A wire loop enclosing a semi-circle of radius a is located on the boundary of a uniform magnetic field of induction $\text{B}\left(\text{figure}\right)\text{.}$ At the moment  t= 0 the  loop is  set into roation with a constant angular acceleration $\text{α}$  about an axis  0  coinciding with a line of vector $\overrightarrow{B}$ on the boundary . If the emf induced in  the  loop as a function of time t is $e=-\frac{B{a}^2\alpha t}{x}$ Find the value of $x$.