Why current density is defined?

Question

I feel that the reason to define thing like current density is that we want to use the directional nature of the current like a vector quantity and since electric current is not a vector so we define something which has same direction as current but a vector? is is true?

Answer 1

We can define vector and scalar versions of both total current and current density:

$I$ (scalar) = magnitude of the total current in some defined region (e.g. electrical current in a wire) = amount of charge passing a given plane, per unit time

$\bf I$ (vector) = just like scalar $I$ only now it is a vector with the direction indicating the direction of the flow (or average direction if the flow is not uniform)

$j$ (scalar) = magnitude of the current density (equal to current per unit area) = amount of charge passing a given plane at a point, per unit area of that plane, per unit time (with the plane perpendicular to the flow)

${\bf j}$ (vector) = just like $j$ only now it is a vector whose magnitude is $j$ and whose direction is the direction of the flow.

You can always use other letters of course, but $I$ and $j$ are quite commonly used for electric current and electric current density.