# Is current a tensor or a scalar quantity? [duplicate]

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?

• – John Rennie Jul 27 '20 at 10:45
• @John Rennie, I'm clear on the vector part I have edited the question. It was about scalar or tensor. A small mistake – Tesla's Coil Jul 28 '20 at 5:55
• Please reconsider your downvotes as the post has been edited. – Tesla's Coil Jul 28 '20 at 6:00
• It wasn't meant to be what it was at first – Tesla's Coil Jul 28 '20 at 6:00
• Both scalars and vectors are tensors. A scalar is a rank $0$ tensor and a vector is a rank $1$ tensor. – John Rennie Jul 28 '20 at 6:54

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.

• the question was aimed at scalar or tensor. A small mistake was made which has been edited. As per your answer it seems as though tensors are a bigger picture and scalars and vectors are both types of tensors. Please reconfirm – Tesla's Coil Jul 28 '20 at 5:57
• And @Dale, I know that why current density is a vector and current isn't, because Current is the dot product of current density with area vector. – Tesla's Coil Jul 28 '20 at 5:59
• @Teslas Coil confirmed. Both scalars and vectors are tensors. – Dale Jul 28 '20 at 11:09
• thanks for clearing the confusion – Tesla's Coil Jul 28 '20 at 12:27
• I am unable to accept this answer – Tesla's Coil Jul 28 '20 at 12:28

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..

• Thanks. Wish if I could accept all answers – Tesla's Coil Jul 28 '20 at 12:27