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It is not necessary to place this burden on Kirchhof's loop law. It is
valid even for non ideal capacitors and inductors; eg, it even works for
an open circuit - a highly fringing capacitor situation.
Stating K's current law in the familiar form: "In steady state, the net
current into any point is zero", this is simply a statement of charge
conservation and applies even to volume current distributions. It is
inapplicable only during the transient startup when (mostly) surface charge
distributions are being established to drive the steady state current.