Question

Is current density a scalar or a vector quantity?

Answer 1

Firstly we try to recall concepts of scalar and vector quantity, scalar quantity has only magnitude and vector quantity has magnitude and direction both. Now think that current density has the only magnitude or has direction also.

Complete step by step solution:
Before thinking about the question we will understand the concepts of vector and scalar quantity. A quantity that has magnitude, as well as direction is known as vector quantity but it doesn’t have a position, it is represented by an arrow. Some examples of vector quantity are velocity and force and the other side a quantity that has only magnitude, no direction is known as a scalar quantity. Some examples of scalar quantity are mass and speed.
Now, we will understand the current and current density. Current is produced when electric charge flows in a direction. Its unit is $Ampere$. The current is a scalar quantity. Now, we will be able to understand the concept of current density - The amount of current flowing in per unit area is known as the current density. It is the ratio of the amount of current flowing and the area of current flowing, the current density is represented as$J$and its unit is $Ampere/{m^2}$. Current density is a vector quantity because it’s a product of charge density and velocity, here charge density is a scalar quantity and velocity is a vector quantity, which makes current density also a vector quantity.

Note: Point to be note is, we should never think that unit of current density is $Ampere/{m^2}$, here $Ampere$ is the unit of current and ${m^2}$is the unit of area, current and area both are scalar quantities then the current density will also be a scalar quantity.