By Yuval Neeman

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**Example text**

4 Effective moment calculation of force and torque 29 These equations indicate that the force and torque on a particle in an AC electric field will consist of two components: a constant (average) term and a time-varying term at twice the electric field frequency. For particles in the size range from 1 to 1000 jam, any motion due to the time-varying term is usually damped heavily by the viscosity of the suspension medium, so that only the time-average term is important. Nevertheless, double-frequency components are present and observable when using low-frequency electric fields in DEP experiments.

8b) where A and B are unknown coefficients to be determined using the boundary conditions. 8a) is the imposed uniform electrostatic field, while the second term is the induced dipole term due to the CjQ CjQ fluid: 8, Fig. 2 Dielectric sphere of radius R and permittivity e^ immersed in a dielectric liquid of permittivity €l and subjected to a uniform electric field of magnitude Eo. 2 Lossless dielectric particle in an electric field 11 particle. The boundary conditions are applied at r=R, the surface of the particle.

29) is replaced by 4ne[. When a lossless dielectric particle is subjected to an alternating electric field, the various moments induced in the particle can be positive (parallel to EQ) or negative (antiparallel to Eo), depending upon the relative magnitude of ex and e^. The addition of dissipation adds the further complication of a phase lag between the induced moment and the applied electric field. 30) may be rewritten to illuminate this important point. 32) is the same as the relaxation time identified in the transient analysis of Appendix D.

### Algebraic theory of particle physics; hadron dynamics in terms of unitary spin currents by Yuval Neeman

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