A wire is bent as a parabola $y=\text{c}{x}^2$ is located in a uniform magnetic field of magnitude B perpendicular to the xy plane as shown. At the instant t = 0 a long metal rod starts translating from the vertex of the parabola with a constant acceleration a along positive y–axis. The induced emf across the points of contact of the rod with the wire is given by $\epsilon =2\text{By}\sqrt{\frac{\text{ka}}{\text{c}}}$ ; where k = ___.