A 4.00wb/m^2 magnetic field is directed perpendicular to the plane of a 100 turns loops which has a radius of 0.100m.The loop is rotated through 180 degreein 0.200s

Determine the magnitude of induced emf in the loop

Recall Faraday's Law of electromagnetic induction, saying that induced emf is directly proportional to the rate of change of magnetic flux linked to it, or:

E = -\frac{d\phi}{dt}

Now, we know that the total magnetic flux at any instant through the coil is \phi = nAB\cos\theta

Where n is the number of turns in a coil, A is the area, B is the magnetic field and theta the angle which the coil does with the direction of the magnetic field (initially perpendicular, hence maximum flux and therefore, cos)

Now, the coil is rotating, and the angle theta at any time t is given by

\theta = \omega t

Where omega is the angular velocity.

This gives induced emf:

E = -\frac{d\(nAB \cos(\omega t)\)}{dt} = nAB \omega \sin(\omega t)

Can you attempt your question now? Post your workings and what you get :)