Let n be the number of free electron available per cubic metre of the conductor material. Let v be the axial drift velocity. In time dt, distance travelled would be vdt . If A is the cross section of the conductor, then the volume is vAdt . If e is the charge of each electron then total charge which crosses the section in time dt is dq=nAev.dt. Since current is the rate of flow of charge, it is given as i=dq/dt=(neAv.dt)/dt i=venA Current density, J=i/A=vne Ampere/m2. Normal J for copper conductor= 1.55 x 10^6 A/m2, n=10^29, e=1.6x10^-19 coulomb, v=9.7 x 10^-5 m/s = 0.58 cm/min.
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