# Electromotive force

Electromotive force, abbreviated emf (denoted ${\displaystyle {\mathcal {E}}}$ and measured in volts),[1] is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator.[2] A device that converts other forms of energy into electrical energy (a "transducer") provides an emf as its output.[3] (The word "force" in this case is not used to mean mechanical force, as may be measured in pounds or newtons.)

In electromagnetic induction, emf can be defined around a closed loop of conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop.[4] For a time-varying magnetic flux linking a loop, the electric potential scalar field is not defined due to a circulating electric vector field, but an emf nevertheless does work that can be measured as a virtual electric potential around the loop.[5] (While electrical charges travel around the loop, their energy is typically converted into thermal energy due to the resistance of the conductor comprising the loop.)

In the case of a two-terminal device (such as an electrochemical cell) which is modeled as a Thévenin's equivalent circuit, the equivalent emf can be measured as the open-circuit potential difference or "voltage" between the two terminals. This potential difference can drive an electric current if an external circuit is attached to the terminals.

Devices that can provide emf include electrochemical cells, thermoelectric devices, solar cells, photodiodes, electrical generators, transformer and even Van de Graaff generators.[5][6] In nature, emf is generated whenever magnetic field fluctuations occur through a surface. The shifting of the Earth's magnetic field during a geomagnetic storm induces currents in the electrical grid as the lines of the magnetic field are shifted about and cut across the conductors.

In the case of a battery, the charge separation that gives rise to a voltage difference between the terminals is accomplished by chemical reactions at the electrodes that convert chemical potential energy into electromagnetic potential energy.[7][8] A voltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:[9]

A source of emf can be thought of as a kind of charge pump that acts to move positive charge from a point of low potential through its interior to a point of high potential. … By chemical, mechanical or other means, the source of emf performs work dW on that charge to move it to the high potential terminal. The emf of the source is defined as the work dW done per charge dq: = dW/dq.

In the case of an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which in turn creates a voltage difference between the generator terminals. Charge separation takes place within the generator, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further charge separation impossible. Again, the emf is countered by the electrical voltage due to charge separation. If a load is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines is Faraday's law of induction.

Around 1830, Michael Faraday established that the reactions at each of the two electrode–electrolyte interfaces provide the "seat of emf" for the voltaic cell, that is, these reactions drive the current and are not an endless source of energy as was initially thought.[10] In the open-circuit case, charge separation continues until the electrical field from the separated charges is sufficient to arrest the reactions. Years earlier, Alessandro Volta, who had measured a contact potential difference at the metal–metal (electrode–electrode) interface of his cells, had held the incorrect opinion that contact alone (without taking into account a chemical reaction) was the origin of the emf.

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