Is current a tensor or a scalar quantity?

Question

Is current a tensor or a scalar quantity? The internet seems to be divided on this one. Tensors are too complicated. So I am unable to find an answer. Can someone please clearly state whether it is a scalar or a vector?

Answer 1

Current density is a vector, $\vec J$, and it must be a vector based on where it shows up in Maxwell’s equations.

Current is $I=\int_A \vec J \cdot d\vec A$, where $A$ is an area and $d\vec A$ is a directed normal vector to a differential element of $A$. So, since it is the dot product of two vectors, current is a scalar.

Most of the confusion is not whether or not current is a vector but rather whether or not you are using current or current density in a particular instant.

Note, both scalars and vectors are tensors. Scalars are tensors of tank 0, and vectors are tensors of rank 1.

Answer 2

I think this question is more about the distinction between scalars, vectors and tensors than anything having to do with electric current.

Both scalars and vectors are special cases of tensors. Current is a scalar. Current density is a vector. Because scalars and vectors are tensors this means current and current density are both tensors.

The above is all being very pedantic with terminology about tensors. In practice, you will very rarely hear physicists refer to scalars or vectors as tensors. While technically scalars and vectors are tensors, when physicists use the word tensor they typically mean a tensor which is not a scalar and is not a vector. That is, a tensor of order $\ge 2$. This is perhaps why you've had some confusion..