  We study the self force acting on static electric or scalar charges inside or
outside a spherical, massive, thin shell. The regularization of the self force
is done using the recently-proposed Mode Sum Regularization Prescription. In
all cases the self force acting on the charge is repulsive. We find that in the
scalar case the force is quadratic in the mass of the shell, and is a second
post-Newtonian effect. For the electric case the force is linear in the shell's
mass, and is a first post-Newtonian effect. When the charge is outside the
shell our results correct the known zero self force in the scalar case or the
known repulsive, inverse-cubic force law in the electric case, for the finite
size of the shell. When the charge is near the center of the shell the charge
undergoes harmonic oscillations.
