In this study, motions of a charged rod-like particle under the action of an applied electric field through a capillary are examined when the characteristic length scale($1_c$) of the particle is much smaller than the capillary radius. Electro-osmotic velocity in the absence of the particle is determined assuming that the electric double layer adjacent to the capillary wall is very thin compared with the capillary radius. In calculating the electrophoretic velocity of a single particle, we consider two asymptotic limits based on the thickness($\lambda_D$) of electric double layer adjacent to the particle surface relative to the particle radus(b). When $b/\lambda_D \gg 1$, electrophoretic mobility is shown to be isotropic and independent of the particle orientation relative to the direction of the electric field, but, depends on the $\zeta$-potential of the particle($\zeta_p$). On the other hand, when $b_C/\lambda_D \gg 1$, the mobility is anisotropic and a function of the particle orientation and net charge($Q_p$) contained in the particle. The relationships between $\zeta_p$ and $Q_p$ for the two asymptotic cases are determined employing the fundamental singularity solutions for the Debey-Huckel equation. The dipole moment of a charged particle is also calculated utilizing the fundamental solution of the Laplace equation for the disturbed electric field induced by an ambient electric field. Finally the distribution of the particle orientation and the corresponding birefringence are calculated using the Smoluchowski equation when the particle is immersed in the uniform electroosmotic flow at the steady state.
