A charged particle of specific charge (charge/mass) `alpha` released from origin at time `t=0` with velocity `vec v = v_0 (hat i + hat j)` in uniform magnetic field `vec B = B_0 hat i.` Coordinates of the particle at time `t= pi//(B_0 alpha)` are

Options

A. `(v_0 / (2B_0 alpha) ,(sqrt 2v_0)/(alpha B_0), (-v_0)/ (B_0 alpha) )`
B. `(v_0 / (2B_0 alpha) ,0, 0 )`
C. `(0 ,(2v_0)/(B_0 alpha), (v_0 pi)/ (2 B_0 alpha) )`
D. `((v_0 pi)/ (B_0 alpha) ,0,(-2v_0)/(B_0 alpha) )`

Answer

d

Explanation

`alpha=q/m`, path of the particle will
be a helix of time period,
`T=(2pim)/(Bq)=(2pi)/(B_0alpha)`
The given time `t=pi/(B_0q)=T/2`
`:.` Coordinateof particle at time `t=T//2`
would be `(v_xT//2),0,-2r)`
Here, `r=(mv_0)/(B_0q)=(v_0)/(B_0alpha)`
`:.` The coordinate are `((v_0pi)/(B_0q),0,(-2v_0)/(B_0alpha))`