  Electromagnetic fields of an accelerated charge are derived from the first
principles using Coulomb's law and the relativistic transformations. The
electric and magnetic fields are derived first for an instantaneous rest frame
of the accelerated charge, without making explicit use of Gauss's law, an
approach different from that available in the literature. Thereafter we
calculate the electromagnetic fields for an accelerated charge having a
non-relativistic motion. The expressions for these fields, supposedly accurate
only to a first order in velocity $\beta$, surprisingly yield all terms exactly
for the acceleration fields, only missing a factor $1-\beta^2$ in the velocity
fields. The derivation explicitly shows the genesis of various terms in the
field expressions, when expressed with respect to the time retarded position of
the charge. A straightforward transformation from the instantaneous rest frame,
using relativistic Doppler factors, yields expressions of the electromagnetic
fields for the charge moving with an arbitrary velocity. The field expressions
are derived without using Li\'{e}nard-Wiechert potentials, thereby avoiding
evaluation of any spatial or temporal derivatives of these potentials at the
retarded time.
