I know that electric current is a scalar quantity and hence it should not follow vector addition. But I have read that equal currents in opposite directions will cancel out each other so is this kind of addition not a kind of vector addition?... where while adding we are including their directions also. So please explain that even when current doesn't follow vector addition then why the currents which are equal and opposite in direction will cancel out each other?
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$\begingroup$ Because underlying the scalar approximation is that it is really a vectorial quantity beneath. It was never a scalar to begin with. There are a lot of such things in physics. $\endgroup$– naturallyInconsistentCommented Sep 30, 2023 at 17:43
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$\begingroup$ @naturallyinconsistent. Suggest you read Dale's answer carefully. $\endgroup$– Philip WoodCommented Oct 1, 2023 at 11:20
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$\begingroup$ @PhilipWood that answer is not in disagreement with mine. "vectorial quantity beneath" $\endgroup$– naturallyInconsistentCommented Oct 1, 2023 at 11:53
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1$\begingroup$ @naturallyinconsistent. "Beneath" is open to various interpretations. And why do you say "scalar approximation"? Why approximation? I like the precision of Dale's answer and took the liberty of drawing your attention to it. $\endgroup$– Philip WoodCommented Oct 1, 2023 at 12:07
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$\begingroup$ @PhilipWood and I also liked Dale's answer, except that considering it as a dot product of area and current density to claim that it is a scalar is kinda sad. I was referring to "current density J" as the "beneath", as should be clear to anybody who understands the theory; I was judging that for a student who is confused by current possibly being positive or negative, this would be far beyond their current know-how. I say it is a scalar approximation because I think it is better expressed as a 1D vector, because the directionality does matter. $\endgroup$– naturallyInconsistentCommented Oct 1, 2023 at 12:34
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In my bank account, withdrawals that are equal and opposite to deposits cancel out. Nevertheless, my account balance is not a vector. Mere cancellation of equal and opposite quantities does not imply that a quantity is a vector.
In electromagnetism charge density $\rho$ is a scalar. Current density is a vector $\vec J= \rho \vec v$. Current is the dot product of area and current density $I=\vec J \cdot \vec A$. So $I$ is a scalar. When people are thinking of current as a vector, they are actually thinking of current density $\vec J$. There is nothing wrong with thinking of current density, it is just a different quantity than current.
