In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre. Definition Assume that (SI unit: m2) is a small surface centred at a given point and orthogonal to the motion of the charges at . If (SI unit: A) is the electric current flowing through , then electric current density at is given by the limit: with surface remaining centered at and orthogonal to the motion of the charges during the limit process. The current density vector is the vector whose magnitude is the electric current density, and whose direction is the same as the motion of the positive charges at . At a given time , if is the velocity of the charges at , and is an infinitesimal surface centred at and orthogonal to , then during an amount of time , only the charge contained in the volume formed by and will flow through . This charge is equal to where is the charge density at , and the electric current at is It follows that the current density vector can be expressed as: The surface integral of over a surface , followed by an integral over the time duration to , gives the total amount of charge flowing through the surface in that time (): More concisely, this is the integral of the flux of across between and . The area required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface. For example, for charge carriers passing through an electrical conductor, the area is the cross-section of the conductor, at the section considered. The vector area is a combination of the magnitude of the area through which the charge carriers pass, , and a unit vector normal to the area, The relation is The differential vector area similarly follows from the definition given above: If the current density passes through the area at an angle to the area normal then where ⋅ is the dot product of the unit vectors.