Electromagnetic waves

The previous page showed the generation of a pulse of electromagnetic radiation from an isolated electric charge. In reality, most objects have equal amounts of positive and negative charge, though small separations of these charges will produce electric dipole fields like the one pictured below:

The balance of charges cancels out the leading 1/r² component of the static field, leaving a dipole field that scales as s/r³, where s is the charge separation. However, changes in the charge configurations still produce propagating transverse fields that scale as a/c²r, as before. In particular, if the charges accelerate in a cyclical or continuous manner, the resulting radiative field is a stream of electromagnetic waves, as shown below.

Electromagnetic waves have a characteristic wavelength λ that is c times the characteristic frequency f of the underlying charge motion. The strength of the wave therefore scales as:

There is no known absolute limit on the range of electromagnetic wavelengths, but most familiar forms of electromagnetic waves range from metres (radio) down to femtometres (gamma rays).


Fundamentally, electromagnetic waves can be as short as a few attometres (10-18m), below which electromagnetism per se no longer exists (it is replaced by a hybrid field combining electromagnetic and weak nuclear forces). In principle electromagnetic waves can be as long as the size of the Universe (a few ×1026m), but will not propagate very far through the interstellar medium—and remember, you only start to see propagating wave-like behaviour when you're several wavelengths from the source (closer in the 1/r³ near-zone field dominates over the 1/r radiative field).

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Sections marked with provide optional additional mathematical detail.

Start: Gravitational waves demystified
Analogy: Electromagnetic fields
Electromagnetic field of an accelerated charge
  Derivation of the radiative electromagnetic field
Electromagnetic waves
Gravitational tidal field
  Equivalence between dipole and tidal field
Gravitaional waves
  Formulae and details
Differences between gravitational and electromagnetic radiation
Gravitational wave spectrum