The rate of change of magnetic flux linkage with a rotating coil
Write down an equation for the flux through the coil as a function of angle.


$$\Phi =BNA\sin \theta$$  

where A is the area of the coil, N is the number of turns in the coil and theta is the angle between the B field and the plane that the coil lies in.


Differentiate the equation once with respect to angle. The result is the rate of change of flux through the coil as it rotates.


$$\frac{d\Phi}{d\theta} =BNA\cos \theta $$


Set the result equal to zero and solve for the angle.


$$0=BNA\cos \theta $$

$$\theta = 90, 270$$