Microscopic view of Ohm's Law.
J=I A
Definition: current density
density vector J where direction of J is the direction of the current.
(current per area in a conductor). We also define current
J is related to the average speed vdrift of the charge carriers (usually electrons) by ,
n is the number of carrier per volume, q is the charge per carrier (usually q = e).
Proof: Consider a wire with carrier density n (#/volume), cross-sectional area A, and drift speed vdrift. In a time ∆t, all the charges move an average distance ∆x = vdrift ∆t.