Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields  $\overrightarrow{E}=E_0\widehat{j}and\overrightarrow{B}=B_0\widehat{j}.$ At time t =0, this charge has velocity $\overrightarrow{\upsilon }$ in the in the x-y plane, making an angle θ with the x-axis. Which of the following option(s) is (are) correct for time t > 0 ?

If $\theta =0^o$, the charged particle is projected along x- axis, due to magnetic field, $\overrightarrow{B}$ the charged particle will tend to move in a circular path in y-z plane but due to force of electric field $\overrightarrow{E}$, the particle will move in a helical path with increasing pitch. Hence options (A) and (B) are wrong. If  $\theta ={10}^o$, we can resolve velocity into two rectangular components. One along x-axis

(v cos 10°) and one along y- axis (v sin 10°). Due to v cos 10°, the particle will move in circular path and due to v sin 10° plus the force due to electric field, the particle will undergo helical motion with its pitch increasing. If θ = 90°, the charge is moving along the magnetic field. Therefore the force due to magnetic field is zero. But the force due to electric field will accelerate the particle along y-axis.