Why does induced current in loop vary twice with rotation of coil?

[trelek2]

A square loop of wire of side a is rotating with frequency \omega in a magnetic field. I understand that at time t, a magnetic field B=B_{0}sin\omega t passes through the loop. But why does the current induced in the loop vary twice with the frequency of rotation? What is the expression of the current induced?

 

[GRDixon]

A square loop of wire of side a is rotating with frequency \omega in a magnetic field. I understand that at time t, a magnetic field B=B_{0}sin\omega t passes through the loop. But why does the current induced in the loop vary twice with the frequency of rotation? What is the expression of the current induced?

The emf induced around the contour of the coil is proportional to the rate at which the magnetic flux through the coil varies in time. This variation undergoes two min/max/min cycles per rotation of the coil. Hence current in the coil pulses twice per revolution. The current induced can be calculated from Maxwell's equation for the curl of E, plus Ohm's law.