a coil starts perpendicular to a magnetic field of 0.365 tesla , it has a length of 0.15 cm and a height of 0.25 cm , it rotates with a frequency of 1800 rotation / min . it also has 30 turns
calculate the mean induced Emf during quarter a rotation
emf = rate of change of magnetic flux / sec
The Attempt at a Solution
i have already solved the problem , during quarter a rotation , the magnetic field goes from 0.365 to 0 because in a quarter rotation , the coil goes from 90 degrees to 0 degrees with the field .
a quarter rotation takes a time of 1/30 /4 = 1/120 sec.
but i dont really want to find that , i want to use calculus to find the exact rate of change at a particular moment
now weber = area * field * sin theta
where theta is the angle between the coil and the field
now the rate of change of weber = area * field * cos theta * rate of change of theta .
when it takes a quarter of rotation , the theta will be 0 so cos theta = 1 , but how do i exactly find the rate of change of theta ?
if it takes 360 degrees / (1/30) seconds , is that the rate of change of theta ? , how do you exactly find dtheta / dt ?