Help Me Understand: Magnetic Flux Problem Solution

[pyroknife]

I'm having problems understanding this solution (attached.) I don't understand how they got 2*magnetic flux out of the change in the magnetic flux in the bottom of the attachment. Can someone explain that to me?

 

[sandy.bridge]

Essentially there are two periods of rotation that need to be considered. For the first interval, the area is decreasing from its maximum to minimum value (relative to the perpendicular B field). Moreover, an interval follows such that the area that the flux is passing through is increasing from its minimum to maximum value.

 

[pyroknife]

Essentially there are two periods of rotation that need to be considered. For the first interval, the area is decreasing from its maximum to minimum value (relative to the perpendicular B field). Moreover, an interval follows such that the area that the flux is passing through is increasing from its minimum to maximum value.

Thanks I figured it would be something like that, but I don't understand why there are 2 periods, is this kind of a fixed case?

 

[sandy.bridge]

Visualize the coil being flipped over. At first, the flux lines are passing through a maximum area, and as time proceeds, the area decreases (since the coil is being flipped, less flux is passing through) until it reaches its minimum (no flux). It then starts to increase its area as it continues to be flipped.

Take a piece of paper and flip it. Assume the B field is pointing down. As you are flipping the piece of paper, the area which the b field passes through decreases to a minimum when its plane is parallel to the B vectors, then increases until it is at a 90 degree angle.