  We consider current-induced domain wall motion and, the reciprocal process,
moving domain wall-induced current. The associated Onsager coefficients are
expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the
effective Gilbert damping coefficient $\alpha_w$ and the effective out-of-plane
spin transfer torque parameter $\beta_w$ are dominated by spin-orbit
interaction in combination with scattering off the domain wall, and not
scattering off extrinsic impurities. Numerical calculations give $\alpha_w \sim
0.01$ and $\beta_w \sim 1$ in dirty (Ga,Mn)As. The extraordinary large
$\beta_w$ parameter allows experimental detection of current or voltage induced
by domain wall motion in (Ga,Mn)As.
