The word change means you have to know before and after.
Case1
If I turn the coil 30 degrees. The change in flux is flux after - flux before. It is never the flux at the 30 degree position.
Since flux is BA (before) and BAcos30 (after) the change is (1-0.866)BA which is 0.134 BA. Rate of change of flux is dividing the change by time taken. If the time taken is 0.1s , the induced e.m.f = 1.34 NBA= 1.34(50 x 0.18T x 0.02)= 0.24 V
Case2
A 180 degrees turn would mean a change of + BA to -BA which amount to 2BA. (Similar to the change of momentum of 2 mv when the ball bounces back). The induced e.m.f = 2NBA/0.1s = 3.6 V
These values are average induced e.m.f.
Case 3(with ref. to case 2)
The maximum induced e.m.f of coil = BANw where w the angular velocity can be calculated as 180(pi rad) /0.1s = 31.4 rad per s.The maximum induced emf = 5.65 V
pic taken from http://www.rfcafe.com/references/electrical/Electricity
