Electric Current — A Short History

The ancient Greek, seemingly, first observed that after rubbing amber with a cloth it attracts small pieces of lint, as we now know, by electrostatic forces. In this lies the origin of the word electric as {{\eta\lambda\epsilon\kappa\tau\rho}}o (electro) is the Greek word for amber. In 1785, Coulomb first published the inverse square law governing the forces of charged point-like bodies. Twenty years after Volta discovered the battery and for the first time electric current could be studied, Oersted in 1820 was first to demonstrate the link between electric current and magnetism. Inspired by this, Ampere was quick to announce a few months later the force between conductors carrying a current.  This force is the basis that defines the electric current, the ampere [1]. After that, one ampere second defined the coulomb, the unit for electric charge.

[1] The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to  newton per meter of length.

The 19th century natural philosophers conceptualised  an electric fluid,  J.J. Thomson discovered the electron in 1897 and the physical explanation for electric currents in solids, liquids and gases emerged as the electron-drift, or ion-drift. Today, in one form or another, this explanation appears in the descriptions for photoelectric effects, superconductivity, plasma physics, semiconductors, electro-chemistry, etc.

Modern explanation for electric current

The discovery of the electron in 1897 is credited to JJ Thomson. Soon afterwards, Paul Drude in 1900 proposed a model for electric conduction using free electrons. In this model it is assumed that the conduction electrons:

  1. do not interact with the cations (“free electron approximation”) except when one of them collides elastically with a cation which happens, on average, times per second, with the result that the velocity of the electron abruptly and randomly changes its direction (“relaxation-time approximation”);
  2. maintain thermal equilibrium through collisions, in accordance with Maxwell–Boltzmann statistics (“classical-statistics approximation”);
  3. do not interact with each other (“independent-electron approximation”).

This model explains electric current as follows,

When a potential difference exists between two points along a conducting wire, a uniform electric field E is established along the axis of the wire. This field exerts a force  that accelerates the electrons:

    \[-qE=m \frac{{\rm d} \nu}{{\rm d} t}\]

and in the time  that is on the order of the collision time  the electrons attain a velocity

    \[\nu=-\frac{qE}{m}\tau.\]

The electron motion consists of successive periods of acceleration interrupted by collisions, and, on average, each collision reduces the electron velocity to zero before the start of the next acceleration.

To obtain an expression for the current density ,

    \[\vec J = n q \vec\nu_{av},\]

we assume that the average velocity  of the electrons is given by Eq. (1.17), so we obtain

    \[\vec J =\left(\frac{nq^2}{m}\right) \vec E\]

.

Early adopters of the Drude model:

  • Townsend (1903) described gas discharge, he postulated that light emitting plasma is energised by the collisions of accelerated electrons with the atoms of the gas.
  • Einstein (1905) Photoelectric current as electrons ejected from an illuminated surface to a nearby conductor, with kinetic energy received from the absorption of radiation. These ejected electrons form the basis of a photocurrent.
  • Frenkel (1926), Wagner and Schottky (1931), Jost (1933) described, for semiconductors, electron and hole conduction.
  • In 1933 Arnold Sommerfield ‘quantumised’ Drude’s model
  • Bardeen, Cooper, and Schrieffer (1957) electron pairs (Cooper pairs) as an explanation to superconductivity.

The migration of charged particles, be it electrons, protons, or molecular ions is the accepted explanation to physically explain electric current. Explanations ranging from superconductors to plasma physics use Drude’s philosophy, even though it is blatantly wrong and disproved in the article: Electric Current is Not an Electron Drift!