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

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