A particle of charge q and mass m starts moving from the origin under the action of an electric field `vec(E) = E_(0)hat(i)` and a magnetic field `vec(B) = B_(0)hat(i)` with a velocity `vec(v) = v_(0)hat(j)`. The speed of the particle will become `2v_(0)` after a time

Options

A. `t =2 mV_(0)`
B. `t= ( 2Bq)/( mV_(0))`
C. `t= ( sqrt( 3) Bq)/( mV_(0))`
D. `t =(sqrt( 3) mV_(0))/(qE)`

Explanation

E is parallel to `overset( 1) (B) ` &`overset( 1) (V)` is perpendicular to both. Therefore, to path of the particle is a helix with increasing pitch. Speed of particle of at any timet is
`V = sqrt(V_(x)^(2) +V_(y)^(2) +V_(z)^(2))`, Here `V_(z)^(2) +V_(y)^(2) =V_(0)^(2)`
`V= 2V_(0) rArr V_(x) =sqrt(3) V_(0)` `:. t = (V_(x) )/(a_(x)) =( sqrt(3)V_(0))/( qE//m) rArr t= (sqrt(3) m V_(0))/(qE)`