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Comment by jkabrg | Hacker News Reader

The amount of charge in an area stays constant because of Kirckhoff's laws, so dQ/dt=0 always. Wouldn't a better definition be:

  I = q v . A

where q is charge density. A is an area (actually, a normal vector to some flat cross-section, with magnitude equal to size of area), and v is velocity of the charged particles. I'm using the dot product.

If we check the units: (coulombs * metres^{-3}) * (metres * seconds ^{-1}) * metres^{2} = coulombs / seconds

By the way, I fudged the above to make "charge density" have units $coulombs * metres^{-3}$. I'm not the best person at physics.

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> The amount of charge in an area stays constant because of Kirckhoff's laws, so dQ/dt=0 always.

Eh what? No. There seems to be some huge misunderstanding here. First of all, charge is not "in an area". It's in volumes, and flows through areas. And the amount of charge in a volume is absolutely not constant (in general). If you think it is, then please explain what happens when you rub a balloon on your hair, or why/when lightning strikes.

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.

Okay, that's much more nuanced than "dQ/dt = 0 always".

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