University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2020
Views:

45

Pages:

9
Author:

Campbell Wagner

Definition of Electric Current (Macroscopic view) average current: amount of charge Q that passes through area during time t ΔQ Iav  Δt instantaneous current: dQ I= dt unit of current: Ampere (A): C A= . s While current is a scalar (not a vector), it has a sign associated with it (sense of direction!): the direction of flow. Example 1: 3.8x1021 electrons (charge carriers) passed through an area in a wire in 4 minutes. What was the average current? Q Ne I av   t t 3.8 10 1.6 10    A 21 Iav  4  60  Iav  2.53A 19 Current Density Current density J is current per area or, equivalently, (charge per time) per area. Unit of J: A/m2 directions are important … • Current density is a vector (direction is direction of velocity of positive charge carriers) dA J • current density J flowing through infinitesimal area dA produces infinitesimal current dI  J  dA • total current passing through A is I  J  dA q = ∫σ dA surface . J cross section A of wire if J is uniform and parallel to dA: I I   J  dA  J  dA  JA  J  A surface surface Microscopic view of electric current • carrier density n (number of charge carriers per volume) • carriers move with speed v • number of charge carriers that pass through volume: num n ber x volume  volume  n vt A volume • amount of charge passing through volume: Q  q nvt A • divide by t to get the current: • and by A to get the current density: Q I  nqv A t J  nqv Currents in Materials Metals are conductors because they have “free” electrons, which are not bound to metal atoms. In a cubic meter of a typical conductor there roughly 1028 free electrons, moving with typical speeds of 1,000,000 m/s… …but the electrons move in random directions, and there is no net flow of charge, until you apply an electric field. The velocity that should be used in the equation for current density J  n q v. is not the charge carrier’s instantaneous velocity Instead, use the net or drift velocity v d (left over after the random motions is averaged out) J  n q vd . Example 2 : the 12-gauge copper wire in a home has a crosssectional area of 3.31x10-6 m2 and carries a current of 10 A. The electron density in copper is 8.49x1028 electrons/m3. Calculate the drift speed of the electrons. I vd  neA 10C/s vd  (8.49 1028 m-3 )(1.60 1019 C)(3.31106 m2 ) vd  2.22 104 m/s