Problem 3.292

A wire loop enclosing a semi-circle of radius $a$ is located on the boundary of a uniform magnetic field of induction $B$ (Fig. 3.80). At the moment $t=0$ the loop is set into rotation with a constant angular acceleration $\beta$ about an axis $O$ coinciding with a line of vector $\mathbf{B}$ on the boundary. Find the emf induced in the loop as a function of time $t$. Draw the approximate plot of this function. The arrow in the figure shows the emf direction taken to be positive.v