Conceptual Understanding in Introductory Physics XIX: Why is current not a vector?

This is a very quick post addressing a frequently asked conceptual question. Maybe it my heightened awareness, but I’ve also seen this question asked a lot on various physics Q&A sites lately. It’s a question that gets to the heart of how vectors are often defined, loosely and incorrectly, in introductory physics. Here’s the question.

Given that current (either electron current or conventional current) has both magnitude and direction, why is it not, and indeed cannot be, defined as a vector quantity whereas the closely related quantity current density is defined as a vector quantity.

The answer, I think, lies in one single simple property of vectors that does not apply to current. What do your students say?

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