The basic process of generating currents with magnetic fields is called induction; this process is also called magnetic induction to distinguish it from charging by induction, which uses the electrostatic Coulomb force.
The emf may be defined as the rate at which energy is drawn from a source per unit current flowing through a circuit.
Going back to our sail analogy, it would be proportional to the force of the wind on the sail. It is called the magnetic flux