There is a uniform electric field $E$in the region between two parallel plates. A charged particle with a specific charges enters the region with a speed $u$, in a direction parallel to the plates. The length of each plate is $L$. The time taken to come out of the plates is $t$ and it suffers a vertical displacement $\Delta$. Also as the particle crosses the plates, its direction of motion changes by an angle $\theta$, then