Past exam of the physics 2 paper of the University of Oxford / 2019 / 4 / Solution

Let $\theta =\omega t+{\theta }_0$ be the angle between the coil's area normal and the magnetic field. Its magnetic flux linkage is $\Lambda =NB\pi r^2\cos \theta$. Consequently Faraday's law of induction givesThe sign refers to the winding orientation used to define the normal. The initial phase ${\theta }_0$ depends on the chosen time origin; one can set it to zero when the normal first points along $+x$. The minimum absolute value is zero, attained at $\theta =m\pi$: the coil's normal is parallel or antiparallel to the $x$-axis, and the plane of the coil is perpendicular to that axis. At this orientation the magnetic flux is extremal and its derivative with respect to time vanishes.