# Does a correct application of the Lorentz force to find induced emf need resistance?

The emf between two points is defined as the work done per unit charge on the charge when moved (along a given and stated path) between those two points. To find the emf due to a magnetic field the usual integral is (considering a closed coil): $$\text{emf}=\int{ \vec v \times \vec B \cdot d \vec r}$$ But should it not be:
$$\text{emf}=\int{ (\vec v \times \vec B +\vec F) \cdot d \vec r}$$ where $\vec F$ is the force on the particles due to resistance or is this taken care for in the self inductance of the coil?

• A "resistive" force would typically depend on the velocity of the particles, not just their position. What you are looking at is the combination of an emf and the work done by a general (not necessarily conservative) force. The latter is not enough to characterize "resistance" in the sense of electrodynamics (maybe I misunderstand your question?). The self-inductance of a coil depends on the magnetic material inside its field volume, so, yes, there is a material dependent property there, but it's usually expressed by using magnetization rather than charge displacement against restoring forces. Apr 26, 2015 at 19:42