Why is current a scalar quantity but current density a vector quantity?

Electric current (I) through a given area of a conductor is the rate of flow of electric charge through the area.Conventionally the direction of electric current is taken along the direction of motion of positive charges.

For a quantity to be a vector:

- it has to have magnitude and direction
- it has to obey the laws of vector addition .

Current satisfies the first but fails the second therefore it is a scalar quantity.

i.e if two currents meet at a junction, the total current of the resultant will be the algebraic sum of the two current and not the vector sum.So even though current has direction, it is a scalar quantity.

On the other hand current density (J) is the current per unit area perpendicular to the direction of flow.

J = I / A

Current density at a point inside the conductor is a vector whose direction is the direction of flow of charge at that point and whose magnitude is the current through a unit area perpendicular to the direction of flow.Hence current density satisfies the conditions for a quantity to be vector