According to Eq. 4.5, the force on a single dipole is (p · ∇)E, so the net force on a dielectric object is
F = (p · ∇)E (4.5)
F =\int( P \cdot \nabla) E _{ ext } d \tau (4.69)
[Here E _{\text {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 _{\text {ext }} Use Eq. 4.69 to determine the force on a tiny sphere, of radius R, composed of linear dielectric material of susceptibility \chi_{e} , which is situated a distance s from a fine wire carrying a uniform line charge λ.