to its amplitude squared. For electromagnetic waves, this means intensity can be expressed as
    Iave=cε0E022,Iave=cε0E022, size 12{I rSub { size 8{"ave"} } = { {ce rSub { size 8{0} } E rSub { size 8{0} } rSup { size 8{2} } } over {2} } } {}

    where IaveIave size 12{I rSub { size 8{"ave"} } } {} is the average intensity in W/m2W/m2 size 12{"W/m" rSup { size 8{2} } } {}, and E0E0 size 12{E rSub { size 8{0} } } {} is the maximum electric field strength of a continuous sinusoidal wave.

  • This can also be expressed in terms of the maximum magnetic field strength B0B0 size 12{B rSub { size 8{0} } } {} as
    I ave = cB 0 2 2μ 0 I ave = cB 0 2 2μ 0 size 12{I rSub { size 8{"ave"} } = { { ital "cB" rSub { size 8{0} } rSup { size 8{2} } } over {2m rSub { size 8{0} } } } } {}

    and in terms of both electric and magnetic fields as

    Iave=E0B02μ0.Iave=E0B02μ0. size 12{I rSub { size 8{"ave"} } = { {E rSub { size 8{0} } B rSub { size 8{0} } } over {2m rSub { size 8{0} } } } } {}
  • The three expressions for IaveIave size 12{I rSub { size 8{"ave"} } } {} are all equivalent.
PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/college-physics-ap-courses/pages/1-connection-for-ap-r-courses
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/college-physics-ap-courses/pages/1-connection-for-ap-r-courses
Citation information

© Mar 3, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.