Magnetic flux linkage and area as a vector

[Jimmy Jazz]

Homework Statement

A circular coil of diameter 24 mm has 40 turns. The coil is placed in a uniform magnetic field of flux density 85 mT with its plane perpendicular to the field lines.

a) i Calculate the area of the coil

ii The flux linkage through the coil.

b) The coil was reversed in a time of 95 ms.

Calculate

i the change of flux linkage through the coil.

ii the magnitude of the induced emf

Homework Equations

Flux linkage = NBA
EMF = rate of change of flux linkage

The Attempt at a Solution

Part a I am ok with ai) area = 4.5x10^-4 and flux linkage is BNA = 1.53 mWb
In part b I struggled to see why the answer was 3.06 mWb and not a change of 1.53 to zero as it rotated.
my logic being that it changes from 1.53 to zero as it rotated for the first 90 degrees then back to 1.53.

I remember reading area is a vector so if this is true does it mean the flux linkage is changing from 1.53 mWb to -1.53 mWb, This would give me the correct answer in the back of the textbook.

Is there anyway of seeing this without knowing that area is a vector as this is not in the textbook as a principle taught on my course.

Thanks you for any help
Jimmy

 

[Jimmy Jazz]

I have just made the connection with my data sheet and the formula BANcos(theta)
Then the angle between a normal to the coil and the field with give the necessary change of sign on rotation through 180 degrees.
Is there any way of simply explaining why the area that the field lines cut changes as a cos function as the coil is rotated?