Plane Electromagnetic Waves from Maxwell's Equations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Light from two equations

Science · Electricity & Magnetism · ages 21-22
Name ______________________   Date ____________

  1. What is the wave speed in terms of the constants?

    • mu0 times epsilon0
    • 1 over root mu0 epsilon0
    • mu0 over epsilon0

  2. Which two laws are substituted into each other to give the free space wave equation?

    • Faraday and Ampere Maxwell
    • Gauss electric and Gauss magnetic
    • Ohm and Coulomb

  3. A radio wave has frequency 150 million Hz. Using c equals 300 million m/s, what is its wavelength in metres?

    Answer: ______________

  4. In a plane wave in empty space, what is E divided by B at any point and instant?

    • 1 over c
    • c
    • c squared

  5. How are E and B arranged in a plane wave?

    • At random angles that change every cycle
    • Parallel to each other, both along the travel direction
    • Perpendicular to each other and to travel

  6. Putting the lab values of mu0 and epsilon0 into 1 over root mu0 epsilon0 gives about 300 million m/s, the measured speed of light.

    Circle one:   True   False

  7. Why is the match between 1 over root mu0 epsilon0 and the speed of light strong evidence that light is electromagnetic?

    • The constants were measured with charges and currents, not light
    • Maxwell chose the constants after the fact so they would fit light
    • The derivation assumed the speed of light at its first step

  8. A student claims radio and gamma differ in wave speed in vacuum. What is wrong?

    • Bands differ only in frequency; all travel at c
    • Gamma rays move slower because each carries more energy
    • Radio waves are longitudinal, so they move at another speed
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Light from two equations W1-mt_27tbaYcxCM-s1

  1. 1 over root mu0 epsilon0 · The substitution produces 1 over mu0 epsilon0 as the speed squared.
  2. Faraday and Ampere Maxwell · Cross substitution between the two curl equations produces the wave equation.
  3. 2 · Wavelength is c divided by frequency: 300 million over 150 million is 2.
  4. c · E and B rise and fall in step, and E divided by B equals c everywhere.
  5. Perpendicular to each other and to travel · The solution oscillates transversely with E over B equal to c everywhere.
  6. True · The wave speed predicted from the two measured constants equals the measured speed of light, which is why light is an electromagnetic wave.
  7. The constants were measured with charges and currents, not light · mu0 and epsilon0 come from electric and magnetic measurements. Light never enters, yet the speed of light comes out.
  8. Bands differ only in frequency; all travel at c · One wave equation covers the whole spectrum; frequency changes while c stays fixed.
Worksheet · LightMySky