Is electric current is a vector quantity?

Answer 1

-Electric current is the rate at which charge flows through a surface.
-Electric current is often just called current.
-As a scalar it has magnitude only.
-The symbol for current is I (italic).
-In equation form, current can be written …
Iave = Δq/Δt(average current)

I = lim Δq/Δt = dq/dt ( instantaneous current )
Δt → 0
-The SI unit of current is the ampère [A].
The ampère is a fundamental unit defined by the results of an electromagnetic experiment.
The unaccented spelling ampere is also acceptable.
The shortened form amp is often used in informal communication.
-Current density is a quantity related to electric current.
The symbol for current density is J (bold).
As a vector it has magnitude and direction.
By definition, current density is the product of charge density (ρ) and velocity (v).
The magnitude of current density is also equivalent to the ratio of current (I) to area (A).
In equation form, current can be written
… J = ρv, vector definition
J = I/A ,magnitude equivalent
-The SI unit of current density is the ampère per square meter [A/m2].
Microscopic Description of Current
The macroscopic phenomena of electric current can be described by the net motion of microscopic charged particles.
In equation form, the microscopic description of current and current density can be written … I = nqAv J = nqv
microscopic current microscopic current density
Where …
I = electric current [A]
J = current density [A/m2]
n = particle density [particles/m3]
q = charge per particle [C]
v = drift velocity [m/s]
A = area [m2]

Answer 2

No, definitely a scalar quantity.

Current is defined as I = ∫ J ∙ da, where both J and da are vectors. The internal (or dot, or scalar) product of two vectors is a scalar. Period.

Those who have taken a course in vector analysis will be able to recall that, while da, differential area, can be legitimately be regarded as a vector, the same cannot be said of area in general. For, while it is true that a direction can be assigned to an infinitesimal area, that's just impossible to do with certain surfaces. A sphere, for instance; or any curved surface, even if not closed on itself.

As much can be said for current. Which specific direction could anyone assign to current circulating in a coil? Which is the direction of current in an electroplating bath when a metal electrode is introduced inside a hollow cylinder in order to plate the inside? Which direction, when current flows through a grounding rod?

In computing a current, both the magnitude and relative direction of the area through which charge comes across is important, along with charge flow itself. Thus, a very large number of moving charge carriers could exist, and still the current thru a certain area be null, if none of those charges goes across that area.

As for phasors, those mathematical entities contrived to simplify analysis of ac circuits, no, they aren't true vectors, although in some respects admittedly there's a strong resemblance. Voltage, defined as work per unit charge, is also a scalar, not a vector. However, both voltage and current are regarded as phasors in ac circuit theory.

Answer 3

Actually it depends on exactly what you mean by current, but I believe the answer to your question is no. I assume you're asking about current as in V = IR (Ohm's Law). In this case current is a scalar quantity (Coulomb's per second). The reason some people think it's a vector is because you typically draw arrows on a circuit diagram for which direction the current is flowing. However, this can be determined by a reference direction and then either plus or minus current, no vector is needed. Another way to think about it is via Kirchoff's Current Law (KCL), which states that the current flowing into a junction equals the current leaving the junction. Again, it doesn't matter the angle the current enters at, just whether it's entering or leaving. Therefore, current is a scalar quantity.

If however you were looking at the current per unit area (J-vector) in electromagnetic physics, that obviously is a vector, but in circuit schematics or calculations current is a scalar.

Answer 4

If you're talking about DC or resistive components, then you can use a scalar representation for current. But, if your analysis is for AC and you have reactive components, then yes, current (and voltage) is a vector. This is because the voltage and current are out of phase by a certain angle. When you use inductors and capacitors with AC, you have a phase shift. So, you're measuring both the magnitude and angle, thus it's a vector.

Answer 5

Yes.

Answer 6

Yes, it has magnitude and direction.