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Electromotive force

From Wikipedia, the free encyclopedia


Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. It is measured in volts.

Sources and unit of measurement

Sources of electromotive force include electric generators (both alternating current and continuous current types), batteries, and thermocouples (in a heat gradient). [1] Electromotive force is often denoted by \mathcal{E} or (script capital E).

Electromotive force is measured in (V) volts (in the International System of Units equal in amount to a joule per coulomb of electric charge). 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).


The term origin is attributed to Alessandro Volta (1745–1827), who invented the voltaic pile. The term "electromotive force" originally referred to the 'force' 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). 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 strength. [2]

Electromotive force has been stated to be the force that has the disposition to produce a circuit's electric current and is, under normal conditions, called voltage. [3]

In physics, the unit of emf is the "energy per unit electric charge", so the "force" term of "electromotive force" is misleading to a degree. The expansion of the acronym is considered obsolete.[citation needed] 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 use of the term "emf" is in decline but it is still found in introductory and technical level texts on electricity.[citation needed]

Explanation of electromotive force

In electrodynamics, a measure of electromotance indicates the tendency for electric charge to flow around a circuit or other closed curve. An emf is also commonly used to express the strength of a compact source of electrical energy. The electromotive force of a device is defined to be the amount of energy gained per unit charge that passes through it in the "uphill" direction. It has units of joules per coulomb, otherwise more commonly known as the volt.

If the vector field f is the force per unit charge on a charge carrier, the emf around a circuit C is

\mathcal{E}=\oint_C\mathbf{f}\cdot d\mathbf{l}.[4]

Like the electric potential at a point and the voltage between two points, the emf around a loop is measured in volts. Unlike the first two quantities, the emf is sensitive to non-electrostatic forces, since the force f can include magnetic, chemical, mechanical, and gravitational components.[5]

Electromotive force in thermodynamics

When multiplied by an amount of charge de the emf ℰ yields a thermodynamic work term ℰde that is used in the formulism for the change in Gibbs free energy when charge is passed in a battery:

dG = -SdT + VdP + ℰde

The combination ℰ.e 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 (a measurable quantity) to the change in entropy when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy ΔrS of the electrochemical reaction that lends the battery its power.

\left(\frac{\partial \mathcal{E}}{\partial T}\right)_e= -\left(\frac{\partial S}{\partial e}\right)_T

Electromotive force and potential difference

If no external circuit is connected to a source of emf, an electric current cannot exist (Ohm's Law). 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 charges separated by the mechanism generating the emf [6]. 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 polarity of this measured potential difference is always opposite to that of the generated emf. The value of the emf for the battery (or other source) is the value of this 'open circuit' voltage. The emf itself cannot be measured directly.

Electromotive force generation

Commonly, electromotive force is generated by electrochemical reaction (e.g., a fuel cell). Dissimilar metals in contact also produce what is know as a contact electromotive force or contact potential (eg., the volta effect). Absorption of radiant or thermal energy (e.g., a solar cell or a thermocouple). Some other sources include thermocouples, thermopiles, and photodiodes.

Electromagnetic induction is a means of converting mechanical energy, i.e., energy of motion into electrical energy. The electromotive force generated in this way is often referred to as motional electromotive force. Motional emf is ultimately due to the electrical effect of a time-varying magnetic field. In the presence of such 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

\mathcal{E} = -L { di \over 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. The current at any instant t is then given by

i(t) = { 1 \over R}   \left(   E - L {di \over dt} \right)

where E is the electromotive force of the source, i is the instantaneous current, and R is the resistance of the resistor connected in series with the inductor, in the circuit.


  • Griffiths, David (1999). Introduction to Electrodynamics, 3e, Prentice-Hall. ISBN 0-13-805326-X. 
  1. ^ John S. Rigden, (editor in chief), Macmillan encyclopedia of physics. New York : Macmillan, 1996.
  2. ^ Edward J. Rothwell and Michael J. Cloud, Electromagnetics. CRC Press. Pg 22. ISBN 0-8493-1397-X
  3. ^ John Markus, Neil Sclater, McGraw-Hill electronics dictionary. New York, McGraw-Hill, Edition 5th ed., international 3rd ed. c1994. ISBN 0-07-113486-7 ISBN 0-07-040434-8
  4. ^ Griffiths, Introduction to Electrodynamics, p.293
  5. ^ Griffiths, Introduction to Electrodynamics, p.285; "...or trained ants with tiny harnesses."
  6. ^ Roberts, Dana: "How batteries work: A gravitational analog", Am. J. Phys., 51,829 (1983)

Ohm's Law (PDF in German)

See also

  • Electric potential
  • Electrochemical potential
  • Faraday paradox
  • Magnetomotive force
  • Potentiometer
  • Thermoelectric effect

Further reading

  • Andrew Gray, "Absolute Measurements in Electricity and Magnetism", Electromotive force. Macmillan and co., 1884.
  • Charles Albert Perkins, "Outlines of Electricity and Magnetism", Measurement of Electromotive Force. Henry Holt and co., 1896.
  • John Livingston Rutgers Morgan, "The Elements of Physical Chemistry", Electromotive force. J. Wiley, 1899.
  • George F. Barker, "On the measurement of electromotive force". Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge, American Philosophical Society. January 19, 1883.
  • "Abhandlungen zur Thermodynamik, von H. Helmholtz. Hrsg. von Max Planck". (Tr. "Papers to thermodynamics, on H. Helmholtz. Hrsg. by Max Planck".) Leipzig, W. Engelmann, Of Ostwald classical author of the accurate sciences series. New consequence. No. 124, 1902.
  • Nabendu S. Choudhury, "Electromotive force measurements on cells involving [beta]-alumina solid electrolyte". NASA technical note, D-7322.
  • Henry S. Carhart, "Thermo-electromotive force in electric cells, the thermo-electromotive force between a metal and a solution of one of its salts". New York, D. Van Nostrand company, 1920. LCCN 20020413
  • Hazel Rossotti, "Chemical applications of potentiometry". London, Princeton, N.J., Van Nostrand, 1969. ISBN 0-442-07048-9 LCCN 69011985 //r88
  • Theodore William Richards and Gustavus Edward Behr, jr., "The electromotive force of iron under varying conditions, and the effect of occluded hydrogen". Carnegie Institution of Washington publication series , 1906. LCCN 07003935 //r88
  • G. W. Burns, et al., "Temperature-electromotive force reference functions and tables for the letter-designated thermocouple types based on the ITS-90". Gaithersburg, MD : U.S. Dept. of Commerce, National Institute of Standards and Technology, Washington, Supt. of Docs., U.S. G.P.O., 1993.

External articles

  • Doug Gingrich, "Physics lecture notes, electronics", Direct Current Circuits, Electromotive Force (EMF). University of Alberta, Department of Physics, 1999.
  • Advanced Physics lecture notes, "Electromagnetism", Faraday’s Law—Electromagnetic Induction. Electromotive Force". Semiconductor Physics Group, Department of Physics, University of Cambridge, 2006. (PDF)
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