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 combine into the free space wave equation?

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

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

    Answer: ______________

  4. What is E divided by B in a plane wave?

    • Zero
    • c
    • It varies wildly

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

    • At random angles
    • Parallel to each other and to travel
    • Perpendicular to each other and to travel

  6. Maxwell theory predicts a wave speed that happens to equal the measured speed of light.

    Circle one:   True   False

  7. Why does the numerical match stop looking like coincidence?

    • It falls out of two lab measured constants with no extra tuning
    • Light was assumed first
    • Constants were tuned to fit

  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 need a medium
    • Radio waves are longitudinal
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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. 1 · Wavelength is c over frequency: 300 million over 300 million is 1.
  4. c · At every instant the electric part exceeds the magnetic part by exactly c.
  5. Perpendicular to each other and to travel · The solution oscillates transversely with E over B equal to c everywhere.
  6. True · Evaluating 1 over root mu0 epsilon0 gives the light speed, so light is electromagnetic.
  7. It falls out of two lab measured constants with no extra tuning · The speed drops out of Faraday plus Ampere Maxwell with measured constants only.
  8. Bands differ only in frequency; all travel at c · One equation rules the spectrum; frequency changes while c stays fixed.
Worksheet · LightMySky