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Induced emf)
An electromotive force (emf) is the "force", measured in volts, that is produced by interaction between a current and a magnetic field, at least one of which is changing. Since the word "force" now has a very specific meaning in physics, and an emf is not a force in this sense, the expansion of the acronym is considered obsolete; or at best, an embarrassing historical artifact. (The term is attributed to Alessandro Volta.)
The emf describes the electrical effect of a changing magnetic field. In the presence of a magnetic field, the electric potential and hence the potential difference (commonly known as voltage) is undefined (see the former) — hence the need for distinct concepts of emf and potential difference. Technically, the emf is an effective potential difference included in a circuit to make Kirchhoff's voltage law valid: it is exactly the amount from Faraday's law of induction by which the line integral of the electric field around the circuit is not zero. The emf is then given by L di/dt, where i is the current and L is the inductance of the circuit.
Given this emf and the resistance of the circuit, the instantaneous current can be computed with Ohm's Law, for example, or more generally by solving the differential equations that arise out of Kirchhoff's laws.
Emf is often used as a synonym for any potential difference, irrespective of the source of the potential difference. (E.g., a battery, charged capacitor, or electret might be the source.) This usage is considered obsolete.
In certain cases, it is possible to make a mathematical analogy between electrical circuits and one-dimensional mechanical systems, in which the emf plays the role of the "force" in the equations. The origin of the term "electromotive force", however, did not employ such a strict analogy; it simply referred to the strength 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). (c.f. Oxford English Dictionary, "electromotive force".) Maxwell's 1865 explication of what are now called Maxwell's equations used the term "electromotive force" for what is now called the electric field.
See also