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Question -

A particle of mass m 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 L and an uniformelectric field E 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 L is given by,

t

In the vertical direction,initial velocity, u = 0

According to the thirdequation of motion, vertical deflection s 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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