  The impact of the strongly attractive electromagnetic field of heavy nuclei
on electrons in quasi-elastic (e,e') scattering is often accounted for by the
effective momentum approximation. This method is a plane wave Born
approximation which takes the twofold effect of the attractive nucleus on
initial and final state electrons into account, namely the modification of the
electron momentum in the vicinity of the nucleus, and the focusing of electrons
towards the nuclear region leading to an enhancement of the corresponding wave
function amplitudes. The focusing effect due to the attractive Coulomb field of
a homogeneously charged sphere on a classical ensemble of charged particles
incident on the field is calculated in the highly relativistic limit and
compared to results obtained from exact solutions of the Dirac equation. The
result is relevant for the theoretical foundation of the effective momentum
approximation and describes the high energy behavior of the amplitude of
continuum Dirac waves in the potential of a homogeneously charged sphere. Our
findings indicate that the effective momentum approximation is a useful
approximation for the calculation of Coulomb corrections in (e,e') scattering
off heavy nuclei for sufficiently high electron energies and momentum transfer.
