There exist uniform magnetic and electric fields of magnitudes 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,-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

Its time period will be: `T=(2pim)/(qB)=2pis`
Changing the view, the particle seems to move in a circular path in (X-Z) plane as shown
After `pi` second, the particle will be at point 'P' (after completing harl circle), 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 coordinates of the particle are `(0,((pi)^2)/2,2)`