A thin uniform conducting disc of radius r and mass m rests on a horizontal tabletop where a uniform magnetic field of induction B pointing vertically upwards exists. Coefficient of friction between the disc and the tabletop is $\mu$. Two points $P_1$ and  $P_2$ on the rim of the disc are connected with two flexible wires, which facilitate a current to flow through the disc. The contact points $P_1$ and  $P_2$  subtend an angle $\theta$ at the centre of the disc. Minimum current must flow through the disc so that it begins to slide is  $\frac{\mu mg}{xBr\sin (\theta /y)}$. Find x + y? Acceleration of free fall is g.