According to Eq. 4.5, the force on a single dipole is (p ?? ??)E, so the net force on a dielectric object is [Here Eext 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 you must either add a compensating surface term, or (better) stick with Eext, which suffers no such discontinuity.] Use Eq. 4.69 to determine the force on a tiny sphere of radius R, composed of linear dielectric material of susceptibility Xe, which is situated a distance s from a fine wire carrying a uniform line charge λ.

F = [(P. V)Eext dt. (4.69)