  In classical electrodynamics all the measurable quantities can be derived
from the gauge invariant Faraday tensor $F_{\alpha\beta}$. Nevertheless, it is
often advantageous to work with gauge dependent variables. In [4],[2] and [8],
and in the present note too, the transformation of the vector potential in
Lorenz gauge to that in Coulomb gauge is considered. This transformation can be
done by applying a projection operator that extracts the transverse part of
spatial vectors. In many circumstances the proper projection operator is
replaced by a simplified transverse one. It is widely held that such a
replacement does not affect the result in the radiation zone. In this paper the
action of the proper and simplified transverse projections will be compared by
making use of specific examples of a moving point charge. It will be
demonstrated that whenever the interminable spatial motion of the source is
unbounded with respect to the reference frame of the observer the replacement
of the proper projection operator by the simplified transverse one yields, even
in the radiation zone, an erroneous result with error which is of the same
order as the proper Coulomb gauge vector potential itself.
