A search coil of $N$ turns is rotated at a constant angular frequency $\omega$ in a uniform magnetic field. The magnetic flux linkage through the coil varies with time $t$ according to the equation:

$$N\Phi ={\Psi }_0\cos (\omega t)$$

where ${\Psi }_0$ is the maximum flux linkage and $T$ is the period of rotation of the coil.

At what time $t>0$ does the magnitude of the induced electromotive force (emf) in the coil first equal half of its maximum value?