After reading the reasons for considering electric current as a scalar quantity, I was confused at a point which read "The magnitude and direction of current does not depend upon the direction of the flow of charge, that's why electric current is a scalar." What does it mean? How can it be explained in atomic point of view?
[Physics] What does it mean for electric current to be a scalar
electric-currentelectromagnetism
Best Answer
This strikes me as a particularly poorly worded explanation. I might even go as far as to say that it's outright incorrect. There are two equally valid ways to explain why current is a scalar quantity, and not a vector quantity despite the fact that it does move in a particular direction:
Current is only measured as the amount of charge passing through a particular cross sectional area. Mathematically this is represented by the following equation: $$I=\int{\int_S{\vec{J}\cdot \hat{n}dA}}$$
where $\vec{J}$ is the current density.
Current is the derivative of charge with respect to time. In other words, it's the amount of charge passing through a cross sectional area at any given time, or the amount of charge leaving or entering a particular enclosed area. This is mathematically expressed as $$I=\frac{dq}{dt}$$
Again, a scalar quantity. When measuring a current, there could be several different charge sources flowing in various different directions. Current only measures the net amount of these charges that flows through an area at any given time. Depending on the direction the charge flow is moving, it may contribute more or less to the overall current through the area. When direction is important, current density is normally the quantity considered.