# What is the difference between electric potential, voltage and electromotive force?

This is a confused part ever since I started learning electricity. What is the difference between voltage and electromotive force (emf)? Both of them have the same SI unit, right? I would appreciate an answer.

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You forgot to ask for meaning of "potential". –  Georg Oct 5 '11 at 20:04

EDIT: Put simply, potential difference is the work done by electrostatic force on a unit charge, while EMF is the work done by anything other than electrostatic force on a unit charge.

I don't like the term "voltage". It seems to mean anything measured in volts. I'd rather say electric potential and electromotive force.

And the two are fundamentally different.

Electrostatic field is conservative, that is, over any loop $l$ we have $\oint_l \vec{E}\cdot\mathrm{d}\vec{l}=0$. In other words, the line integral of electrostatic field does not depend on the path, but only on end points. So we can define point by point a scalar value electrostatic potential $\varphi$, such that $$\varphi_A-\varphi_B=\int_A^B \vec{E}\cdot\mathrm{d}\vec{l},$$

or

$$q \left( \varphi_A-\varphi_B \right)=\int_A^B q\vec{E}\cdot\mathrm{d}\vec{l},$$

so $q\Delta\varphi$ equals the work done by electrostatic force.

In pratical application, electrons (and other carriers) flow in circuits. Since electrostatic field is conservative, it alone cannot move electrons in circles; it can only move them from lower potential to higher potential. You need another kind of force to move them from higher potential to lower ones in order to complete a cycle. This other force could be chemical, magnetic or even electric (vortex electric field, different from electrostatic field), and their equivalent contribution is called electromotive force. $$\mathrm{E.M.F.}=\int_\text{Circuit} \frac{\vec{F}}{q}\cdot\mathrm{d}\vec{l}$$

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your explanation (which repeats what I said regarding useful work) is confusing because it doesn't account for the difference in potentials when the circuit is not closed in a loop and which is called alternatively emf or voltage. –  ganzewoort Oct 6 '11 at 14:16
Also, observing electrons traveling spontaneously from lower potential to higher potential, as in your reply, is conterintuitive. Since it's a matter of conventions it would be preferable to choose a convention in a reverse sense. –  ganzewoort Oct 6 '11 at 14:23
@ganzewoort: Well, my explanation may be confusing, but potential and emf are fundamentally different. Even when the circuit is not closed, potential difference is not the same as emf. –  C.R. Oct 6 '11 at 14:52
first it should be understood that emf doesn't apply only for a closed loop, as you have inferred. As for whether or not it is a potential difference, it is, in the sense which I already explained. –  ganzewoort Oct 6 '11 at 15:01
@ganzewoort: I concede I was wrong about closed loop. But your explanation is not an explanation at all. You just describe how you measure the two, but does not address the conceptual difference. And your explanation is wrong. EMF cannot be directly measured. For example, the EMF of an inductor with non-zero resistance is different from the potential difference, and the only thing you can directly measure is that difference. –  C.R. Oct 6 '11 at 15:13
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Anyway the simple answer is e.m.f. is not a force in the mechanical sense. It measures the amount of work to be done for a unit charge to travel in a closed loop of a conducting material.

Let's make it more clear. In static case (ignoring time variation of any magnetic field), electric field at a point can be derived solely from a scalar as the negative of the gradient of this scalar. This scalar at any point is called the "electric potential" at that point. If two points are at different potentials then we say there exists a potential difference. Obviously it is the difference in the potentials that matters and not their absolute values. One can therefore arbitrarily assign a value zero for some fixed point who's potential may be considered constant and compare the potentials of other points with respect to it. In this way one need not have to always speak of potential difference but simply potentials.

Now, often this "electric potential" at some point in a conductor or a dielectric is called "voltage" at that point assigning the value of the voltage to be zero for earth since the potential of earth is constant for all practical purposes.

If there is no variation of magnetic field then the work done by an unit charge in a closed loop will be $0$. But if the magnetic field varies then it will be non zero. Recall the formula $$\nabla \times {E} = \frac {\partial {B}}{\partial {t}}$$

What it really implies is, it is impossible for an electric field, derived solely from a scalar potential, to maintain an electric current in a closed circuit. So an e.m.f. implies presence of some source other then a source which can only produce a scalar potential.

The following equation tells the whole story:

$$E = -\nabla \phi - \frac{\partial A}{\partial t}$$ $\phi$ is the scalar potential and $A$ is the vector potential.

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People downvote sometimes not because you are wrong, but because you are repeating other people's answers without adding anything new. –  Ron Maimon Oct 6 '11 at 16:53
sb1, your explanation again fails to explain the open-circuit emf. Even more interestingly, I'm curious to hear your explanation as to how the Faraday's law you're mentioning accounts for the voltage drop measured across a unipolar generator. This, perhaps, is for a separate question to be asked in stackexchange. –  ganzewoort Oct 6 '11 at 17:01
@ganzewoort: "e.m.f. implies presence of some source other then a source which can only produce a scalar potential." That means the electric field is not conservative any more. That's all. In open circuit condition, a voltage will be generated between the ends which is not just the difference of scalar potential at the two ends. As for unipolar generator, yes, it will be a good idea to ask as a separate question. –  user1355 Oct 6 '11 at 17:52
I agree about the scalar potential (I think you've explained it very well and doesn't repeat what's been said so far). However, scalar potential is only a mathematical construct, created for convenience, which isn't inherent in the phenomena. I'm adding a separate question regarding the unipolar generator. –  ganzewoort Oct 6 '11 at 18:43

Actually these are are same thing but usage is at different places.

Whenever we talk about batteries or a DC system, we use the Potential difference, as there is potential difference of 3.7 Volt.

The phrase "electro-motive force" (EMF) is used when a conductor cuts the flux inside the machine (Transformer, Generator, etc)

Voltage is used as Output from an electrical machine.

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Electromotive force (Note; not a force) is simply the source of voltage in a circuit.

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Voltage is a potential difference, due to the energy dissipation. Emf is a potential difference, due to the energy generation.

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"Voltage is a potential difference, due to the energy dissipation" are you sure? What about the voltage across an Inductor? –  user1355 Oct 7 '11 at 7:27
@sb1 Ok, for non-DC replace "dissipation" with "dissipation and consumption". –  Martin Gales Oct 10 '11 at 7:44
Sorry still wrong. A.C. or D.C., energy is always conserved in a pure inductor and never "consumed" or "dissipated". If you apply a dc source across an inductor through a resistance then energy will be dissipated but again by the resister ($I^2r$ loss)and not by the inductor. In practice, an inductor will always have some resistance and a portion of energy will be dissipated and but again that's because of the resistance. –  user1355 Oct 11 '11 at 15:41
@sb1 At a time when the energy is converted into magnetic energy of the inductor, there is no difference, is the energy conserved or not. At this time the conductor draw energy from the circuit like a resistor. At a time when the inductor returns the stored energy into the circuit it works like a generator(a source of emf). –  Martin Gales Oct 12 '11 at 7:56
No point in arguing :( You don't even know the meaning of consumption, dissipation, even energy conservation. –  user1355 Oct 12 '11 at 8:54
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potential difference and e.m.f has same unit because of voltage. firstly,potential difference is is define as the work done upon charge , while e.m.f(electro motive force) is the potential differnce maintain across the battery.we are normally cosidering the external cicuit there is also an inner circuit. V=IR
and E.M.F=Ir+IR sice E.M.F=I(r+R) therefore E.M.F=Ir+IR
AS WE KNOW V=IR
E.M.F=V+Ir

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