I've always heard that maxwell's equations contains essentially all of eletromagnetic theory. However, there's one thing I'm having trouble doing for myself: deriving the magnestatics equations from the maxwell's equations. Of course: it's clear that if you put ∂[t]E=∂[t]B=0 (partial derivative in relation to time), you get the magnostatic equations. What I'm wondering is: can we get that ∂[t]E=∂[t]B=0 by assuming steady currents (∂[t]ρ=0) and using the maxwell's equations? The motivation for this question is that the condition for being in magnostatics is steady currents, so the Maxwell's equations should reflect: (Steady currents)⇒(Magnostatics equations). I believe I've proved the other direction of the implication, but not the one above, that is the most interesting for me: it would mean that, given the maxwell's equation, we can never have non-static situations coming from a "static" current distribution. Please contribute.