(a) A deutron and an `alpha`-particle are placed in uniform electric field. Find the ratio of their accelerations.
(b) A charged particle `(q,m)` is placed in uniform electric field `E`. Find its kinetic energy after time `t`.
(c ) An electron `(-e , m)` is given velocity `v_(0)` along a uniform electric field `E`. After how much time , electron will return to its original position ?

Explanation

(a) Deutron : mass `2m` , charge `e`
`alpha`- particle : mass `4m`, charge `2e`
`(a_(d))/(a_(alpha)) = (e E //2m)/(2 eE //4m) = (1)/(1)`
(b) Acceleration of charged particle
`a = (qE)/(m)`
Velocity after time `t`
`v = u + at = 0 + (qE)/(m) t = (qEt)/(m)`
`K.E. K = (1)/(2) mv^(2) = (q^(2) E^(2) t^(2))/(2m)`
(c ) Retardation of electron
`a = (eE)/(m)`
The electron will stop after time
`v = u - at rArr 0 = v_(0) - (eE)/(m) t`
`t = (mv_(0))/(eE)`
The electron will return to `O` after time
`T = 2t = (2mv_(0))/(eE)`