  We develop an approach to calculate the self-force on a charged particle held
in place in a curved spacetime, in which the particle is attached to a massless
string and the force is measured by the string's tension. The calculation is
based on the Weyl class of static and axially symmetric spacetimes, and the
presence of the string is manifested by a conical singularity; the tension is
proportional to the angular deficit. A remarkable and appealing aspect of this
approach is that the calculation of the self-force requires no renormalization
of the particle's field. This is in contract with traditional methods, which
incorporate a careful and elaborate subtraction of the singular part of the
field. We implement the approach in a number of different situations. First, we
examine the case of an electric charge in Schwarzschild spacetime, and recover
the classic Smith-Will force in addition to a purely gravitational contribution
to the self-force. Second, we turn to the case of electric and magnetic dipoles
in Schwarzschild spacetime, and correct expressions for the self-force
previously obtained in the literature. Third, we replace the electric charge by
a scalar charge, and recover Wiseman's no-force result, which we generalize to
a scalar dipole. And fourth, we calculate the force exerted on extended bodies
such as Schwarzschild black holes and Janis-Newman-Winicour objects, which
describe scalarized naked singularities.
