Expert: Daniel Mazur - 6/22/2007

Question
1.Is Electric current a scalar or vector? Please explain.
2. Mention some of the quantities which are scalars but have the sense of flow?

Answer
1. Quite generally, electric current is a vector, although in some problems we can work with it as if it was a scalar. It describes a flow of charge per unit time at a point in space (for example, in a circuit). This flow of charge has a direction in space, hence current is a vector. In a wire, which limits the current flow to one dimension, the vector character of current is (can be) taken care of just by using positive current for one direction and negative current for the opposite one. However, this plus/minus distinction makes current a "one-dimensional vector". The vector character becomes completely clear and significant when one starts thinking about magnetic field produced by flowing current. Please read the discussion here for more: https://carnot.physics.buffalo.edu/archives/2006/02_2006/msg00462.html

2. It is not clear to me, what "the sense of flow" means here. I assume the questioner asks about the *flux* quantities, which are often defined as scalars.

In the college terms (you said nothing about your education level, so I need to cover this), wherever something "flows", it has a character of a VECTOR FIELD. Then flux scalar is defined as a "surface integral of a vector field", in mathematical words it is a double-integral (surface integration) of the scalar product of the vector field and the vector-like surface element (direction defined as the normal to the surface element). Examples of these flux quantities are electric flux, magnetic flux, radiative energy flux. In an ocean you can even define water flux quantities that would be of particular importance in areas of distinct warm and cold streams.