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

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 below
After `pi`-seconds the particle will be at point `P` , hence `x` coordinate will be `0` For linear motion along `y`-direction. ltbgt `y(pi)=0(pi)+1/2(Eq)/m(pi)^(2)`
`y(pi)=pi^(2)/2` and `OP=2` Hence the coordinate `(0,pi^(2)/2,2)`.