  In this letter, we discuss generation of magnetic field from cosmological
perturbations. We consider the evolution of three component plasma (electron,
proton and photon) evaluating the collision term between elecrons and photons
up to the second order. The collision term is shown to induce electric current,
which then generate magnetic field. There are three contributions, two of which
can be evaluated from the first-order quantities, while the other one is fluid
vorticity which is purely second order. We estimate the magnitudes of the
former contributions and shows that the amplitude of the produced magnetic
field is about $\sim 10^{-19} {\rm G}$ at 10Mpc comoving scale at the
recombination. Compared to astrophysical and inflationary mechanisms for
seed-field generation, our study suffers from much less ambiguities concerning
unknown physics and/or processes.
