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Wikipedia gives two formal definitions of the electromotive force:

One in case of a closed loop, in which case the the EMF is supposed to be the path integral of the electric field (and all other forces effectively acting on charge carries) along that loop.

The other one in case of a device with isolated terminals, in which case the EMF is supposed to be the negative difference of the electrostatic potential (coulomb potential) created by the charges at the terminals.

None of these definitions deals with devices (like a resistor, or a capacitor, for example) that are part of an electric circuit. Is there a definition that deals with an arbitrary devices inside an electric circuit (for example a resistor in an electric circuit which is neither short circuited, nor isolated)?

My proposition as a general formula to calculate the EMF along an electric device is to choose a path connecting the two terminals of the device along conductors inside the device, and then integrating along that path all forces that act on force carriers (all electric fields, conservative or rotational, lorentz-force, and effective chemical and thermal forces). Would that formula generalize the two definitions given at wikipedia?

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  • $\begingroup$ Could the downvoter explain his downvote? I'd like to improve the question in case it is unclear / confusing. $\endgroup$ – Quantumwhisp May 14 at 9:33
  • $\begingroup$ FYI it wasn’t me $\endgroup$ – Bob D May 14 at 10:52
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Wikipedia isn’t always the best source. The Hyperphysics website defines emf as the energy per unit charge (voltage) made available by an energy source, such as a battery or generator. With this definition the voltage across a resistor is not an emf since a resistor dissipates energy rather than makes energy available. The voltage across a charged capacitor, on the other hand, is an emf since it stores energy in its electric field.

Hope this helps.

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  • $\begingroup$ To be honest, I don't think the hyperphysics website is the best source either (at least if you refer to this hyperphysics.phy-astr.gsu.edu/hbase/hframe.html) website. For example, I find problematic that they don't discuss the problem of assigning a voltage to nonconservative electric fields. Additioinally, this physics.princeton.edu/~mcdonald/examples/volt.pdf princton article suggests (footnote 18 on page 10) that you can assign an emf also to a resistor. $\endgroup$ – Quantumwhisp May 14 at 8:29
  • $\begingroup$ @Quantumwhisp You can always find different definitions for things. But the mainstream definitions usually refer to it as a source of energy per unit charge. Here are just a few .physicsforums.com/threads/what-is-the-definition-of-emf. 588037/merriam-webster.com/dictionary/electromotive%20forcehttps://… britannica.com/science/electromotive-force. Some, like the following, say it can ALSO be defined as simply the voltage across an element. $\endgroup$ – Bob D May 14 at 10:41
  • $\begingroup$ @Quantumwhispvhttps://www.chegg.com/homework-help/definitions/electromotive-force-4 $\endgroup$ – Bob D May 14 at 10:45
  • $\begingroup$ Suppose we are changing the magnetic flux through an open-circuit coil of wire. Would you say that there are two emfs, the Faraday's law emf and an emf in the opposite direction due to build-up of opposite charges on the end-regions of the wire? [I simply want to know your opinion.] $\endgroup$ – Philip Wood May 14 at 11:35
  • $\begingroup$ @BobD I am sorry, but none of the sources you link give a definition of EMF that is unambigous. Defining it as voltage is not sufficient, because there are many different meanings associated with voltage. The same goes for "potential", as it is not clear what potential is meant to be, or wether potential can be assigned to the situation in a meaningful way. Defining it as "energy gained per charge unit" isn't unambigous either, because it is not specified what should happen to the charge in order to gain energy. $\endgroup$ – Quantumwhisp May 16 at 8:07
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In view of the comments on my original answer, I offer this as an alternative.

In my working years I was an IEEE Surge Protective Devices (SPD) working group chairman. Although IEEE has many SPD standards, even after years of debate it was difficult to get agreement on just how to define the damn things.

Definitions aside, there is something different about a device where you can measure a voltage across its terminals when no current is flowing (e.g., batteries, charged capacitors), and a device where you cannot measure a voltage across its terminals when no current is flowing (e.g., a resistor). Maybe you can call the voltage on the first an emf and on the latter as simply voltage. In which case, you might say that all emfs are voltages but not all voltages are emfs. Or you might not. And then there are devices that don’t fit neatly into one category or another (e.g. inductors. See @Phillip Woods comments)

I’m not asking you to agree with me, nor am I asking you to accept this “answer”. My only point is that getting agreement on a definition can be a futile exercise. In that spirit I wish you luck in developing your proposition.

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  • $\begingroup$ It seems there is a misunderstanding about my last comment: The questions it contained were not meant to point out your answer is wrong. I accept your definition of the emf as the energy some unit of charge gets. The additional questions in that last comment were meant as actual questions that I have about that definition of yours, to make your answer more clear. $\endgroup$ – Quantumwhisp May 17 at 9:54
  • $\begingroup$ @Quantumwhisp I think you may be right. I will revise my original answer in an attempt to answer your questions. $\endgroup$ – Bob D May 17 at 20:25

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