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A paraticale of mass m and charge (-q) entersthe region between the two charged plates initially movingalong x-axiswith speed v_(x). The lengthof plateis L and a uniform electricfieldE is maintainedbetweenthe plates. Show that the verticale deflection of the particleat the faredge of the plate is qEL^(2)//(2m v_(x)^(2)). Comparethis motionwith motion of a projectille in gravitional field. |
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Answer» Solution :In the verticledirection, initial velocity, `u = 0` accleration, `a = (F)/(m) = (qE)/(m)` , deflection,`s = y = ?` , time takento crossthe FIELD, `t = ("distance")/("velocity") = (L)/(v_(x))` This is becausevelocity along the horizonatalis constant. From `s = ut + (1)/(2) at^(2) , y = 0 + (1)/(2) ((qe)/(m)) ((L)/(v_(x)))^(2) , y = (qE L^(2))/(2m v_(x)^(2))` Comparison shows that THECASE is exactly similarto motion a horizontalprojectile in a graviationalfiled, where we find `y = (1)/(2) g t^(2)` |
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