An electron is projected with an initial speed 1.90×106 {\ m m/s} into the unifo

Question

An electron is projected with an initial speed 1.90×106 { m m/s} into the uniform field between the parallel plates in the figure . 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 two plates is .01m and the length of the plates is .02m

If the electron just misses the upper plate as it emerges from the field, find the speed of the electron as it emerges from the field?

Explanation / Answer

Data is missing in the problem, such as separation between plates and length of the field So i am giving hint: Let us consider X = length of the plates y = separation between plates vo = initial velocity Time taken to reach upper end of the plate t = X / vo The vertical distance travelled y = 0.5 a t^2 = 0.5 a (X/vo)^2 ==> a = 2 y (Vo/X)^2 Therefore Vf = Vo + a t = Vo + [2 y (Vo/X)^2 ] * (X / Vo) = Vo + (2yVo / X) Therefore Vf = Vo + (2yVo / X)

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