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A charged particle of specific charge \( \alpha\left(=\frac{q}{m}\right) \) is released from origin at \( t=0 \) with velocity \( \vec{v}=v_{0}(\hat{i}+\hat{j}) \) in uniform magnetic field \( \vec{B}=B_{0} \hat{i} \).
Coordinates of particle at time \( \mathbf{t}=\frac{\pi}{\mathrm{B}_{0} \alpha} \) are
(1) \( \left(\frac{v_{0}}{2 B_{0} \alpha}, \frac{\sqrt{2} v_{0}}{\alpha B_{0}}, \frac{-v_{0}}{B_{0} \alpha}\right) \)
(2) \( \left(\frac{-\mathrm{v}_{0}}{2 \mathrm{~B}_{0} \alpha}, 0,0\right) \)
(3) \( \left(0, \frac{2 \mathrm{v}_{0}}{\mathrm{~B}_{0} \alpha}, \frac{\mathrm{v}_{0} \pi}{2 \mathrm{~B}_{0} \alpha}\right) \)
(4) \( \left(\frac{\mathrm{v}_{0} \pi}{\mathrm{B}_{0} \alpha}, 0, \frac{-2 \mathrm{v}_{0}}{\mathrm{~B}_{0} \alpha}\right) \)
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