There exist uniform magnetic and electric fields of magnitudes 1 T and 1 V m^-1, respectively, along positive y-axis. A charged particle of mass 1 kg and charge 1 C is having velocity 1 ms^-1 along x-axis and is at origin at t= 0.

Then, the coordinates of the particle at time $\pi \mathrm{s}$ will be

detailed solution

Correct option is D

The particle will move in a non-uniform helical path with increasing pitch as shown in figure.Its time period will be: T=2πmqB=2πsChanging the view, the particle seems to move in a circular path in(X-Z) plane as shown in figure.After π seconds, the particle will be at point 'P' (after completing half circle), hence X-coordinate of P will be 0.y(π)=0(π)+12Eqm(π)2=π22z=2r=2mv/qB=2 m Hence, the coordinates of the particle are 0,π22,2