  In this paper, we revisit in detail the effects of primordial magnetic fields
on big bang nucleosynthesis (BBN) including a discussion of the magnetic field
geometry and the anomalous magnetic moment. The presence of magnetic fields
affects BBN by (1) increasing the weak reaction rates; (2) increasing the
electron density due to changes to the electron phase space; and (3) by
increasing the expansion rate of the universe, due both to the magnetic field
energy density and to the modified electron energy density. Of the effects
considered, the increase in the expansion rate due to the magnetic field energy
is the most significant for the interests of BBN. The allowed magnetic field
intensity at the end of nucleosynthesis (0.01 MeV) is about $2 \times 10^{9}$G
and corresponds to an upper limit on the magnetic field energy density of about
28\% of the neutrino energy density ($\rho_B \le 0.28 \rho_\nu$).
