Electric generators and alternators operate by induction using a coil and a permanent magnet. In a generator, an emf is induced in a coil by rotating the permanent magnet relative to the coil. In the alternator in your car, the coil rotates and the magnets are fixed - it's the same process. If you flip a coil in a uniform magnetic field, for example, the flux precisely changes sign, so an emf is induced in the coil. We saw an example of this on Tuesday.
Induction plays a key role in the aurora, as explained further below.
One of the simpler ones is the magnetic bottle. Recall that field density is related to the density of field lines, so the field is stronger at the ends than in the middle. Let the uniform field in the middle of the diagram be oriented along the z-axis. Bm near the ends of the diagram is larger than Bo and will be discussed shortly. We have learned that this particle will spiral as it drifts toward the high-field region.