How to calculate the Induced Voltage Given Spinning Conducting Loop? Intro to Electromagnetics problem
From the perspective of the lines of flux, if the coil is at 90 degrees to these lines, the coils area is maximized i.e. the maximum number of lines of flux flow thru the coil and the induced emf would be maximum. If the plane of the coil were rotated 90 degrees to be in line with the lines of flux, the effective area of the coil (from the perspective of the lines of flux) is zero and there will be no induced emf.

At any point in between, the "effective area" changes as a sin(angle) function, where "angle" is 90 degrees when the coil is totally across the field lines and zero when it is in line.

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