If is a real constant, the continuity equation is satisfied by the charge and current distributions. The given j represents current flowing in toward

If α is a real constant, the continuity equation is satisfied by the charge and current distributions. The given j represents current flowing in toward the origin of coordinates. But the given ρ is translationally invariant, i.e., it does not distinguish any origin of coordinates. Resolve this apparent conflict.

p(r, t) = at j(r, t) = - = r. 3