It is shown that local perturbations in nonuniform unmagnetized plasmas can give rise to linearly growing electromagnetic fields on both electron and ion time scales. The plasma vorticity and compressibility couple due to density inhomogeneity, giving rise to instabilities with partially transverse and partially longitudinal characteristics in electron plasmas for omega(pe)</=omega and in electron-ion plasmas for omega(pe)</=omega as well as omega<<omega(pe) (where omega(pe) is the electron plasma oscillation frequency). It is reconfirmed that the pure transverse modes due to the thermoelectric term do not appear in nonuniform unmagnetized electron plasmas. Furthermore, it has been found that the thermal fluctuations in a collisionless inhomogeneous electron plasma happen on a slower time scale of the order of 1/c(s)k (where c(s) is the ion sound speed). It seems that in the presence of a steep density gradient the ion acoustic wave becomes electromagnetic. Since the curl of electric field becomes nonvanishing in the presence of a density gradient, any nonuniform plasma can have magnetic field fluctuations in the limit omega<<omega(pe) as well. It is suggested that in the limit omega<<omega(pe) the ion dynamics becomes important and a pure electron plasma model to study magnetic field instability is not useful. The estimate for the magnitude of slowly and rapidly growing magnetic fields using the electron-ion plasma model in a special range of parameters turns out to be of the order of megagauss, in good agreement with the experimental observations.