AC generator -- Understanding coil voltages as function of position

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In an AC generator, voltage is maximized when the coil is aligned parallel to the magnetic field, as this orientation results in zero magnetic flux through the coil. Conversely, the voltage drops to zero when the coil is perpendicular to the magnetic field, where the magnetic flux is at its maximum. The key to understanding this phenomenon lies in the change of flux; voltage is induced by the rate at which the coil cuts through magnetic flux lines. The coil experiences the greatest change in flux when moving perpendicular to the magnetic field lines, leading to maximum induced voltage. This relationship highlights the importance of coil orientation in generating electrical power.
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Homework Statement


In an ac generator
Voltage is maximum when the coil is parallel to the direction of magnetic field (B)
Voltage is minimum (0) when the coil is perpendicular to the direction of magnetic field (B)

I'm trying to understand why.

Homework Equations

The Attempt at a Solution


A voltage is induced when there is a change in flux.
When the coil is parallel to the magnetic field the flux going through it is 0.
When the coil is perpendicular to the magnetic field the flux going through it is maximum.

I understand that it is the CHANGE in flux that causes a current to be induced. But I am still a bit confused about WHY the viltage is maximum when the coil is parallel to the field
 
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When are the flux lines being cut with the greatest speed? When the loop is moving parallel or perpendicular to the flux lines?
 

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