# Is electric current a scalar quantity?

According to the definition of a Scalar quantity that i have read in class 9 is that ''those quantities which has only magnitude but no direction is known as a scalar quantity''.....But in class 10 i read that charges need to flow in a particular direction in order to form a electric current......From this argument we can conclude that a current has a specified directions which denies the definition of being a scalar quantity......

That definition of a vector quantity is a little too simple. It needs to not only have direction, but the directions need to add depending on the angles between them in a specific way to give an overall equivalent quantity.

Current in a circuit isn't really a vector quantity, it has direction but that is equivalent to just the sign of the current. You can have a positive current going in one direction and a negative current in the other - they will still add but not in a vector sense.

Perhaps there needs to be a 3rd term in between scalar and vector.

• In the Maxwell equations, $\nabla\times\vec B = \mu_0 (\vec J + \epsilon_0 \partial_t \vec E)$, the current $\vec J$ is most certainly a vector quantity. I suspect your answer (and the question) is talking about currents in an electric circuit, but it might be worthwhile to mention that, in general, current is indeed a vector quantity. Apr 19 '15 at 17:19
• @ACuriousMind - good point, I was think in terms of the question Apr 19 '15 at 18:13

Current is what is known as a pseudoscalar. This justification for this comes from the definition of current. Current, $I$, is defined as the net flow of charge per unit time through some surface. We define a vector field called the current density, $\vec{J}$, that describes the net flow of charge density at each point in space. It's related to the charge density ($\rho$, charge per unit volume), and mean velocity at each point, $\vec{v}$, by: $$\vec{J} = \rho \vec{v}.$$ If $\vec{J}$ is constant, then the net time rate at which charge is flowing through some flat surface with area $A$ is given by: $$I = A \hat{n} \cdot \vec{J},$$ where $\hat{n}$ is a vector that has length $1$ and is perpendicular to $A$ (it's a 'surface normal'). $A$ is flat, though, so the definition of $\hat{n}$ is ambiguous (it's perpendicular, but on which side of $A$?). The usual choice in lower level physics class is to just tell students to pick a direction and stick with it. At higher levels, $\hat{n}$ is defined by a cross product, in the case of a parallelogram, and an integral of cross products in general. That makes $\hat{n}$ a pseudovector. Since $\vec{J}$ is an ordinary vector, the result of the dot product must be a pseudo scalar.

Punchline: current density $\vec{J}$ is unambiguous because it is an ordinary vector, and $I$ depends on which direction you define to be positive flow for positive charges through the surface.

A point O where current 4A and 3A enter at an angle of 60° but output current is 7A where output current doesn't depend upon input current. So, current flows simple algebraic sum, due to this reason current is a scalar quantity.