Maximum EMF in a rotating coil, in an AC generator?

[ducks_1234]

Homework Statement

Im currently in my last year of high school, and I'm writing a report on AC generators. I've heard a number of different things from different sources. When the coil is perpendicular to the magnetic field, maximum magnetic flux is flowing through the coil. This is then at a minimum when the coil is parallel to the field.

EMF is induced when there is a rate of change of magentic flux through the loop. Why then is EMF at a maximum when the coil is parallel? i.e it was turned from being perpendicular to now being parallel.

Any help would be greatly appreciated!

Homework Equations

EMF = $$\Delta$$ ( $$\phi$$2 - $$\phi$$1) / $$\Delta$$ t

The Attempt at a Solution

My attempt is my failed understanding of the concept.

 

[G01]

The EMF depends not on the flux through the coil, but instead on the rate of change of the flux through the coil, as you said.

When the coil is parallel the flux may be 0, but the rate of change of the flux is not zero. At that point, the flux is increasing at it's fastest rate. This is why the EMF is at its highest positive value at this point.

Does this make sense?

(In order to actually compute the rate of change of the flux in this problem, you'll need calculus, and more information about how the coil is rotating.)