I think the diagrams of an AC generator and a DC generator are not quite correct. I believe that the generated EMF changes direction, and is momentarily zero, when the rotating magnet points directly at the coils, not when it's perpendicular to them.

 

Draw the magnetic field lines. When they are perpendicular to the coil, there is no induced voltage.

 

Draw the magnetic field lines. When they are perpendicular to the coil, there is no induced voltage.

But the induced EMF doesn't depend on the magnetic flux itself, but rather on how quickly the flux is changing.

 

If the EMF induced in the coil depended directly on the magnetic flux through the coil, you wouldn't need to rotate the magnet. Just set it up pointing at the coil, and leave it there. Lots of flux through the coil, that way. But the flux isn't changing. So that won't work.

 

If the EMF induced in the coil depended directly on the magnetic flux through the coil, you wouldn't need to rotate the magnet. Just set it up pointing at the coil, and leave it there. Lots of flux through the coil, that way. But the flux isn't changing. So that won't work.

...And what would be the change in flux if there is none?

 

...And what would be the change in flux if there is none?

It could be anything.

If the flux were zero at all times, then of course it wouldn't be changing. But if all you know is that the flux is zero at one particular time, that doesn't tell you anything about how fast it's changing. You also need to know what it was a short time ago, and what it will be a short time later.

For example, if it was negative a short time ago, and now is zero, and will be positive a short time later, then it's increasing, and the induced EMF will be in one direction. If it was positive a short time ago, and now is zero, and will be negative a short time later, then it's decreasing, and the induced EMF will be in the opposite direction.