Electromotive force
In electromagnetism and electronics, electromotive force or electromotance, denoted, is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical transducers provide an emf by converting other forms of energy into electrical energy. Other types of electrical equipment also produce an emf, such as batteries, which convert chemical energy, and generators, which convert mechanical energy. This energy conversion is achieved by physical forces applying physical work on electric charges. However, electromotive force itself is not a physical force, and ISO/IEC standards have deprecated the term in favor of source voltage or source tension instead.
An electronic–hydraulic analogy may view emf as the mechanical work done to water by a pump, which results in a pressure difference.
In electromagnetic induction, emf can be defined around a closed loop of a conductor as the electromagnetic work that would be done on an elementary electric charge if it travels once around the loop.
For two-terminal devices modeled as a Thévenin equivalent circuit, an equivalent emf can be measured as the open-circuit voltage between the two terminals. This emf can drive an electric current if an external circuit is attached to the terminals, in which case the device becomes the voltage source of that circuit.
Although an emf gives rise to a voltage and can be measured as a voltage and may sometimes informally be called a "voltage", they are not the same phenomenon.
Overview
Devices that can provide emf include electrochemical cells, thermoelectric devices, solar cells, photodiodes, electrical generators, inductors, transformers and even Van de Graaff generators. In nature, emf is generated when magnetic field fluctuations occur through a surface. For example, the shifting of the Earth's magnetic field during a geomagnetic storm induces currents in an electrical grid as the lines of the magnetic field are shifted about and cut across the conductors.In a battery, the charge separation that gives rise to a potential difference between the terminals is accomplished by chemical reactions at the electrodes that convert chemical potential energy into electromagnetic potential energy. A voltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:
In an electrical generator, a time-varying magnetic field inside the generator creates an electric field via electromagnetic induction, which creates a potential difference between the generator terminals. Charge separation takes place within the generator because electrons flow away from one terminal toward the other, until, in the open-circuit case, an electric field is developed that makes further charge separation impossible. The emf is countered by the electrical voltage due to charge separation. If a load is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines is Faraday's law of induction.
History
In 1801, Alessandro Volta introduced the term "force motrice électrique" to describe the active agent of a battery.This is called the "electromotive force" in English.
Around 1830, Michael Faraday established that chemical reactions at each of two electrode–electrolyte interfaces provide the "seat of emf" for the voltaic cell. That is, these reactions drive the current and are not an endless source of energy as the earlier obsolete theory thought. In the open-circuit case, charge separation continues until the electrical field from the separated charges is sufficient to arrest the reactions. Years earlier, Alessandro Volta, who had measured a contact potential difference at the metal–metal interface of his cells, held the incorrect opinion that contact alone was the origin of the emf. It is independent of size of the cell but depends on the nature of the electrolyte used.
Notation and units of measurement
Electromotive force is typically denoted by the symbol . It represents the energy provided by a source per unit electric charge. The standard unit of emf in the International System of Units is the volt .In a device without internal resistance, if an electric charge passing through that device gains an energy via work, the net emf for that device is the energy gained per unit charge:. Like other measures of energy per charge, emf uses the SI unit volt, which is equivalent to a joule per coulomb.
Electromotive force in electrostatic units is the statvolt.
Formal definitions
a source of emf that is open-circuited, a charge separation occurs between the negative terminal N and the positive terminal P.This leads to an electrostatic field that points from P to N, whereas the emf of the source must be able to drive current from N to P when connected to a circuit.
This led Max Abraham to introduce the concept of a nonelectrostatic field that exists only inside the source of emf.
In the open-circuit case,, while when the source is connected to a circuit the electric field inside the source changes but remains essentially the same.
In the open-circuit case, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf.
Expressed mathematically:
where is the conservative electrostatic field created by the charge separation associated with the emf, is an element of the path from terminal N to terminal P, denotes the vector dot product, and is the electric scalar potential.
This emf is the work done on a unit charge by the source's nonelectrostatic field when the charge moves from N to P.
When the source is connected to a load, its emf is just
and no longer has a simple relation to the electric field inside it.
In the case of a closed path in the presence of a varying magnetic field, the integral of the electric field around the closed loop may be nonzero.
Then, the "induced emf" in the loop is:
where is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary, but stationary, closed curve through which there is a time-varying magnetic flux, and is the vector potential.
The electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative.
That is, the "induced emf" is not a "voltage" in the sense of a difference in the electric scalar potential.
If the loop is a conductor that carries current in the direction of integration around the loop, and the magnetic flux is due to that current, we have that, where is the self inductance of the loop.
If in addition, the loop includes a coil that extends from point 1 to 2, such that the magnetic flux is largely localized to that region, it is customary to speak of that region as an inductor, and to consider that its emf is localized to that region.
Then, we can consider a different loop that consists of the coiled conductor from 1 to 2, and an imaginary line down the center of the coil from 2 back to 1.
The magnetic flux, and emf, in loop is essentially the same as that in loop :
For a good conductor, is negligible, so we have, to a good approximation,
where is the electric scalar potential along the centerline between points 1 and 2.
Thus, we can associate an effective "voltage drop" with an inductor, and consider it as a load element in Kirchhoff's voltage law,
where now the induced emf is not considered to be a source emf.
This definition can be extended to arbitrary sources of emf and paths moving with velocity through the electric field and magnetic field :
which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.
The term
is often called a "motional emf".
In (electrochemical) thermodynamics
When multiplied by an amount of charge the emf yields a thermodynamic work term that is used in the formalism for the change in Gibbs energy when charge is passed in a battery:where is the Gibbs free energy, is the entropy, is the system volume, is its pressure, and is its absolute temperature.
The combination is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature to the change in entropy when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is:
If a mole of ions goes into solution the charge through the external circuit is:
where is the number of electrons/ion, and is the Faraday constant and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:
where is the enthalpy of reaction. The quantities on the right are all directly measurable. Assuming constant temperature and pressure:
which is used in the derivation of the Nernst equation.
Distinction with potential difference
Although an electrical potential difference is sometimes called an emf, they are formally distinct concepts:- Potential difference is a more general term that includes emf.
- Emf is the cause of a potential difference.
- In a circuit of a voltage source and a resistor, the sum of the source's applied voltage plus the ohmic voltage drop through the resistor is zero. But the resistor provides no emf, only the voltage source does:
- * For a circuit using a battery source, the emf is due solely to the chemical forces in the battery.
- * For a circuit using an electric generator, the emf is due solely to a time-varying magnetic forces within the generator.
- Both a 1 volt emf and a 1 volt potential difference correspond to 1 joule per coulomb of charge.
The electric charge that has been separated creates an electric potential difference that can be measured with a voltmeter between the terminals of the device, when not connected to a load. The magnitude of the emf for the battery is the value of this open-circuit voltage.
When the battery is charging or discharging, the emf itself cannot be measured directly using the external voltage because some voltage is lost inside the source.
It can, however, be inferred from a measurement of the current and potential difference, provided that the internal resistance already has been measured:
"Potential difference" is not the same as "induced emf".
The potential difference between two points A and B is independent of the path we take from A to B.
If a voltmeter always measured the potential difference between A and B, then the position of the voltmeter would make no difference.
However, it is quite possible for the measurement by a voltmeter between points A and B to depend on the position of the voltmeter, if a time-dependent magnetic field is present.
For example, consider an infinitely long solenoid using an AC current to generate a varying flux in the interior of the solenoid.
Outside the solenoid we have two resistors connected in a ring around the solenoid.
The resistor on the left is and the one on the right is, they are connected at the top and bottom at points A and B.
The induced voltage, by Faraday's law is, so the current. Therefore, the voltage across the resistor is and the voltage across the resistor is, yet the two resistors are connected on both ends, but measured with the voltmeter to the left of the solenoid is not the same as measured with the voltmeter to the right of the solenoid.