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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?

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  • $\begingroup$ 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. $\endgroup$ – CuriousOne Apr 26 '15 at 19:42
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B fields can not create emf except when there is changing magnetic flux, from Faraday's law. In practice a resistance would be needed unless the material was superconductive in which case all the B field (i.e. magnetic flux density) is expelled from the conductor. The E field times a charge integrated over a path will give the emf or voltage and unless superconductivity is present a resistance is present. If superconductive an impedance from Lenz's law will limit the current.

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