A generalization of the dipolar force

The static dipolar force is generalized to time-dependent classical distributions of dipoles and electromagnetic fields. This force may exhibit a remarkable resonance character for induced dipoles, related to the pole structure of the polarizabilities. The resonance phenomenon is illustrated for two macroscopic polarizable bodies, with mutually induced polarizations, using the well-known Lorentz-Drude model for the dielectric response with optical dispersion and a characteristic (resonance) frequency. Specifically, the calculations are performed for distances much longer than the dimension of the bodies (“point-like” bodies), but shorter than the characteristic wavelength (sub-wavelength, stationary, near-field regime). The polarizations are induced via a localized external field acting upon only one body. The force is practically vanishing for distinct substances and acquires a non-vanishing value for identical substances. It falls off as the 7-th power of the distance, being reminiscent of the van der Waals-London force. The conditions of validity of this resonance phenomenon are emphasized. Particular cases corresponding to independent external fields or two isolated, interacting bodies (closed system) are also analyzed, with similar conclusions regarding the resonance character of the force.