  We propose a systematic and constructive way to determine the
exchange-correlation potentials of density-functional theories including vector
potentials. The approach does not rely on energy or action functionals. Instead
it is based on equations of motion of current quantities (force balance
equations) and is feasible both in the ground-state and the time-dependent
setting. This avoids, besides differentiability and causality issues, the
optimized-effective-potential procedure of orbital-dependent functionals. We
provide straightforward exchange-type approximations for different density
functional theories that for a homogeneous system and no external vector
potential reduce to the exchange-only local-density and Slater X$\alpha$
approximations.
