There exist uniform magnetic and electric fields of manitudes 1T and `1Vm^-1` respectively, along positive y-axis. A charged particle of mass 1kg and charge 1C is having velocity `1ms^-1` along x-axis and is at origin at t=0. Then, the coordinates of the particle at time `pis` will be

Options

A. `(0,1,2) m`
B. `(0,-pi^(2),-2) m`
C. `(2,pi^(2)//2,2) m`
D. `(0,pi^(2)//2,2)m`

Answer

D

Explanation

The particle will move in a non-uniform helical path with increasing pitch as shown below.

Its time period will be : `T=(2pim)/(qB)=2pi` seconds
Changing the view, the particle is seemed to move in a circular path in `(X-Z)` plane as shown below

After `pi`-seconds the particle will be at point `'P'` (after completing half circule), hence `X` coordinate of `P` will be `0`.
`y(pi)=0(pi)+1/2 (Eq)/m(pi)^(2)=(pi^(2))/2`
`z=2r=2mv//qB=2m`
Hence the coordinate `(0,(pi^(2))/2,2)`