When deriving formulae for RC, RLC, LC circuits, etc., we typically assume that current is steady. Griffiths gave a good explanation of why this assumption is reasonable (he states essentially that nonsteady current forces itself to become steady through electric forces). However, it seems that we also assume a non changing magnetic field when we apply “Kirchhoff's loop rule.” But current of course varies, so the magnetic field changes, and thus the electric field has some curl. So I’m not sure why this assumption is justified. Is the curl of the field negligible, and does the rule hold true practically? If so, why? Edit: I’ve realized that we’re essentially assuming the circuit itself has no inductance; all inductance comes from an inductor that could be present. In addition, the induced forces act only within the inductor itself (so that the voltage drop across the inductor is the emf). Am I correct in this?
Inductance is a property of the conducting wire just like capacitance is a property of a conductor. For a general wire which may be stretched out very long, the actual area it encloses in the loop is so large that inductance is negligible. When we create these circuits, we essentially make this assumption but in practical scenarios, this does somewhat have to be accounted for.