Answer
a) The magnetic flux through the coil is proportional to $cos(\omega t)$, while the induced emf is proportional to $sin(\omega t)$. The max emf occurs when $sin(\omega t)=1$, i,e $(\omega t)=90^{\circ}$. At this time $cos(\omega t)=0$.
b) As in part (a), the flux is a maximum when $cos(\omega t)=1$, i.e. $(\omega t)=0$. Also, $sin(\omega t)=0$. The emf is zero. The basic is that the flux and the emf are always $90^{\circ}$ out of phase. when one is at maximum the other is zero.
Work Step by Step
a) The magnetic flux through the coil is proportional to $cos(\omega t)$, while the induced emf is proportional to $sin(\omega t)$. The max emf occurs when $sin(\omega t)=1$, i,e $(\omega t)=90^{\circ}$. At this time $cos(\omega t)=0$.
b) As in part (a), the flux is a maximum when $cos(\omega t)=1$, i.e. $(\omega t)=0$. Also, $sin(\omega t)=0$. The emf is zero. The basic is that the flux and the emf are always $90^{\circ}$ out of phase. when one is at maximum the other is zero.
