Definition
Electric current density J is simply the electric current I (SI unit: A) per unit area A (SI unit: m2). Its magnitude is given by the limit:
For current density as a vector J, the surface integral over a surface S, followed by an integral over the time duration t1 to t2, gives the total amount of charge flowing through the surface in that time (t2 − t1):
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 mass passes through, A, and a unit vector normal to the area, . The relation is .
If the current density J passes through the area at an angle θ to the area normal, then
where · is the dot product of the unit vectors. This is, the component of current density passing through the surface (i.e. normal to it) is J cos θ, while the component of current density passing tangential to the area is J sin θ, but there is no current density actually passing through the area in the tangential direction. The only component of current density passing normal to the area is the cosine component.
Read more about this topic: Current Density
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