In electromagnetism, and related fields in solid state physics, condensed matter physics etc. current density is the electric current per unit area of cross section. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the electric current density is measured in amperes per square metre.
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“We set up a certain aim, and put ourselves of our own will into the power of a certain current. Once having done that, we find ourselves committed to usages and customs which we had not before fully known, but from which we cannot depart without giving up the end which we have chosen. But we have no right, therefore, to claim that we are under the yoke of necessity. We might as well say that the man whom we see struggling vainly in the current of Niagara could not have helped jumping in.”
—Anna C. Brackett (1836–1911)