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

Question

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.

Answer 1

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.

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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. $$\mathrm{E.M.F.}=\int_\text{Circuit} \frac{\vec{F}}{q}\cdot\mathrm{d}\vec{l}$$

Answer 2

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.

Answer 3

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.

Answer 4

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

Answer 5

A very short answer:

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

Answer 6

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

Answer 7

EMF is used as a more general term to also include those situations where the integral of the electric field around a closed curve is not zero, so that the E field doesn't come from a pure potential. Usually, when people say potential, they mean that the potential is a function of the position, and when they say EMF, they mean it is a function of the loop.

You have nonintegrable E fields when you have changing magnetic fields, an inductance. Since the "voltage" is usually used for the pure electrical potential, people call the voltage produced by an inductance an "EMF". Outside the circuitry, the fields are negligible usually, and the EMF at any point is the electrostatic potential at that point. But inside the circuitry, in inductors, there's a difference.

Answer 8

Potential, voltage and emf are practically the same thing. Potential is the value of volts of a given electrode you measure with respect to some standard electrode whose potential is considered zero (Normal Hydrogen Electrode (NHE), saturated calomel electrode (SCE) etc.) Voltage is the difference between two thus measured potentials of two electrodes. So, you see, potential is same as voltage but one of the electrodes is considered conditionally of potential zero. The term electromotive force you'd use in the stead of voltage if you intend to talk about the change of the Gibbs free energy which would amount to the useful work you can get from the given Galvanic element, say. In any event, that's just splitting hairs in my opinion, so you can use those terms interchangeably as long as it is clear what the reference electrode is.