I was referring to Kirchhoff's first law which only applies to circuits -- that example is enough to show that I=dQ/dt is wrong. I wasn't considering the cases

I was referring to Kirchhoff's first law which only applies to circuits -- that example is enough to show that I=dQ/dt is wrong. I wasn't considering the cases you're talking about (lightning etc.) because only one example is needed to prove an equation wrong. I could easily produce a single specific example where dQ/dt=0 but there is clearly a non-zero current present. And you can talk about charge in an area (sort of) if you multiply charge density by area; the result has units coulombs * metre^{-1}. I thought counting charge in a cross-section of wire was something people did, one way or another, even if the units aren't Coulombs but Coulombs*metre^{-1}. I could very easily have misunderstood something. With the clarifications above, I'm not clear on what though.