Physic Labs

Electrodynamics

Electromagnetic radiation from a dipole

Observe the field geometry of an oscillating dipole and the angular radiation pattern. Check qualitatively that radiated power follows sin⁡2θ\sin^2\theta and scales as ω4p02\omega^4 p_0^2, per ⟨dP/dΩ⟩=μ0ω4p02sin⁡2θ/(32π2c)\langle dP/d\Omega\rangle = \mu_0\omega^4 p_0^2\sin^2\theta/(32\pi^2 c).

Advanced

Equipment

  • Two interactive models (Model A / Model B) projecting dipole field and its consequences
  • Sliders for amplitude/source and wavelength/scale
  • Sliders for frequency/velocity and viewing angle
  • Readout of quantities versus parameters

Procedure

  1. Survey the angular radiation pattern

    In Model A, drag the viewing-angle slider from 0 to 90°. The field is strongest perpendicular to the dipole axis and vanishes along it — the sin⁡2θ\sin^2\theta law: no radiation along the dipole axis.

  2. Vary frequency and source amplitude

    Keep the viewing angle at maximum radiation, then raise the frequency slider: read the relative power and test the ω4\omega^4 dependence — doubling frequency raises radiated power about 16-fold. Then vary the source amplitude to check the p02p_0^2 scaling.

  3. Compare the two models

    Switch to Model B to see the complementary consequence (far radiation zone versus near field, or wave polarization). Change the wavelength/scale and note: radiation fields appear only when charge accelerates; predict what happens as frequency tends to 0 before checking.

Simulation

Experiment history

In 1865 James Clerk Maxwell completed the electromagnetic field equations and deduced electromagnetic waves traveling at the speed of light. Oliver Heaviside and J.J. Thomson later analyzed the field of an accelerated charge; Joseph Larmor in 1897 gave the dipole radiation formula that bears his name. Heinrich Hertz confirmed the prediction experimentally in 1886–1888: a dipole oscillator in his laboratory emitted radio waves he detected with a wire loop several meters away. Hertz's experiments both vindicated Maxwell's theory and opened the way to Marconi's wireless telegraphy a decade later.

Related physicists

James Clerk MaxwellMichael FaradayHeinrich Rudolf Hertz

Related library topics

Electromagnetic radiation from a dipole