A Particle of Mass M And Charge (−q) Enters the Region Between the Two Charged Plates Initially Moving Along X-axis with Speed Vx - Physics

A particle of mass and charge (−q) enters the region between the two charged plates initially moving along x-axis with speed vx (like particle 1 in Fig. 1.33). The length of plate is and an uniform electric field is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL2/ (2mv_s^2).

Solution

Charge on a particle of mass m = − q

Velocity of the particle = vx

Length of the plates = L

Magnitude of the uniform electric field between the plates = E

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

a=F/m

However, electric force, F=qE

Therefore, acceleration, a=(qE)/m                 ...(1)

Time taken by the particle to cross the field of length is given by,

t="lenght of the plate"/"Velocity of the particle"=L/v_x     ...(2)

In the vertical direction, initial velocity, u = 0

According to the third equation of motion, vertical deflection of the particle can be obtained as,

s=ut+1/2at^2

s=0+1/2("qE"/m)(L/v_x)^2

s=(qEL^2)/(2mV_x^2)          ...(3)

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

(qEL^2)/(2mV_s^2). This is similar to the motion of horizontal projectiles under gravity.

Notes

Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.

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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 1 Electric Charge and Fields
Q 33 | Page 50