# Current Density

## Current Density

Current density is a point is defined as the amount of current flowing per unit area round that point provided area is normal to the direction of current. It is denoted by J.

Current Density (J) = Current (I)/ Area (A).

The unit of current of current density is A/ m². Current density is a vector quantity. So, it must have direction also. Its direction at a point is the direction of motion of the positive charge or direction of current at that point.

Average Current Density: Let, through an area ΔA around a point P, a current Δi is passing normal to the area. Then the average current density over the area is given by:

Average Current Density (Javg) = Δi/ ΔA.

Current Density at a Point: Now suppose we want to find current density at point P in the above figure. Take an infinitesimally small area dA around point P. Let the current through this small area is di. Then, the current density at point P is given by:

Current Density (J) = di/ dA.

If Current is not Perpendicular to Area: Here we divide the current by the component of area in the direction of the current. Hence, the average current is given by:

Average Current Density (Javg) = Δi/ ΔA cosθ.

We can also write it as,

Δi = Javg ΔA cosθ

$$\Delta i=\overrightarrow{{{J}_{avg}}}\,\times \,\Delta A$$.

Current Density at P: Take an infinitesimally small area dA around point P. Let the current through this small area is di. Then then current density at point P is given by:

Current Density (J) = di/ dA cosθ.

We can also write it as,

di = J dA cosθ

$$di=\overrightarrow{J}.\overrightarrow{dA}$$.

$$i=\int{\overrightarrow{J}.\overrightarrow{dA}}$$.