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A particle of mass 10^(-3) kg and charge...

A particle of mass `10^(-3)` kg and charge 1.0 c is initially at rest At time t=0 the paritcle comes under the influence of an electric field `hat (E )(t)=E_(0) sin omega t hat(i)` where `E_(0) =1.0 N C^(-1)` and `omega =10^(3) rad s^(-1)` consider the effect of only the electrical force on the particle .Then the maximum speed in m `s^(-1)` attained by the paritcle at subsequent times is ______________

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The correct Answer is:
2
`F = qE = qE_(0) sin omega t therefore " " a = (qE_(0))/(m) sin omega t :" " int_(0)^(v) dv = int_(0)^(t) = (qE_(0))/(m) sin omega t dt`
`rArr V = (qE_(0))/(m) [(-cos omega t)/(omega)]_(0)^(t) " " rArr V = (qE_(0))/( omega m) ( 1 - cos omega ) therefore " " V_(max) = 2 (qE_(0))/(omega m) = 2 (l(l))/((l0^(3)) l0^(-3))= 2m//s`
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