Electromotive force (EMF)

Electromotive force — historically abbreviated EMF, a term coined by Volta in 1801 — is a measure of the energy per unit charge that some non-electrostatic source delivers to a circuit. The name is a misnomer twice over: EMF is not a force (it has units of volts, energy per charge, not newtons), and it is not always "electro" in origin. A chemical battery delivers EMF from redox reactions at its electrodes. A thermocouple delivers EMF from the Seebeck effect at a bimetallic junction. A solar cell delivers EMF from photons striking a p–n junction. An electromagnetic induction process delivers EMF from a changing magnetic flux. All of these are lumped together under the single quantity ε, the work per unit charge that the source does as charges are carried from its low-potential terminal to its high-potential terminal.

Mathematically, EMF is the closed-loop integral of the effective force per unit charge around the circuit: ε = ∮ (F_source/q) · dℓ. In electrostatics alone, this integral is zero — the electrostatic field is conservative, ∮E·dℓ = 0 — so a purely electrostatic circuit cannot drive a steady current. Something non-conservative has to enter: a battery's chemical field, an induction-induced non-conservative electric field (∇×E_ind = −∂B/∂t), a motional EMF from v×B acting on charges in a moving wire. EMF is a measure of that non-conservative contribution, and its existence is what drives currents.

In circuit analysis, EMF sources are drawn as idealised voltage sources — the ε's in Kirchhoff's voltage law around a loop, balancing the iR drops across resistors and the q/C voltages across capacitors. The "terminal voltage" measured across a real battery with current flowing differs from its EMF by the internal-resistance drop: V_term = ε − Ir. For a resistanceless source like an ideal induction coil, V_term equals ε exactly. The unit of EMF is the volt, the same unit used for electric potential differences — both are energy per charge — but the physical origins of the two are distinct and it is worth holding them apart conceptually.