A particle of mass `m` and charge `q` is lying at the origin in a uniform magnetic field `B` directed along x-axis. At time t = 0, it is given a velocity `v_0`, at an angle` theta` with the y-axis in the xy-plane. Find the coordinates of the particle after one revolution.

Explanation

`R - (mv_(0)cos theta)/(Bq), T = (2 pi m)/(Bq)`
Pitch `x = v_(0) sin theta T = v_(0) sin theta (2 pi m)/(Bq)`
After every time `t = nT, n = 0, 1, 2,…` particle touches x-axis.
After time `t = T`:
`x = (2 pi mv_(0) sin theta)/(Bq), y = z = 0`
(b) `K = (1)/(2)mv^(2) = qV`
`v = sqrt((2q V)/(m))`
Pitch of helical path
`p = v cos theta T`
As `theta` is small, `cos theta ~= 1`
`p = vT = sqrt((2q V)/(m)).(2pi m)/(Bq)`
`= sqrt((8pi^(2)mV)/(qB^(2))) = sqrt((8pi^(2)mV)/(eB^(2)))`