Physic Labs

Electrodynamics

Electromagnetic waves in vacuum

Observe a plane electromagnetic wave in vacuum: E\mathbf E, B\mathbf B, and the propagation vector k\mathbf k are mutually perpendicular, traveling at c=λfc=\lambda f. Adjust amplitude, wavelength, and frequency, then check the Poynting vector S=E×B/μ0\mathbf S=\mathbf E\times\mathbf B/\mu_0.

Undergraduate

Equipment

  • Virtual plane wave with E (orange) and B (teal) vectors on a 3D canvas
  • Amplitude, wavelength, frequency, and view-angle sliders
  • Model A/B buttons and Pause
  • Readouts for $\mathbf E\perp\mathbf B\perp\mathbf k$ and $\mathbf S=\mathbf E\times\mathbf B/\mu_0$

Procedure

  1. Check the transverse character

    In figure 1, drag the view-angle slider to rotate the plane wave: E oscillates along one axis, B along a perpendicular axis, both transverse to propagation — confirm the readout 'E ⟂ B ⟂ k'.

  2. Verify $c=\lambda f$

    Read wavelength λ and frequency f on the sliders: the product λf must give c≈3,0×108c\approx3{,}0\times10^8 m/s. Double f and watch λ halve to keep the speed constant — electromagnetic waves do not disperse in vacuum.

  3. Read the Poynting energy flow

    Switch to figure 2 (or model B): the Poynting vector S=E×B/μ0\mathbf S=\mathbf E\times\mathbf B/\mu_0 points along propagation. Rotate the view and verify the right-hand rule E×B always points along k.

Simulation

Experiment history

James Clerk Maxwell unified electricity and magnetism in the equations published in 1865; solving them in vacuum yields a wave equation with speed 1/μ0ε01/\sqrt{\mu_0\varepsilon_0} — equal to the measured speed of light, so Maxwell concluded that light is an electromagnetic wave. The radio waves predicted by the theory were generated and detected by Heinrich Hertz in 1887–1888: sparks in a transmitter excited oscillations in a receiving loop meters away. The energy-flow vector is named for John Henry Poynting, who derived it in 1884 while analyzing energy transport in the electromagnetic field.

Related physicists

James Clerk MaxwellMichael FaradayHeinrich Rudolf Hertz

Related library topics

Electromagnetic waves in vacuum