  We present (asymptotically) exact expressions for the mobility and
electrophoretic mobility of a weakly charged spherical particle in an $1:1$
electrolyte solution. This is done by analytically solving the electro and
hydrodynamic equations governing the electric potential and fluid flow with
respect to an electric field and a nonelectric force. The resulting formulae
are cumbersome, but fully explicit and trivial for computation. In the case of
a very small particle compared to the Debye screening length ($R \ll r_D$) our
results reproduce proper limits of the classical Debye and Onsager theories,
while in the case of a very large particle ($R \gg r_D$) we recover, both, the
non-monotonous charge dependence discovered by Levich (1958) as well as the
scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the
previously unknown coefficients and corrections. The main applicability
condition of our solution is charge smallness in the sense that screening
remains linear.
