# Induced EMF on a rotating coil

1. Dec 2, 2013

### B4ssHunter

1. The problem statement, all variables and given/known data

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

2. Relevant equations
emf = rate of change of magnetic flux / sec

3. 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 ?

2. Dec 3, 2013

θ=ωt

3. Dec 3, 2013

### rude man

Not right. See below.

The way you described the orientation of the field, it's weber = area x field x cos(theta). So let's be scientific and say ψ = AB cosθ. I use ψ since phi never shows up in my toolbar. θ is the angle between the B field and the normal to the coil. You have to be precise when you say " ... a coil starts perpendicular to a magnetic field ... ". That could mean that two of the four sides of the coil are perpendicular to the field. Anyway, we start at θ = 0 and go to θ = π/4.

So, what is the emf induced in the coil at any moment? Hint: Faraday plus hint of post #2.

And, 1800 rotations per minute is how much dθ/dt?