  In this paper, we investigate the impact of the electromagnetic scattering
caused by other objects in nonfree space on the time averaged force exerted
upon a Rayleigh particle, which is conventionally referred to as the backaction
effect. We show that backaction modifies the gradient force, radiation
pressure, and spin curl force exerted upon Rayleigh particles, and gives rise
to an additional force term which stems from the gradient of the backaction
field in nonfree space. As a numerical example, we look into the trapping of a
dielectric nanoparticle at the center of curvature of a spherical mirror, and
study how it is affected by the backaction effect. We show that backaction can
enhance the force exerted upon the particle, reshape the trapping potential,
and shift the equilibrium position of the particle.
