electromotive

Electromotive force, usually abbreviated emf, is the energy supplied per unit charge by a source of electric energy to drive current around a circuit. Measured in volts, emf is not a physical force acting on charges; it is a potential-energy term describing how much energy a source can impart to charges as they circulate.

Emf arises in sources such as chemical batteries, dynamo generators, and solar cells. The symbol ε (or E) is used for emf. In a practical circuit, the current I is governed by both the emf and the resistance of the source itself; for a source with internal resistance r, the terminal voltage is V = ε − I r.

Mathematically, emf around a closed loop can be expressed as the line integral of the electric field: ε = ∮ E · dl. This expresses the work done per unit charge by non-electrostatic forces as charges traverse the loop, including inside energy-conversion devices. In the presence of magnetic fields, additional forms occur: motional emf ε = ∮ (v × B) · dl, and more generally ε = −dΦ_B/dt when the magnetic flux Φ_B through the loop changes.

In DC circuit theory, emf is treated as the source term that drives current, while the actual voltage across circuit elements reflects drops due to resistance and impedance.