4.5. Magnetic diffusivity equation From Eqs. (4.22) and (4.23)
the Ohmic electric field can be expressed as which inserted into
Eq. (4.19) leads to the magnetic diffusivity equation The first
term of Eq. (4.29) is the dynamo term. The second term of Eq.
(4.29) is the magnetic diffusivity term whose effect is to
dissipate the magnetic field. By comparing the left and the
right hand side of Eq. (4.29), the typical time scale of
resistive phenomena is where L is the typical length scale of
the magnetic field. In a non-relativistic plasma the
conductivity goes typically as T3/2 . In the case of planets,
like the earth, one can wonder why a sizable magnetic field can
still be present. One of the theories is that the dynamo term
regenerates continuously the magnetic field which is dissipated
by the diffusivity term . In the case of the galactic disk the
value of the conductivity (13) is given by 7 × 10-7 Hz. Thus,
for L kpc t 109(L / kpc)2 sec. In Eq. (4.30) the typical time of
resistive phenomena has been introduc