A particle having charge that of an electron and mass 1.6x 10-30 kg is projected with an initial speed u at an angle 45° to the horizontal from the lower plate of a parallel plate capacitor as shown in figure. The plates are sufficiently long and have separation 2 cm. The maximum value of velocity of particle not to hit the upper plate is W×106 m/s. Take electric field between the plates = 103 V/m directed upward. The value of W is________

Resolving the velocity of particle parallel and perpendicular to the plate. Force on the charged particle in downward direction normal to the plate = eE∴Acceleration a=eEm, where m is the mass of charged particle.The particle will not hit the upper plate, if the velocity component normal to plate becomes zero before reaching if, i.e.,0=u⊥2−2ay, with y≤d where d, distance between the plates.∴ Maximum velocity for the particle not to hit the upperplate (for this y= d=2 cm)u⊥=2ay=2×1.6×10−19×103×2×10−21.6×10−30=2×106m/sumax=u⊥/cos⁡45∘=22×106m/s=8×106m/s