According to Eq. 4.5, the force on a single dipole is (p · ∇)E, so the net force on a di...

According to Eq. 4.5, the force on a single dipole is (p · ∇)E, so the net force on a dielectric object is

Equation 4.69

[Here E_ext is the field of everything except the dielectric. You might assume that it wouldn’t matter if you used the total field; after all, the dielectric can’t exert a force on itself. However, because the field of the dielectric is discontinuous at the location of any bound surface charge, the derivative introduces a spurious delta function, and it is safest to stick with E_ext.] Use Eq. 4.69 to determine the force on a tiny sphere, of radius R, composed of linear dielectric material of susceptibility χ_e, which is situated a distance s from a fine wire carrying a uniform line charge λ.

Reference equation 4.5