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).

Gamma ray burst: thermal radiation from a relativistic shock wave passing through a plasma. X-ray image of the Sun: nonthermal radiation (bremmstrahlung) from plasma in the Sun's magnetic field. Ordinary galaxy in visible light: thermal radiation at stellar surface temperatures (a few thousand kelvins). Map of fluctuations in cosmic microwave background: thermal radiation at background temperature (3 kelvins). Radio jet from an active galaxy: nonthermal (synchrotron) radiation from jet crossing magnetic fields.

• Short wavevelengths (X-rays, gamma rays) are produced by nuclear energy transitions, or thermal radiation from matter at nuclear energies, or by high-energy nonthermal particle acceleration (e.g. from dense plasmas confined by strong electromagnetic fields). Nuclei start to dissociate under radiation in the sub-picometre range, and individual nucleons have rest energies equivalent to femtometre-wavelength photons, which broadly sets the upper end of photon energies that typically arise from matter in the present-day Universe.
• Mid wavelengths (ultaviolet through infrared) are mostly produced by atomic energy transitions, and by thermal radiation from "ordinary" (atomic) matter. A photon wavelength of around 10nm or less is sufficient to break most molecular bonds and ionize atoms, and sets the short end of the ultraviolet band. At the other end, the lowest temperatures normally found in nature are around 3 kelvins, emitting thermal radiation at wavelengths around 1mm: this is often considered to be at the short end of the microwave band.
• Long wavelengths (microwaves and radio waves) are produced by non-thermal large-scale coherent electromagnetic processes, such as unshielded electrical equipment, or from diffuse plasmas accelerated by magnetic fields. The Earth's ionosphere blocks radio waves longer than about 10m, while interstellar plasma blocks waves longer than about 10km, which sets the long-wavelength limit of radio astronomy.

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).

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