Electric Current Density
Electric Current Density
The Electric Current Density is denoted by the vector symbol (J). Electric current is measured in Amps (which is equal to charge per second [C/s]). The current density (which is a volume current density) is measured in Amps per meter squared [A/m^2], because the current flows in a direction, and the area is measured normal/perpendicularly/orthogonally to that. This is shown in Figure 1:
Figure 1. Electric Current I (Top) is The Total Charge Flow Per Second. Current Density J (bottom) is the Current over a Specified Cross Section.
The total electric current (I) can be related to the current density (J) by summing up (or integrating) the current density over the area where charge is flowing:
Note that the current density is often not constant, so a weighted summation (Equation [1]) is needed. Finally, suppose a medium (material) has an electric conductivity given by (which is measured in Siemens/meter, which is the oppose (inverse) of resistance per length). Then the electric current density can be related to the Electric Field by Equation [3]:
You may not recognize Equation [3], but it is actually famous  this is Ohm's Law. You probably know from electric circuits that V=IR, which relates voltage, current and resistance. In Equation [3], the Efield is analogous to voltage, current density is analogous to current, and the conductivity is the inverse of resistance. This is where Ohm's Law for circuits comes from. Equation [3] states that in a material with a nonzero conductivity, an Efield will produce an electric current.
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