Electric Current and Drift Velocity

Identify the microscopic quantities n, e, A, and v_d. Convert area to m^2 if needed. Substitute in I = neAv_d. For direction questions, remember conventional current follows the electric field in a metal, while electron drift is opposite.

A useful diagram shows a metallic wire connected to a cell, electric field from positive to negative potential, conventional current along the electric field, and electron drift opposite to it. Label A as cross-sectional area and mark v_d for electron drift.

Writing I = nAv_d without the electronic charge e gives a dimensionally wrong answer and usually an unrealistically large value.

Electric current is the rate of flow of electric charge through a cross-section of a conductor. Drift velocity is the small average velocity with which free electrons move opposite to the applied electric field inside a conductor.

Electric current is the rate of flow of electric charge through a cross-section of a conductor. Drift velocity is the small average velocity with which free electrons move opposite to the applied electric field inside a conductor. Key formulae: I = dq/dt, where I is current in ampere, dq is charge in coulomb, and dt is time in second; v_d = eEτ/m, where e is electronic charge in coulomb, E is electric field in volt per metre, τ is relaxation time in second, and m is electron mass in kilogram; I = neAv_d, where n is number density in m^-3 and A is area in m^2. Use these for steady current in a metallic conductor under an applied electric field. In a copper wire connected to a cell, electrons drift from the negative terminal side toward the positive terminal side, while conventional current is taken from positive to negative through the external circuit.

When an electric field is applied across a metallic conductor, free electrons do not rush through the wire at very high speed. They undergo frequent collisions with ions and acquire a small average drift velocity. The measurable current depends on the number density of electrons, charge of each electron, area of cross-section, and drift velocity. This microscopic model explains why current starts almost immediately in a circuit even though individual electrons drift slowly. Key formulae: I = dq/dt, where I is current in ampere, dq is charge in coulomb, and dt is time in second; v_d = eEτ/m, where e is electronic charge in coulomb, E is electric field in volt per metre, τ is relaxation time in second, and m is electron mass in kilogram; I = neAv_d, where n is number density in m^-3 and A is area in m^2. Use these for steady current in a metallic conductor under an applied electric field. A wire has n = 8.0 x 10^28 m^-3, A = 1.0 x 10^-6 m^2, and drift velocity v_d = 2.0 x 10^-4 m s^-1. Current I = neAv_d = (8.0 x 10^28)(1.6 x 10^-19)(1.0 x 10^-6)(2.0 x 10^-4) A = 2.56 A. This means 2.56 C of charge crosses any section of the wire each second. Questions may ask for the relation between current and drift velocity, the direction of electron drift, a derivation using relaxation time, or a numerical calculation of current, area, or drift speed. Writing I = nAv_d without the electronic charge e gives a dimensionally wrong answer and usually an unrealistically large value.