But the average current density may be different from the current density at a point, if the current density is not uniform.

Imagine an area delta S inside a conductor at right angles to the current flow. As the area approaches zero, we get the current density at a point. This is expressed as:

Now consider an area dS at an angle theta to the flow as shown below:

In this case the current flowing through the area is given by:

Notice that the cosine term deals with the angle between the normal to the area and the direction of the current.

In the applet below, change the angle between the area and the field, and see how the magnitude of the current density is affected.