  We obtain static gauge field configurations for SU(2) Yang-Mills gauge theory
in the absence of chromo-magnetic field. We also present a systematic way to
obtain such configurations for SU(3) and SU(4) YM gauge theories by realizing
their Lie algebras in terms of SU(2). Generalization of our method to SU(N)
gauge theory with N>2 is straight forward. The gauge fields thus obtained are
complex. We investigated the issue of uniform as well as real chromo-electric
field with these configurations. Furthermore, we investigated the possible
class of vacuum solutions for the gauge fields and found that they are gauge
inequivalent to the usual vacuum configuration $A^a_{\mu}=0$.
