Are you being as pedantic as to ask for "through an area"? Because that's literally the defined relationship between current and charge.
I = q v . A
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.
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.
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.
It's also an especially bad idea to claim the time derivative of current is the the double derivative of charge, given that these are two very different notions of derivative.
To clarify, claiming current is the derivative of charge is like claiming the current of a river is the derivative of it's water level.
i(t) = dQ(t) / dt
"To clarify, claiming current is the derivative of charge is like claiming the current of a river is the derivative of it's water level." This statement is wrong, while water in some cases provides a decent analogy for electricity, this is not one of them.
Contravariant is simply saying that it's being stated and used as if it holds generally; but that's not the case.
This thread quickly dismissed 'through an area' as pedantic, but as far as I can tell that really is the crux of the debate: this simplified form of the equation only holds for scalar flux - viz. constant over and perpendicularly through a fixed flat surface.
In the generalised form, `I` is a function of the area at a point.
Note that the alternative would be that the wire somehow accumulates charge as it passes current, which clearly isn't happening.
As for your "wire" example, you're conveniently ignoring that a single (open-ended) wire isn't a closed circuit and as such there can be no current (and hence no accumulating charge). And if it's a closed circuit, then there are other elements in the circuit that consume or generate charge.
The claim is that current density J is different from the time rate of change of charge density dρ/dt.
That is not to say they are unrelated; they are related by the continuity equation,
dρ/dt = -∇·J.
I would actually go a step further than this and say that current is actually properly defined as the source of magnetic field. On the conventional definition of current, it is physically impossible for current to flow through a capacitor, but we speak of that all the time. So the True Current Density is just
J + ε dE/dt
That's actually (still, and somewhat) how the Ampere is defined. There are ongoing efforts to change this though.
I... prefer to avoid discussions like this one, but I thought you might appreciate this part :-).
Honestly I'm confused why it's turning out to be such a controversial point that there's a difference between a change in charge and the movement of charges.
Heck in their diagram they claim that the voltage across an inductor is the double derivative of its charge, but inductors can't even hold charge so it's unclear what they're trying to say. They also claim that the charge across a resistor is somehow related to the integral of the voltage across it, but again (ideal) resistors can't really hold charge. The only way to interpret this supposedly 'universal' periodic system is by interpreting charge and its derivatives in different ways depending on context, which isn't convincing in a supposedly universal system.
The problem is mainly that the criticism you are making is not great for pedagogy. What is being called “charge” is probably something like “disposition to accumulate charge” or so, in the same way that force is not actually mass times acceleration, but it's mass times a disposition to accelerate, so that you can do things like measure my weight-force even though I’m not falling through the floor.
The dispositional truth of the matter is fundamentally more cognitively complex to teach than the simple rule that you get when you say that everything does what it's disposed to do, and so everybody has memorized the version of the definitions that has no dispositions, and gets very confused when you point out that aspect of those definitions.
That's a good mathematical model of the behavior of the elements from a pedagogical perspective, though confusing for more advanced readers.
(This caught my attention because I had up to that point believed that electrical fields are always conservative, and this demonstrates that not to be true: an electron traveling around the loop in such a manner will eventually return to its starting point having done non-zero work)
What is dQ/t you may ask? It's the time derivative of charge. It's the change in charge over time, the rate of flow of charge.
I=Q/t
Current=Charge/Time
Amps=Coulombs/Second
I don't know how to make this clearer.
My electro mag skills are a little rusty, but I don’t think that’s the right analogy. You wouldn’t say that the speed of a runner is the derivative of their height, similarly when someone is running you wouldn’t try to say that their speed isn’t a derivative of their height, as their height is more or less constant “for the length of the run”.
Similarly, it isn’t the height of the runner, but the distance they’ve covered, it isn’t the depth of the river, but how much water has passed through, it isn’t the static charge of the wire, but how much charge has passed through.
The point is that this component alone ties flow to accumulation, whereas generally your other components (resistors=thin pipes, wires=thick pipes, batteries=Archimedes screws, inductors=turbines connected to flywheels) do not accumulate volumes of water inside of them. Flow needs to make sense even without accumulation due to flow-balance, just like force needs to make sense even in situations where velocity stays constant due to force-balance.
We can probably agree that the amount of charge passing through is different from the change to the total charge.
And in my opinion something like a 'periodic system' can't just treat both the same. It's especially bad to derive identities by taking the time derivative (or anti-derivative) on one side and switching between current and charge on the other.