# Electromotive force

Electromotive force (emf) is a measure of the strength of a source of electrical energy. The unit of emf is the volt (energy per unit electric charge) and so the term 'force' is misleading. Thus, the expansion of the acronym is considered obsolete or at best, an embarrassing historical artifact. (The term is attributed to Alessandro Volta.). Nonetheless, it is sometimes helpful to picture emf as analogous to a force or a pressure such as when making a mechanical or liquid analogy of an electric circuit.

The term "electromotive force" originally 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.

Commonly, emf is generated by chemical reaction (e.g., a battery or a fuel cell), absorption of radiant or thermal energy (e.g., a solar cell or a thermocouple), or electromagnetic induction (e.g., a generator or an alternator). Electromagnetic induction is a means of converting mechanical energy, i.e., energy of motion into electrical energy. The emf generated in this way is often referred to as motional emf.

Motional emf is ultimately due to the electrical effect of a changing magnetic field. In the presence of a changing 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.

Regardless of how it is generated, emf causes an electric current through a circuit connected to the terminals of the source. For example, the chemical reaction that separates electric charge onto the two terminals of a battery proceeds as long as there is an external circuit through which electrons can flow from the '-' terminal to the '+' terminal and thereby recombine with the positive ions.

However, if an external circuit is not connected, an electric current cannot exist. Thus, between the terminals of the source, there must exist an electric field that exactly cancels the generated emf. The source of this field is the electric charge separated by the mechanism generating the emf. For example, the chemical reaction in the battery proceeds only to the point that the electric field between the separated charges is strong enough to stop the reaction. This electric field between the terminals of the battery creates an electric potential difference that can be measured with a voltmeter. The value of the emf for the battery (or other source) is the value of this 'open circuit' voltage.

The use of the term emf is in decline but it is still found in introductory and technical level texts on electricity. Within Electrical Engineering, the term emf is occasionally used for a voltage produced by electromagnetic induction. However, the term induced voltage is preferred.

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