  We examine the electromagnetic fields in the neighbourhood of a "point
charge" in arbitrary motion and thereby determine the Poynting flux across a
spherical surface of vanishingly small radius surrounding the charge. We show
that the radiative power losses from a point charge turn out to be proportional
to the scalar product of the instantaneous velocity and the first
time-derivative of the acceleration of the charge. This may seem to be in
discordance with the familiar Larmor's formula where the instantaneous power
radiated from a charge is proportional to the square of acceleration. However,
it seems that the root cause of the discrepancy actually lies in the Larmor's
formula which is derived using the acceleration fields but without a due
consideration for the Poynting flux associated with the velocity-dependent
self-fields "co-moving" with the charge. Further, while deriving Larmor's
formula one equates the Poynting flux through a surface at some later time to
the radiation loss by the enclosed charge at the retarded time. Poynting's
theorem, on the other hand, relates the outgoing radiation flux from a closed
surface to the rate of energy decrease within the enclosed volume, all
calculated {\em for the same given instant} only. Here we explicitly show the
absence of any Poynting flux in the neighbourhood of an instantly stationary
point charge, implying no radiative losses from such a charge, which is in
complete conformity with energy conservation. We further show how Larmor's
formula is still able to serve our purpose in vast majority of cases. It is
further shown that Larmor's formula in general violates momentum conservation
and in the case of synchrotron radiation leads to a potentially wrong
conclusion about the pitch angle changes of the radiating charges, and that
only the radiation reaction formula yields a correct result, consistent with
the special relativity.
