Figure shows a metal ball of mass 50 kg and radius  $\frac{2}{\sqrt{\pi }}m$   is placed on an insulating uncharged stand. In space, an upward uniform electric field  $5\times {10}^{5}N/C$  is switched on. A stream of light ions is incident on the ball from left side at a speed  $2\times {10}^{6}m/s$  as shown in figure. If charge on the ball at t = 0 was zero and incidence of ions starts at this moment, find the time in seconds at which ball will be lifted up from the stand. The charge density of ion beam is  $5\times {10}^{-12}C/m^3.$  Assume that all charge incident on the ball is absorbed. (Take $g=10m/s^2$  )