Electromotive force (emf, $\backslash mathcal\{E\}$) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors. For a given device, if an electric charge Q passes through that device, and gains an energy U, the net emf for that device is the energy gained per unit charge, or U/Q. This has units of volts, or newton meters per coulomb, and hence can be thought of as a voltage induced by the device in question. Since force has the unit of the newton, emf is a misnomer, but one that over time has resisted change.

In most circuits current is driven by a so-called "source of emf", which usually is a voltaic cell (or battery, which consists of voltaic cells in series and/or in parallel) or the power company. For a voltaic cell the source of emf is the chemical reactions that occur at each of the electrode-electrolyte interfaces, so that a voltaic cell can be thought of as two "surface pumps" of atomic dimension. The reactions at the electrode-electrolyte interfaces provide the "seat" of emf for the voltaic cell. For the power company, the source of emf is electromagnetic induction, which is more extended than an atomic size, but nevertheless is confined to the power generation building, usually many miles from the user.

Sources and unit of measurement

Sources of electromotive force include electric generators (both alternating current and continuous current types), batteries, and thermocouples (in a heat gradient). Electromotive force is often denoted by $\backslash mathcal\{E\}$ or ℰ (script capital E).

Electromotive force is measured in volts (in the International System of Units equal in amount to a joule per coulomb of electric charge). Electromotive force in electrostatic units is the statvolt (in the centimeter gram second system of units equal in amount to an erg per electrostatic unit of charge).

Terminology

The term electromotive force is due to Alessandro Volta (1745–1827), who invented the battery, or voltaic pile. "Electromotive force" originally referred to the 'force' with which positive and negative charges could be separated (i.e. moved, hence "electromotive"), and was also called "electromotive power" (although it is not a power in the modern sense). Maxwell's 1865 explanation of what are now called Maxwell's equations used the term "electromotive force" for what is now called the electric field strength.

Formal definition of electromotive force

If the vector field f represents the force per unit charge on a charge carrier, the emf around a circuit C is

$\backslash mathcal\{E\}=\backslash oint\_C\backslash mathbf\{f\}\backslash cdot\; d\backslash mathbf\{l\}.$