An electron is projected with an initial speed = 1.50 An electron is projected w

Question

An electron is projected with an initial speed = 1.50 An electron is projected with an initial speed = 1.50 An electron is projected with an initial speed = 1.50 times 106 m/s into the uniform field between the parallel plates in the figure (Figure 1) . Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. The distance between the plates is 1 cm and they are 2 cm long. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. Suppose that in the figure (Figure 1) the electron is replaced by a proton with the same initial speed . Would the proton hit one of the plates?

Explanation / Answer

vo = vox =1.5.106 m/s ; me = 9.1.10-31 kg

L = 2 cm = 2.10-2 m ; qe = 1.6.10-19 C

d = 1 cm = 1.10-2 m

y = 0.5 d = 5.10-3 m

Analysis motion on horisontal ( x axis )

L = vox.t

t = L/vox................(1)

Analysis motion on vertical ( y axis )

FN = FE with FN = me.a and FE = qe.E

me.a = qe.E

a = qe.E/me................(2)

y = 0.5.a.t2 ...............(3)

subsitute eq(1) and (2) into eq(3) we get :

y = 0.5 (qe.E/me).(L/vox)2

E = (2.y.me.vox)/(qe.L2)

E = 414.1511111111111 N/C

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