1.33 A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along the x-axis with speed vx (like particle 1 in Fig. 1.33). The length of the plate is Land a uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is .
Compare this motion with the motion of a projectile in the gravitational field discussed in Section 4.10 of the Class XI Textbook of Physics.
Charge on a particle of mass m =-q
Velocity of the particle =
Length of the plates = L
The magnitude of the uniform electric field between the plates = E
Mechanical force, F = Mass (m) x Acceleration (a)
Time taken by the particle to cross the field of length L is given by,
In the vertical direction, initial velocity, u = 0
According to the third equation of motion, vertical deflection s of the particle can be obtained as
Hence, vertical deflection of the particle at the far edge of the plate is . This is similar to the motion of horizontal projectiles under gravity.
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