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**Concept of an "area vector" when finding magnetic flux**

Hello,

I'm currently learning basic Electromagnetic Induction, specifically induced emf in a loop. According to my textbook, magnetic flux is defined as:

[tex]\Phi[/tex] = BA cos [tex]\theta[/tex]

Given that the field is uniform and is traveling through a constant area (the loop in this case).

The textbook then says [tex]\theta[/tex] is defined as the angle between the area vector (A) and magnetic field (B). The book's only explanation of an area vector is "Its direction is normal to the loop's plane, and its magnitude is equal to the area of the loop."

My question is, why do we measure the angle with respect to the area vector, and not the plane of the loop? In other words, why do we say magnetic flux is defined as the above equation instead of:

[tex]\Phi[/tex] = BA sin [tex]\theta[/tex] ?

Where [tex]\theta[/tex] is defined as the angle between the loop and the magnetic field.

Thanks in advance...

-Rob-