An electron is projected with an initial speed 1.20 An electron is projected wit

Question

An electron is projected with an initial speed 1.20

An electron is projected with an initial speed 1.20 times 106m/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. 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

The electron travels 0.5 cm distance towards the plate and 2 cm in the direction of the original velocity.
Since the field is uniform, the elctron will experience uniform acceleration perpendicular to the plates.
Time of travel, t = 0.02 / (1.2x 10^6) s.
For vertical motion,
s = (1/2) at^2
=> (1/2) = (1/2) at^2
=> a = 1/t^2
Final vertical velocity = at = (1/t^2) * t = 1/t = 0.6 x 10^8 m/s
Resultant of constant horizontal velocity and final vertical velocity
= ?[ (1.2 x 10^6)^2 + (0.6 x 10^8)^2 ]
= 1.2 x 10^6 * ?[ 1 + 2500 ]
? 0.6x 10^8 m/s.

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