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 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 , 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.,
, with where d, distance between the plates.
Maximum velocity for the particle not to hit the upper
plate (for this y= d=2 cm)