Electromotive Force

Electromotive force is a fundamental concept in electromagnetism and electronics, describing the energy transferred to an electric circuit per unit charge. Although termed a “force”, it is not a mechanical force but an energy-per-charge quantity measured in volts. EMF reflects the ability of a source or physical process to drive electric charge around a complete circuit. It arises from diverse mechanisms, including chemical reactions in electrochemical cells, electromagnetic induction in generators, thermal gradients, photon absorption in photovoltaic devices and other energy-conversion processes.

Overview and Physical Interpretation

Electromotive force, commonly abbreviated emf, represents work done on an electric charge by a source’s internal mechanisms. It can be viewed through a hydraulic analogy: just as a pump imparts mechanical work to push water through a system, an emf source performs work on electric charges to maintain current flow. EMF is therefore associated with energy transformation, not with conventional forces.
The emf of a device is distinct from electric potential difference, although it is frequently measured as a voltage. EMF is the energy supplied per unit charge by the nonelectrostatic forces within a source, while voltage represents the difference in electric potential between two points in a circuit. A device that supplies emf becomes a voltage source when connected to an external load.
In the case of a two-terminal device described using Thévenin’s theorem, the emf corresponds to the open-circuit voltage across the terminals. Once connected to a load, this emf drives current through the external circuit, with internal resistance accounted for in the device’s equivalent model.

Devices and Phenomena Producing EMF

A wide range of systems generate electromotive force through different physical processes:

• Electrochemical cells, in which chemical reactions create charge separation at electrode–electrolyte interfaces.
• Thermoelectric devices, generating emf from temperature differences.
• Solar cells and photodiodes, which convert photon energy into electrical energy.
• Electric generators, where motion in a magnetic field induces emf by electromagnetic induction.
• Inductors and transformers, in which time-varying magnetic flux creates induced voltage.
• Van de Graaff generators, which use mechanical charge transport.
• Geomagnetic processes, where fluctuations in Earth’s magnetic field induce large-scale currents.

In nature, emf arises when magnetic field lines shift relative to conductors. During geomagnetic storms, for example, variations in Earth’s magnetic field induce currents in long transmission lines.

EMF in Batteries and Generators

In electrochemical cells, the separation of charge between terminals originates from redox reactions at the electrodes. These reactions convert chemical potential energy into electromagnetic energy and continue until the electric field established by separated charges opposes further separation in the open-circuit state. When a device is connected to a load, the internal chemical processes continue and the emf drives current through the circuit.
In electric generators, a time-varying magnetic field induces an electric field inside the machine. This generates a potential difference between terminals. Charge separation occurs until an internal electric field forms that prevents additional separation in the open-circuit condition. When an external load is attached, the induced emf drives current by converting mechanical work into electrical energy.

Historical Background

Alessandro Volta introduced the term force motrice électrique around 1801 to describe the operating principle of his voltaic cell. By the 1830s, Michael Faraday established that chemical reactions at electrode–electrolyte boundaries were the true source of the cell’s emf, contradicting earlier theories that attributed emf solely to contact potentials between metal interfaces.
Faraday’s experimental work showed that charge separation continues only until the resulting electric field is strong enough to oppose further chemical action. This recognition anchored emf as an energy-transformation concept within early electrochemistry and laid the foundation for later analytical treatments.

Notation and Units

Electromotive force is typically denoted by the script symbol 𝓔. In the International System of Units, its unit is the volt (V), equivalent to one joule per coulomb. For a charge q gaining energy W while moving through a device free of internal resistance, the emf is the ratio:

• Energy per unit charge, expressed as W/q, conveys the device’s energy-supplying capacity.

In the electrostatic cgs system, emf is measured in statvolts, equal to one erg per electrostatic unit of charge.

Formal Definitions and Internal Fields

Within an open-circuited emf source such as a battery, charge separation produces an electrostatic field pointing from the positive terminal to the negative. To maintain current when a circuit is completed, a nonelectrostatic internal field must act to push charge against this electrostatic gradient. Max Abraham introduced the concept of this internal field to distinguish it from the conservative electrostatic field present between separated charges.
Mathematically, the emf between terminals N and P is expressed by a line integral of the nonelectrostatic electric field along a path inside the source. The integral equals the potential difference between the terminals in the open-circuit case. Only the field responsible for energy transfer to charges contributes; purely electrostatic contact potentials are excluded from the emf calculation, such as those that develop naturally in semiconductor junctions unless they arise directly from energy-absorbing processes like photon excitation in a solar cell.
When the source is connected to a load, the internal distribution of electric fields changes; however, the integral of the nonelectrostatic field still represents the emf delivered to the circuit.

EMF in Time-Varying Magnetic Fields

Electromotive force can also arise around a closed loop of conductor due to a changing magnetic flux. In such cases the closed-loop integral of the total electric field is non-zero, giving an induced emf. This phenomenon is governed by Faraday’s law of induction, which relates the induced emf to the negative time derivative of magnetic flux through the loop.
Because the electrostatic field contributes no net work around a closed path, only the nonconservative component of the electric field accounts for the induced emf. In inductive circuits where current produces magnetic flux, the self-inductance governs the relationship between changing current and induced emf. When the loop includes a specific coiled region with concentrated flux, that region is treated as an inductor, and its emf is localised accordingly.