In a certain region of space, there exists a uniform and constant electric field of magnitude \( E \) along the positive \( y \)-axis of a coordinate system. A charged particle of mass \( m \) and charge \( -q \) \( (q0) \) is projected from the origin with speed \( 2 v \) at an angle of \( 60^{\circ} \) with the positive \( x \)-axis in \( x-y \) plane. When the \( x \)-coordinate of particle becomes \( \sqrt{3} \mathrm{mv}^{2} / q E \) a uniform and constant magnetic field of strength \( B \) is also switched on along positive \( y \)-axis.
\( z \)-coordinate of the particle as a function of time after the magnetic field is switched on is
(1) \( \frac{m v}{q B}\left[1-\cos \left(\frac{q B}{m} t\right)\right] \)
(2) \( -\frac{m v}{q B}\left[1+\cos \left(\frac{q B}{m} t\right)\right] \)
(3) \( -\frac{m v}{q B}\left[1-\cos \left(\frac{q B}{m} t\right)\right] \)
(4) \( \frac{m v}{q B}\left[1+\cos \left(\frac{q B}{m} t\right)\right] \)
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