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Consider the motion of a positive point charge in a region where are simultaneous uniform electric and magnetic field \( \vec{E}=E_{0} \hat{j} \) and \( \vec{B}=B_{0} \hat{j} \). At time \( t=0 \), this charge has velocity \( \vec{v} \) in the \( x-y \) plane, making an angle \( \theta \) with the \( x \)-axis. Which of the following option(s) is(are) correct for time \( t0 \) ?
(1) If \( \theta=0^{\circ} \), the charge moves in a circular path in the \( x-z \) plane
(2) If \( \theta=0^{\circ} \), the charge undergoes helical motion with constant pitch along the \( y \)-axis
(3) If \( \theta=10^{\circ} \), the charge undergoes helical motion with its pitch increasing with time, along the \( y \)-axis
(4) If \( \theta=90^{\circ} \), the charge undergoes linear but accelerated motion along the \( y \)-axis
(JEE Advanced 2013)
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