### 5. THE MAGNETIC FIELD STRENGTH

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;

N(E) dE = N_{0}
E^{-} dE .
For equipartition of energy between magnetic field and
relativistic electrons we have:

B^{2} / B = k
_{E2}^{E1} E N(E) dE
,
where E_{1} and E_{2} 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:

B = 2.3(*k* A *e*)^{2/7}
(e.g. see
Moffat, 1973).
In the above equation *e* is the volume
emissivity (in erg sec^{-1} cm^{-3}), A is given by;

A = C (*a* + 1) / (*a* + 1/2) (V_{2}^{a+1/2} -
V_{1}^{a+1/2}) / (V_{2}^{a+1} -
V_{1}^{a+1/2})
with C = 1.057 × 10^{12} cgs units, *a* =
(-1) / 2 is the spectral index.
The emissivity *e* is also given by:

*e* = 4 / l
_{V1}^{V2}
I_{} dv
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 10^{7} 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.