Electromotive Force - Terminology

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 (that is, 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. But, in his later textbook he uses the term "electromotive force" both for "voltage-like" causes of current flow in an electric circuit, and (inconsistently) for contact potential difference (which is a form of electrostatic potential difference). Given that Maxwell's textbook was written before the discovery of the electron, it is understandable that Maxwell exhibits what (in terms of modern knowledge) is inconsistency in the use of the term "electromotive force".

The word "force" in "electromotive force" is a misnomer:

has turned out to be an unfortunate choice of words which is still with us 160 years later. In all of physics except electromagnetic induction, the term 'force' is reserved for mechanical action on ponderable matter and is measured in units called newtons. In contrast electromotive force is measured in units of volts and causes charge separation.

Nonetheless, the term "electromotive force" has resisted change. "Electromotance", meaning (literally) tendency to move ("-motance") electrical charge, is semantically more accurate, but not widely adopted. Both terms are less common than the abbreviation emf.

These terms (emf, voltage, etc.) have many interpretations and applications, not all necessarily consistent with each other. The emf is typically considered to be the work done per unit charge by a source in creating a separation of positive from negative charges, thereby creating a voltage difference; the work done per unit charge in pushing charge through a battery creating the battery's voltage difference, for example. However, there is not complete unanimity upon this usage. As Sydney Ross says, in excusing himself for avoiding the term emf:

We have refrained from using the term 'electromotive force' or 'e.m.f.' for short; for there is no consistency between different authors in the meaning of the term. … To some authors it is synonymous with 'voltage.' To others it means the open-circuit voltage of a battery. To a third group of authors it means the open-circuit voltage of any two-terminal device. This use is met most often in connection with Thevenin's theorem in circuit theory. To a fourth group it means the work accounted for by agencies other than differences of the (not measurable) Galvani potentials. Such authors equate the current–resistance product of a circuit branch to the sum of voltage plus e.m.f. A fifth group extends this use to field theory. The authors of this group equate the product of current density and resistivity to the sum of electric-field strength plus an e.m.f. gradient. A sixth group applies the term to electromagnetic induction. These authors define e.m.f. as the spatial line integral of the electric-field strength taken over a complete loop. To them the term 'counter e.m.f.' means something.

It is common in some fields, such as circuit theory, to refer to the voltage created by the emf as the emf. Some authors do not distinguish between the emf and the voltage it creates. Some use emf to refer to the open-circuit voltage and voltage to the potential difference when current is drawn. Here is a quotation describing emf as an open-circuit voltage difference:

This buildup of charge on the electrodes tends to oppose the current flow with a 'back voltage' ΔV. On an open circuit, I = 0 the value of ΔV for which I = 0 is defined as the emf ℰ of the cell. That is, ℰ = ΔV_I=0.

This usage does not identify the work done per unit charge in creating the charge build-up as emf, but rather identifies emf with the consequent "back voltage" that arrests current flow in the open-circuit condition. One emphasizes the conversion of energy from other forms to electrical energy, the other emphasizes the resulting electrical potential. This article focuses upon the conversion of other forms of energy to electrical potential energy, and describes some examples of how this conversion comes about.