# What is Electromotive force (EMF)? How is it related to potential difference?

What is Electromotive force (EMF)? How is it related to the potential difference? Is it created by the potential difference in any conductor? Is it a process? Why is it called force?

Does writing EMF instead of voltage make any difference in AC circuits? (Studying alternating current I found some books using EMF while others used voltage.)

Electromotive force, abbreviated as E.M.F and denoted by $\varepsilon$, is not a force. It is defined as the energy utilized in assembling a charge on the electrode of a battery when the circuit is open.Simply, it is the work done per unit charge which is the potential difference between the electrodes of the battery measured in volts. Mathematically, $\textbf{V} = \frac{\textbf{W}}{\textbf{q}}$.

Initially, energy is available in the form of chemical energy. This energy is utilized to take a charge say $+q$ to the anode by overcoming the electrostatic force of attraction due to the the negative charges on the cathode and the electrostatic force of repulsion due to the positive charges on the anode. The chemical energy then gets transformed into electrostatic potential energy present in the electric field between the electrodes of the battery.

I dislike the term EMF (Electromotive force) as it is very confusing.

Electromotive force, also called emf (denoted $\mathcal{E}$ and measured in volts), is the voltage developed by any source of electrical energy such as a battery or dynamo.

Which means that all EMF are voltages but not all voltages are EMF. A voltage is only an EMF if it is a source of energy.

Kind of like the distinction between luminescent light (from a light bulb) and reflected light (from your desk) if you measure it there is no physical measurable difference. The only difference is that one is a source and the other is not.

• I think that definition is too vague, although probably correct. I'd like it better if it pointed out that voltages developed by static charges are not developed by any "source of electrical energy" Mar 6 '14 at 14:19

First The word "force" in this case is not used to mean mechanical force, measured in newtons, but a potential, or energy per unit of charge, measured in volts.

It is neither the creation of potential, nor it is a process and it is not even a force. It came to be known as a force because wrongful interpretation in the past made it seem as if a force from the battery pushed the particles in a circuit. This analysis was obviously discarded later but the name prevails!

In electric circuits emf and potential have a significant difference. While the emf is the potential difference between the terminals of a source in open circuit, the potential is the potential difference betwren the terminals in a closed one.

The potential is defined as $V = \epsilon - Ir$. Here $\epsilon$ is the emf of the source and $Ir$ is tue potential drop in the internal resistance. It is pretty clear that replacing potential with emf in any sort of circuit is not a very wise decision, however sometimes the potential drop in internal resistance is negligible.

There is no creation of anything, but it can be assumed that a circuit creates a voltage when the power, combination of that voltage and any current which would flow from it, has been gained from "outside the circuit" - e.g. through chemical processes (batteries), or electromagnetic processes (dynamo that converts mechanical power to electrical). This very particular voltage is your electromotive force in your circuits, for example the back-emf of the windings of a motor. It's a concept which exists also in magnetic circuits (for the big picture), see magnetomotive force.

It may be pointed out that the word electromotive force is a misnomer. It does not represent force on the carriers of electricity. Instead, it represents the potential difference between the two poles in an open circuit (when no current is drawn from the cell).

The relationship between emf and potential is exactly the same as the relationship between work and potential energy. The emf from a circuit element is the work per unit charge done on the charges in the system. Often that emf is associated with a difference of potential (potential energy per unit charge), in which case the two are interchangeable. Both can be measured in units of volts, and so can be called a "voltage". A resistor applies an emf of -IR to the charges that move through it, and so the potential difference across the resistor is IR (specifically, a drop of IR if following the current).

One case where emf is NOT associated with a potential difference is when it is induced by a change in magnetic flux. In a circuit with induced current, if you add up the potential differences around a circuit you won't get zero, even though you end at the same place you began. That's because the changing magnetic flux through the circuit is doing work (per unit charge) from outside, but there are no two points in the circuit you could put a voltmeter across to measure that directly. Induced emf can still be measured in volts, and so is sometimes called "loop voltage", but that's a voltage without a difference! ;-)

All EMFs are voltages but not all voltages are EMFs. Let me explain.

If the voltage is produced by a non-electrical source we call such a voltage as emf, else if the source is purly electrical we call the voltage as voltage itself and not as EMF.
For example a battery converts chemical energy to electrical energy. Here the source of the voltage is chemical (non-electrical) hence voltage across a battery can be called as an emf. Same with generators, the source is mechanical hence emf, also same with inductors, the source is magnetic, hence emf. But the voltage across a charged capacitor cannot be called as an emf because the source is electric charges which is purely electrical.

Here's a similar explaination from Wikipedia:

In electromagnetism and electronics, electromotive force or EMF (measured in volts) is the electrical action produced by a non-electrical source. Devices (known as transducers) provide an emf by converting other forms of energy into electrical energy, such as batteries (which convert chemical energy) or generators (which convert mechanical energy). Sometimes an analogy to water pressure is used to describe electromotive force. (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

So to sum up, here's the definition of EMF:

The voltage produced by a non-electrical source is called an EMF.

EMF of a sorce may be defined as work to Cary a unit positive charge from lower (negative electrode) to higher (positive electrode) electric motive force

• your answer is almost a verbatim copy of what can be found in the link posted by OP, and as such, pretty useless... Feb 12 '16 at 16:54