  We investigate seed magnetic field generation in the early universe by
radiation force of first stars. In the previous study with steady assumption,
large amplitudes(10^{-15} G for first stars, 10^{-11}G for QSOs) are predicted.
In this study, we formulate this issue in unsteady framework. Then, we consider
a specific model of magnetic field generation around a very massive first star.
Consequently, 1) we find steady assumption is not valid in realistic situation,
and 2) obtain much smaller magnetic field strength than predicted by Langer et
al. (2003). In addition, we find momentum transfer process during
photoionization is more important than Thomson scattering. The resultant
magnetic flux density around the first star is < 10^{-19}G. These seed magnetic
field will not affect subsequent star formation in the neighbor of first stars.
