When a loop rotating in a uniform magnetic field.<br />The magnetic flux is changing which will induce electric field along the loop (produce voltage).<br />If the loop is rotating with constant angular velocity \omega . (The angle is \omega t)<br />The magnetic flux in the loop will be <img class='tex' src="/demolab/smf/teximages/7/2/9/729d2c5b7d077846a82e566b896e43fd.png" alt="\Psi =\int \vec{B}\cdot d\vec{A}= B A cos(\omega t)" /><br />So the induced emf <img class='tex' src="/demolab/smf/teximages/6/d/c/6dc0a65532956de7b64a4cc83d870879.png" alt="= -\frac {d\Psi}{dt}=B A \omega sin(\omega t)" /><br /><br />The following simulation show how it works dynamically.