The hydrodynamic theory of slender bodies is used to model electrophor
etic motion of a slender particle having a charge (zeta potential) tha
t Varies with position along its length. The theory is limited to syst
ems where the Debye screening length of the solution is much less than
the typical cross-sectional dimension of the particle. A stokeslet re
presentation of the hydrodynamic force is combined with the Lorentz re
ciprocal theorem for Stokes flow to develop a set of linear equations
which must be solved for the components of the translational and angul
ar velocities of the particle. Sample calculations are presented for t
he electrophoretic motion of straight spheroids and cylinders and a to
rus in a uniform electric field. The theory is also applied to a strai
ght uniformly charged particle in a spatially varying electric field.
The uniformly charged particle rotates into alignment with the princip
al axes of del E(infinity); we suggest that such alignment can lead to
electrophoretic transport of particles through a small aperture in an
otherwise impermeable wall. The theory developed here is more general
than just for electrophoresis, since the final result is expressed in
terms of a general 'slip velocity' at the surface of the particle. Th
us, the results are applicable to diffusiophoresis of slender particle
s if the proper slip-velocity coefficient is used.