# What does it mean for electric current to be a scalar?

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?

• Where were you reading the reasons for considering electric current as a scalar quantity? Always give the source when you quote something. May 1, 2013 at 3:23
• Without any more context all I can infer is that wherever you are reading this from is just plain wrong. May 1, 2013 at 3:26
• @MichaelBrown Not necessarily. If electric current is defined as the dot-product of a current density vector and vectorial area, the result is a scalar quantity. May 1, 2013 at 3:30
• It's defined as $dq/dt$. Charge is a scalar, and time is a scalar. Therefore $dq/dt$ is a scalar.
– user4552
May 1, 2013 at 4:00
• @Nathaniel But the charge in such a circuit IS moving. And the amount of charge to pass a given point of the circuit over a time dt is dq = Idt. The time derivative in Ben's definition is valid, but it is implied that you have a surface in mind on which the derivative is being taken. May 1, 2013 at 11:07

"...direction of current does not depend upon the direction..."

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:

1. 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.

2. 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.

• I might go so far as to say when direction in important, current density is ALWAYS technically what's being considered, but this is only obvious after being introduced to the Dirac delta function. May 1, 2013 at 5:26

The magnitude of current is the rate of net amount of charge passing through an enclosed area per second. No matter which direction the charges come from, it calculates the net amount of charge passing per second. This is the theoretical definition and is NOT to be confused with an electrical circuit in mind. In an electrical circuit we place a voltage/current source and indicate the direction of current away from the source along conductors. This actually means the direction from higher potential to lower potential. Or even precise, from positive to negative (opposite to that of electron flow). This is utterly different from the quantity mentioned.

As we know, $I=q/t$ where both $q$ and $t$ are scalar quantities. Therefore, current is a scalar quantity.