An emf is induced in a coil when there is a change in magnetic flux, which requires either a change in the magnetic field strength or a change in the area of the coil. In a constant magnetic field, if the coil does not rotate, there is no change in flux and thus no induced emf. Rotating the coil alters the area exposed to the magnetic field, leading to a change in flux and the induction of emf. Additionally, moving a permanent magnet perpendicular to the coil generates an emf, while parallel movement does not. Understanding these principles clarifies the conditions necessary for emf induction in coils.