The various methods of observing the magnetic fields described at the beginning of this review gave the orientation of the magnetic field only. The only exceptions were the Zeeman effect observations, which are possible in some molecular clouds, and the combination of Pulsar rotation measure and dispersion measure. In general we must invoke the argument of equipartition to determine the magnetic field strength.
The energy spectrum of relativistic electrons is;
For equipartition of energy between magnetic field and relativistic electrons we have:
where E1 and E2 are the lower and upper limits of the energy spectrum (and correspond to the cutoff frequencies 1 and 2). The factor k is the ratio of the total energy of cosmic rays to the electron energy. The field strength B (in Gauss) is:
(e.g. see Moffat, 1973). In the above equation e is the volume emissivity (in erg sec-1 cm-3), A is given by;
with C = 1.057 × 1012 cgs units, a = (-1) / 2 is the spectral index. The emissivity e is also given by:
where I is the intensity and l the length (cm) of the source. The parameters k and 1(Hz) are taken often as 100 and 107 respectively (e.g. Sofue et al., 1986).
Although the fundamental question of the applicability of equipartition is often subject of heated discussions the concept as such has stood many attacks. It is a way an 'economical' concept, where the energy between two reservoirs is minimized.