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=(2mv_0)/(qE)`
B. `t=(2Bq)/(mv_0)`
C. `t=(sqrt3Bq)/(mv_0)`
D. `t=(sqrt2mv_0)/(qE)`

Answer

d

Explanation

`vecE` is parallel to `vecB` and `vecv` is perpendicular to both. Therefore, path of the particle is a helix with increasing pitch. Speed of particle at any time t is
`v=sqrt(v_x^2+v_y^2+v_z^2)....(i)`
Here, `v_y^2+v_z^2=v_0^2`
and `v=2v_0 implies v_x=sqrt3v_0`
`v_xa_xt implies sqrt3v_0=(qE)/mt implies t=(sqrt3mv_0)/(qE)`