What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive force (EMF)?

Question

This is a confused part ever since I started learning electricity. What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive force (EMF)? All of them have the same SI unit of Volt, right? I would appreciate an answer.

Answer 1

EDIT: Put simply, a 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.

An 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 the electrostatic field does not depend on the path, but only on endpoints. 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 practical applications, electrons (and other charge carriers) flow in circuits. Since the 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 the 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 nonzero. 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:

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

Answer 3

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 4

To help you understand the difference, think of EMF as a measurement of Work being done and think of Electric Potential Energy as energy that has the "potential" to perform Work. As an analogy, EMF could be thought of (in the Mechanical realm) as one pushing a wheel barrel up a hill. (Or better yet, a car, with gasoline prices as they are today lol.). And think of Electric Potential Energy as the wheel barrel being at the top of the hill. If the wheel barrel was released, its' potential energy would be transformed into several different forms of energy in rolling down the hill (Frictional-Heat, Work done on air resistance; and if it collided with a wall at the bottom and came to rest, its' original Potential Energy would all have been transformed into different forms of energy upon coming to rest at the bottom. Now to get a bit more technical...

A. EMF (Electromotive Force)
work that has been done is by definition, the Work done within the EMF "seat" (the battery in this case) in raising the charges (Chemically) from the negative (-) terminal up to the positive (+) terminal thus maintain the ability to still provide the circuit with current.

B. ELECTRIC POTENTIAL ENERGY
As an analogy (I'll get a little funny on this one), imagine that a Woman and a Man see each other; say from six feet apart. They instantly have an attraction (overbearing) for one-another; enter into a trance and begin walking towards each other. The energy other folks would have to apply to hold both from continuing to walk towards each other, is analogically, the Electric Potential Energy. the folks would be holding the Man and Woman still while they retain their trance - maintain the force to come together. And in a direct definitional realm, it is the potential energy two separated oppositely charged (for positive potential) particles posses in the attraction to come together. As well, such can think of this from the perspective of the energy required to hold the two charges at rest (in a Static State) not allowing them to move towards one-another.

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

The amount of work done by unit charge between any two nodes of current carrying circuit is called the potential difference between those nodes.

The amount of work done against the electric field by displacing (without acceleration) a unit test charge from one terminal to other terminal in an open circuit is called the electromotive force.

Obviously when we deal in static electricity the potential difference between two points in electric field is amount of work done against the electric field by displacing (without acceleration) a unit test charge from one point to another point, off course it doesn't depends on path because the electric field is conservative field.

Same is happen when current is flowing in a circuit, in this case the electric field is confined in physical boundaries of circuit components, but still it is conservative in nature. Hence the potential difference in a current carrying circuit will also the amount of work done by moving a unit test charge from one node to another node. In other scenario we can observe that the charge is already moving in the current carrying circuit, so amount of work done by these moving charges in the current carrying circuit is converted in heat, light, mechanical work etc.

In case of emf, when any circuit is open, the open terminals do have charge density difference, this difference in charge density create an electric field, the work done against this electric field in moving a unit test charge without acceleration from one terminal to another is called the electromotive force..

Answer 7

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 8

All of them have the same SI unit of Volt, right?

Yes, sadly, different quantities that all have the same unit of volt are called "voltages". In this answer, I hope to hope to bring some mathematical clarity. Unfortunately, it may not help the terminological confusion.

The electric field $\vec{E}$ induces a force upon a charge, which is given by the Lorentz Force Equation.

$$\vec{F}=q(\vec{E} + \vec{v}\times\vec{B})$$

Where $\vec{v}$ is the velocity of the charge, and $\vec{B}$ is the magnetic flux density.

A line integral of the $\vec{E}$ field gives us the work the field performs on a unit charge, as it moves along a curve $C$ from point $a$ to point $b$.

$$W = \int_{C:a\rightarrow b}\vec{E}\cdot d\vec{s}$$

The $\vec{E}$ field does not have to be conservative. It is conservative in the absence of time-varying magnetic fields. It is not (globally) conservative if there are time-varying magnetic fields. This is quantified in Maxwell's rendering of Faraday's Law (as rendered in vector calculus by Heaviside):

$$\nabla\times\vec{E} = -\frac{\partial\vec{B}}{\partial t}$$

When an $\vec{E}$ field acts upon a free electron in a conductor, the electron initially accelerates according to the direction and magnitude of the $\vec{E}$ field. However, the electron very soon interacts with the other matter in the conductor, and it's velocity becomes randomized. Thus, current along the length of a normal conductor is not maintained through the inertia of the electrons, but through a constantly (re)applied force from the $\vec{E}$ field along the length of the conductor. This fact finds expression in the microscopic version of Ohm's Law.

$$\vec{J}=\sigma\vec{E}$$

where $\vec{J}$ is the current density and $\sigma$ is the conductivity of the conductor. Where there is no $\vec{E}$ field, in a normal conductor, there is no (macroscopic) current.

Batteries are not "normal conductors", and a battery will cause charges to move against an $\vec{E}$ field. This is one form of electromotive force. Another type of electromotive force is magnetic induction. Magnetic induction creates an electric field, but the direction and magnitude of the vectors in this field do not usually match the $\vec{E}$ field within a conductor. Remember, that the $\vec{E}$ field in an ordinary conductor is fixed by the conductivity of the conductor, and the current density within it.

We will call the component of the total $\vec{E}$ field that is created by a time-varying magnetic field $\vec{E}_{\partial\vec{B}/\partial t}$. Some use the symbol $\vec{E}_{ind}$ to mean the same thing.

Without showing the derivation,

$$\vec{E}_{\partial\vec{B}/\partial t} =\nabla\times\frac{1}{4\pi}\int_{R^3}\frac{\partial\vec{B}(r')}{\partial t}\frac{1}{|r-r'|}d^3r'$$

We are now in a position to state what is the emf induced by a time-varying magnetic field:

$$\mathscr{E}_{\partial\vec{B}/\partial t} =\int_{C:a\rightarrow b} \vec{E}_{\partial\vec{B}/\partial t} \cdot d\vec{s}$$

Note for later that

$$\nabla \cdot \vec{E}_{\partial\vec{B}/\partial t} = 0 $$

This follows from the fact that for any vector field $\vec{A}$,

$$\nabla \cdot (\nabla\times\vec{A}) = 0$$

The divergence of a curl is always 0.

Helmholtz theorem states that every "nice" vector field may be decomposed into a curl-free part (i.e. a conservative part) and a divergence-free part (i.e. a solenoidal part). We have found the divergence-free part of $\vec{E}$. It is just $\vec{E}_{\partial\vec{B}/\partial t}$.

The curl-free part of $\vec{E}$ is just $\vec{E}-\vec{E}_{\partial\vec{B}/\partial t}$. So we will define

$$\vec{E}_{conservative} = \vec{E}-E_{\partial\vec{B}/\partial t}$$

Being conservative, there exists some $\phi$ such that

$$\vec{E}_{conservative}=\nabla\phi$$

We will call $\phi$ the electric scalar potential. Note very well, that we can find such a $\phi$ even when $\vec{E}$ is NOT conservative.

We will call $\Delta\phi$ a potential difference. Note that the value of $\Delta\phi$ between two points is NOT PATH DEPENDENT.

We now have three different integrals that are all measured in volts, (and are thus often called "voltages") but which encapsulate three different concepts.

Total Work performed by electric field:

$$W = \int_{C:a\rightarrow b}\vec{E}\cdot d\vec{s}$$

Magnetically induced emf

$$\mathscr{E}_{\partial\vec{B}/\partial t} =\int_{C:a\rightarrow b} \vec{E}_{\partial\vec{B}/\partial t} \cdot d\vec{s}$$

and electric scalar potential difference

$$\Delta\phi = \int_a^b\vec{E}-\vec{E}_{\partial\vec{B}/\partial t} \cdot d\vec{s}$$

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This analysis, I think is in accord with the statement made in the most up-voted answer:

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.

The only objections that I might raise to the above are 1) that I'm not sure I would call $\nabla\phi$ "the electrostatic force" (which is present in decidedly non-static situations), and 2) how this electrostatic force relates to $\vec{E}$ (and differs from it) is not unambiguously spelled out.

Answer 9

Potential, voltage and EMF are practically the same thing. The 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 measuring the potentials of two electrodes. So, you see, the potential is the same as voltage but one of the electrodes is considered conditionally of potential zero. You'd use The term electromotive force instead 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.