“Hidden” Momentum of a Steady Current Distribution in a System at “Rest”

Can a steady current distribution contain a nonzero total mechanical momentum, often called hidden momentum [1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13], due to the motion of the charge carriers? A steady current distribution Jsteady(r) is one with no time dependence. If the current density Jsteady flows in conductors, they must be at rest. The divergence of a steady current distribution has no time dependence, so the electric charge density ρsteady(r, t) could have at most a linear time dependence, according to the continuity equation ∂ρ ∂t = −∇ · J. (1)