The Drude model of electrical conduction was developed in the 1900s by Paul Drude to explain the transport properties of electrons in materials (especially metals). The Drude model is the application of kinetic theory to electrons in a solid. It assumes that the material contains immobile positive ions and an "electron gas" of classical, non-interacting electrons of density n, each of whose motion is damped by a frictional force, due to collisions of the electrons with the ions, characterized by a relaxation time τ. Electrical conduction is the movement of electrically charged particles through matter. ... // Events and Trends Technology First flight by the Wright brothers, December 17, 1903. ... Paul Karl Ludwig Drude (1863–1906) was a German physicist. ... Properties The electron is a fundamental subatomic particle that carries a negative electric charge. ... Kinetic theory, or kinetic-molecular theory, or collision theory attempts to explain the macroscopic properties of gases by considering their molecular composition and motion. ...

Explanation

The Drude model assumes that an average charge carrier experiences a `drag-coefficient' γ. Under an applied electric field E this leads to the following differential equation: In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...

where denotes average velocity, m the effective mass and q the charge magnitude. In mathematics, there are numerous methods for calculating the average or central tendency of a list of n numbers. ...

The steady state solution () of this differential equation is: For alternative meanings see steady state (disambiguation). ...

where is the mean free time of a charge carrier. μ Is called the mobility. Now, introducing charge carrier density n (= N / V for a homogeneous sample), we can relate average velocity to current density:

This leads to the DC-conductivity σ₀ of the material: DC may stand for: A.P. de Candolle in botanical nomenclature Axiom of dependent choice in set theory (mathematics) Christian Democracy (Italy), a political party in Italy Da capo, a musical term Daimler-Chrysler, a car manufacturer Dartmouth College in Hanover, New Hampshire David Coulthard, British Formula One driver DC...

The Drude model can also predict the current as a response to a time-dependent electric field with an angular frequency ω, in which case

Here it is assumed that

The imaginary part indicates that the current lags behind the electrical field, which happen because the electrons need roughly a time τ to accelerate in response to a change in the electrical field. Here the Drude model is applied to electrons; it can be applied both to electrons and holes, i.e. positive charge carriers in semiconductors.

This simple classical model does a surprisingly good job of explaining DC and AC conductivity in metals, the Hall effect, and thermal conductivity (due to electrons) in metals. Hot metal work from a blacksmith Look up Metal in Wiktionary, the free dictionary In chemistry, a metal (Greek: Metallon) is an element that readily forms ions (cations) and has metallic bonds, and metals are sometimes described as a lattice of positive ions (cations) surrounded by a sea of delocolised... Hall effect diagram, showing electron flow (rather than conventional current). ... In physics, thermal conductivity, λ or k, is the intensive property of a material which relates its ability to conduct heat. ...