Why is current density a vector quantity while current is scalar? [duplicate]

Question

Electric current is considered to be a scalar quantity because it does not follow the rules of vector addition. Then, why is current density called a vector quantity as it is just current/area ?

Answer 1

Technically, current (in a wire) is a vector. However, because of a historical convention, it is denoted as a scalar. In the case of a wire the direction is implicit as it is the local direction of the wire. No such implicit assumption can be made for 2D or 3D current distributions.

A good way to appreciate the difference in how the vectorial nature is denoted is at the level of Biot-Savart law, where one has, for the infinitesimal source element \begin{align} Id\vec \ell &\qquad \hbox{for linear currents}\\ \vec J dV &\qquad \hbox{for (volume) currents} \end{align} with $\vec J$ the current density. Both $Id\vec\ell$ and $\vec J dV$ are vectors. In the first $Id\vec \ell$, the direction is captured in the vectorial element $d\vec \ell$ whereas in the second, the direction is captured in the vectorial density $\vec J$.