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. `((upsilon_(0))/(2B_(0)alpha),(sqrt(2)upsilon_(0))/(alphaB_(0)),(-upsilon_(0))/(B_(0)alpha))`
B. `((-upsilon_(0))/(2B_(0)alpha),0,0)`
C. `(0,(2upsilon_(0))/(B_(0)alpha),(upsilon_(0)pi)/(2B_(0)alpha))`
D. `((upsilon_(0)pi)/(B_(0)alpha),0,(-2upsilon_(0))/(B_(0)alpha))`

Answer

D

Explanation

`alpha=(q)/(m)`, path of the particle will be a helix of time period,
`T=(2pim)/(B_(0)q)=(2pi)/(B_(0)alpha)`

The given time `t=(pi)/(B_(0)alpha)=(T)/(2)`
`:.` Coordinate of particle at time `t=T//2` would be `(upsilon_(x)T//2,0,-2r)`
Here, `r=(m upsilon_(r))/(B_(0)q)=(upsilon_(0))/(B_(0)alpha)`
`:.` The coordinate are `((upsilon_(0)pi)/(B_(0)alpha),0,(-2upsilon_(0))/(B_(0)alpha))`