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 discordant with the familiar Larmor 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 Larmor’s formula, which is
derived using the acceleration fields but without 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 t…