Direct Current Density

Current is known as the flow of charge. By inheritance, the direction of this flow is with the movement of positive charge. The amount of charge δQ flowing through (that is, perpendicular) to a surface, in time δt is given by the formula

 δQ = Iδt, where I stands for the current.

In the limit of infinite simally small time increments, the current I through the surface can be defined as:

Magneto-statics is a field theory and, consequently, the quantities of interest are usually distributed throughout space. As such, the volume current density, j(x, y, z) is frequently employed. If we want current density in terms of the charge carriers, the current density is given by the formula;

where N stands for the number of charge carriers per unit volume (i.e., it is the number density), q is the charge, and v is the average (i.e., drift) velocity of the electrons.

In addition to this, a current density through an open surface “S” is related to the current with the help of the formula: