For a plane wave travelling in free space we know from Maxwell's equations that: Z= E/H=√μ0/ε0 = 377Ω The meaning of the wave impedance is that if we have an electric field oscillating with amplitude E0 in a medium (in this case the vacuum) a magnetic field will be induced with amplitude E0/Z. Now this impedance is frequency independent so my doubt is what happens when ω=0? In a static situation I can create an electrostatic field without having a magnetic field at all. But the intrinsic impedance tells me that a static(?) magnetic field will be induced anyway. How's that possible? Also in metals the wave impedance becomes: √jωμ/σ+jωε So for ω=0 the impedance goes to zero as well, that means that if a static electric field existed in the metal there should be an infinite magnetic field. That can't happen and infact no static electric field can exist in a metal in a electrostatic situation (assuming that the metal is immersed in a static electric field). But if we apply a constant voltage across the metal we can force a static electric field inside the metal. There will be a finite current if σ is finite with an associated finite static magnetic field inside the conductor. But the impedance formula tells me that even if σ isn't infinite (ideal metal), wave impedance should be zero anyway in DC but that isn't possible as it would mean an infinite magnetic field. So why doesn't the formula apply anymore? Maybe because to the applied voltage corresponds a superficial net density of charges on the metal that we must take care of in the Maxwell equation so that expression for the impedance is not correct anymore?