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Question -

A particle of mass andcharge (−q) enters the region between the two charged plates initiallymoving along x-axis with speed vx (like particle 1in Fig. 1.33). The length of plate is and an uniformelectric field is maintained between the plates. Show thatthe vertical deflection of the particle at the far edge of the plate is qEL2/(2m).



Answer -

Charge on a particle ofmass m = − q

Velocity of the particle= vx

Length of the plates = L

Magnitude of the uniformelectric field between the plates = E

Mechanical force, F =Mass (m) × Acceleration (a)

Therefore, acceleration, 

Time taken by the particleto cross the field of length is given by,

t

In the vertical direction,initial velocity, u = 0

According to the thirdequation of motion, vertical deflection of the particle canbe obtained as,

Hence, vertical deflectionof the particle at the far edge of the plate is

. This is similar to the motion of horizontalprojectiles under gravity.

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