Assume the width and height of the loop are d and h.<br />The magnetic flux in the loop is <img class='tex' src="/demolab/smf/teximages/9/6/1/96112ada245302c7c5f15321302f985b.png" alt="\Psi =\int \vec{B}\cdot d\vec{A}= \vec{B}\cdot \vec{A(t)} =B d h \cos\omega t" /><br /><br />So the induced emf <img class='tex' src="/demolab/smf/teximages/6/7/0/670199385c33664aa22a549829356a0e.png" alt="\epsilon= -\frac {d\Psi}{dt}=B (dh) \omega \sin\omega t=BA_{max} \omega \sin\omega t" /><br />