  The effective equations of motion for a point charged particle taking account
of radiation reaction are considered in various space-time dimensions. The
divergencies steaming from the pointness of the particle are studied and the
effective renormalization procedure is proposed encompassing uniformly the
cases of all even dimensions. It is shown that in any dimension the classical
electrodynamics is a renormalizable theory if not multiplicatively beyond d=4.
For the cases of three and six dimensions the covariant analogs of the
Lorentz-Dirac equation are explicitly derived.
