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In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf,^[1][2] denoted ${\displaystyle {\mathcal {E}}}$) is the electrical action produced by a non-electrical source, measured in volts.^[3] Devices (known as transducers) provide an emf^[4] by converting other forms of energy into electrical energy,^[4] such as batteries (which convert chemical energy) or generators (which convert mechanical energy).^[3] Sometimes an analogy to water pressure is used to describe electromotive force.^[5] (The word "force" in this case is not used to mean forces of interaction between bodies).

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.^[6]

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 emf can drive an electric current if an external circuit is attached to the terminals, in which case the device becomes the voltage source of that circuit.

Overview

Devices that can provide emf include electrochemical cells, thermoelectric devices, solar cells, photodiodes, electrical generators, transformers and even Van de Graaff generators.^[7][8] In nature, emf is generated when magnetic field fluctuations occur through a surface. For example, the shifting of the Earth's magnetic field during a geomagnetic storm induces currents in an electrical grid as the lines of the magnetic field are shifted about and cut across the conductors.

In a battery, the charge separation that gives rise to a potential difference (voltage) between the terminals is accomplished by chemical reactions at the electrodes that convert chemical potential energy into electromagnetic potential energy.^[9][10] A voltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:

A (chemical) source of emf can be thought of as a kind of charge pump that acts to move positive charges 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 ℰ of the source is defined as the work dW done per charge dq. ${\textstyle {\mathcal {E}}={\frac {{\mathit {d}}W}{{\mathit {d}}q}}}$.^[11]

In an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which creates a potential difference between the generator terminals. Charge separation takes place within the generator because electrons flow away from one terminal toward the other, until, in the open-circuit case, an electric field is developed that makes further charge separation impossible. 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.

History

In 1801, Alessandro Volta introduced the term ``force motrice électrique" to describe the active agent of a battery (which he had invented around 1798).<sup>[12]</sup> This is called the ``electromotive force" in English.

Around 1830, Michael Faraday established that chemical reactions at each of 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.^[13] 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, held the incorrect opinion that contact alone (without taking into account a chemical reaction) was the origin of the emf.

Notation and units of measurement

Electromotive force is often denoted by ${\displaystyle {\mathcal {E}}}$ or ℰ.

In a device without internal resistance, if an electric charge Q passes through that device, and gains an energy W, the net emf for that device is the energy gained per unit charge, or W/Q. Like other measures of energy per charge, emf uses the SI unit volt, which is equivalent to a joule per coulomb.^[14]

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).

Formal definitions

Inside a source of emf (such as a battery) that is open-circuited, a charge separation occurs between the negative terminal, A, and the positive terminal B. This leads to an electrostatic field ${\displaystyle {\boldsymbol {E}}_{\mathrm {open\ circuit} }}$ that points from B to A, whereas the emf of the source must be able drive current from A to B when connected to a circuit. This led Max Abraham ^[15] to introduce the concept of a nonelectrostatic field ${\displaystyle {\boldsymbol {E}}'}$ that exists only inside the source of emf. In the open-circuit case, ${\displaystyle {\boldsymbol {E}}'=-{\boldsymbol {E}}_{\mathrm {open\ circuit} }}$, while when the source is connected to a circuit the electric field ${\displaystyle {\boldsymbol {E}}}$ inside the source changes but ${\displaystyle {\boldsymbol {E}}'}$ remains essentially the same. In the open-circuit case, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf. ^[16] Mathematically:

where ${\displaystyle {\boldsymbol {E}}_{\mathrm {open\ circuit} }}$ is the conservative electrostatic field created by the charge separation associated with the emf, ${\displaystyle \mathrm {d} {\boldsymbol {\ell }}}$ is an element of the path from terminal A to terminal B, '⋅' denotes the vector dot product, and ${\displaystyle V}$ is the electric scalar potential.^[17] This emf is the work done on a unit charge by the nonelectrostatic "battery" field ${\displaystyle {\boldsymbol {E}}'}$ when the charge moves from A to B.

When the battery is connected to a load, its emf is just, ${\displaystyle {\mathcal {E}}_{\mathrm {source} }=\int _{A}^{B}{\boldsymbol {E}}'\cdot \mathrm {d} {\boldsymbol {\ell }}\ ,}$ and no longer has a simple relation to the electric field ${\displaystyle {\boldsymbol {E}}}$ inside it.

In the case of a closed path in the presence of a varying magnetic field, the integral of the electric field around the (stationary) closed loop C may be nonzero. Then, the "induced emf" (often called the "induced voltage") in the loop is, ^[18]

where ${\displaystyle {\boldsymbol {E}}}$ is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary, but stationary, closed curve C through which there is a time-varying flux ${\displaystyle \Phi _{C}}$ of magnetic magnetic field, and ${\displaystyle {\boldsymbol {A}}}$ is the vector potential. The electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative (i.e., the work done against the field around a closed path is zero, see Kirchhoff's voltage law, which is valid, as long as the circuit elements remain at rest and radiation is ignored ^[19] ). That is, the "induced emf" (like the emf of a battery connected to a load) is not a "voltage" in the sense of a difference in the electric scalar potential.

If the loop C is a conductor that carries current ${\displaystyle I}$ in the direction of integration around the loop, and the magnetic flux is due to that current, we have that ${\displaystyle \Phi _{B}=LI}$, where ${\displaystyle L}$ is the self inductance of the loop. If in addition, the loop includes a coil that extends from point 1 to 2, such that the magnetic flux is largely localized to that region, it is customary to speak of that region as an inductor, and to consider that its emf is localized to that region. Then, we can consider a different loop C' that consists of the coiled conductor from 1 to 2, and an imaginary line down the center of the coil from 2 back to 1. The magnetic flux, and emf, in loop C' is essentially the same as that in loop C, so we can write

For a good conductor, ${\displaystyle {\boldsymbol {E}}_{\mathrm {conductor} }}$ is negligible, so we have, to a good approximation, where V is the electric scalar potential along the centerline between points 1 and 2. Thus, we can associate an effective "voltage drop" ${\displaystyle L\ dI/dt}$ with an inductor (even though our basic uunderstanding of induced emf is based on the vector potential rather than the scalar potential), and consider it as a load element in Kirchhoff's loop law, ${\displaystyle \sum {\mathcal {E}}_{\mathrm {source} }=\sum _{\mathrm {load\ elements} }\mathrm {voltage\ drops} ,}$ where now the induced emf is not considered to be a source emf.^[20]

This definition can be extended to arbitrary sources of emf and moving paths C:^[21]

which is a conceptual equation mainly, because the determination of the "effective forces" is difficult. The term ${\displaystyle \oint _{C}\left\cdot \mathrm {d} {\boldsymbol {\ell }}}$ is often called a "motional emf".

In (electrochemical) thermodynamics

When multiplied by an amount of charge dQ the emf ℰ yields a thermodynamic work term ℰdQ that is used in the formalism for the change in Gibbs energy when charge is passed in a battery:

${\displaystyle dG=-S\,dT+V\,dP+{\mathcal {E}}\,dQ\ ,}$

where G is the Gibbs free energy, S is the entropy, V is the system volume, P is its pressure and T is its absolute temperature.

The combination ( ℰ, Q ) is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature T (a measurable quantity) to the change in entropy S when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is:^[22] Zdroj:https://en.wikipedia.org?pojem=Electromotive_force
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