  A problem of self-energy and self-force for a charged point-like particle in
a higher dimensional homogeneous gravitational field is considered. We study
two cases, when a particle has usual electric charge and a case when it has a
scalar charge, which is a source of a scalar massless minimally coupled field.
We assume that a particle is at rest in the gravitational field, so that its
motion is not geodesic and it has an acceleration a directed from the horizon.
The self-energy of a point charge is divergent and the strength of the
divergence grows with the number of dimensions. In order to obtain a finite
contribution to the self- energy we use a covariant regularization method which
is a modification of the proper time cut-off and other covariant
regularizations. We analyze a relation between the self-energy and self-force
and obtain explicit expressions for the self-forces for the electric and scalar
charge in the spacetimes with the number of dimensions up to eight. General
expressions for the case of higher dimensions are also obtained. We discuss
special logarithmic factors ln(a), which are present both in the self-energy
and self-force in odd dimensions. Finally, we compare the obtained results with
the earlier known results both for the homogeneous gravitational field and for
particles near black holes.
