Electromotive force

Devices that can provide emf include electrochemical cells, thermoelectric devices, solar cells, photodiodes, electrical generators, inductors, transformers and even Van de Graaff generators.

[10][11] In nature, emf is generated when magnetic field fluctuations occur through a surface.

The general principle governing the emf in such electrical machines is Faraday's law of induction.

In 1801, Alessandro Volta introduced the term "force motrice électrique" to describe the active agent of a battery (which he had invented around 1798).

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 the earlier obsolete theory thought.

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.

via work, the net emf for that device is the energy gained per unit charge:

In the open-circuit case, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf.

is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary, but stationary, closed curve

At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature

This Maxwell relation is:[25] If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is: where

Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:[25] where

[33] [34] The question of how batteries (galvanic cells) generate an emf occupied scientists for most of the 19th century.

The "seat of the electromotive force" was eventually determined in 1889 by Walther Nernst[36] to be primarily at the interfaces between the electrodes and the electrolyte.

[37] In batteries, coupled half-reactions, often involving metals and their ions, occur in tandem, with a gain of electrons (termed "reduction") by one conductive electrode and loss of electrons (termed "oxidation") by another (reduction-oxidation or redox reactions).

(A detailed discussion of the microscopic process of electron transfer between an electrode and the ions in an electrolyte may be found in Conway.

)[38] The electrical energy released by this reaction (213 kJ per 65.4 g of zinc) can be attributed mostly due to the 207 kJ weaker bonding (smaller magnitude of the cohesive energy) of zinc, which has filled 3d- and 4s-orbitals, compared to copper, which has an unfilled orbital available for bonding.

If the cathode and anode are connected by an external conductor, electrons pass through that external circuit (light bulb in figure), while ions pass through the salt bridge to maintain charge balance until the anode and cathode reach electrical equilibrium of zero volts as chemical equilibrium is reached in the cell.

[39] The salt bridge has to close the electrical circuit while preventing the copper ions from moving to the zinc electrode and being reduced there without generating an external current.

If the light bulb is removed (open circuit) the emf between the electrodes is opposed by the electric field due to the charge separation, and the reactions stop.

The electromotive force produced by primary (single-use) and secondary (rechargeable) cells is usually of the order of a few volts.

The figures quoted below are nominal, because emf varies according to the size of the load and the state of exhaustion of the cell.

The electromotive force generated by a time-varying magnetic field is often referred to as transformer emf.

The magnitude of this potential difference is often expressed as a difference in Fermi levels in the two solids when they are at charge neutrality, where the Fermi level (a name for the chemical potential of an electron system[44][45]) describes the energy necessary to remove an electron from the body to some common point (such as ground).

At thermodynamic equilibrium, the Fermi levels are equal (the electron removal energy is identical) and there is now a built-in electrostatic potential between the bodies.

Charge separation occurs because of a pre-existing electric field associated with the p-n junction.

[51] Approximately this same current is obtained for forward voltages up to the point where the diode conduction becomes significant.

The current delivered by the illuminated diode to the external circuit can be simplified (based on certain assumptions) to:

[51] Solving the illuminated diode's above simplified current–voltage relationship for output voltage yields: which is plotted against

A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann et al. [ 35 ] and Transition state .
Galvanic cell using a salt bridge
The equivalent circuit of a solar cell , ignoring parasitic resistances.
Solar cell output voltage for two light-induced currents I L expressed as a ratio to the reverse saturation current I 0 [ 52 ] and using a fixed ideality factor m of 2. [ 53 ] Their emf is the voltage at their y-axis intercept.