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Magnetic force on a charged particle is given by \( \vec{F}_{m}=q(\vec{v} \times \vec{B}) \) and electrostatic force \( \vec{F}_{e}=q \vec{E} \). A particle having charge \( q=1 C \) and mass \( 1 \mathrm{~kg} \) is released from rest at origin. There are electric and magnetic fields given by \( \vec{E}=(10 \hat{i}) \mathrm{N} / \mathrm{C} \) for \( x=1.8 \mathrm{~m} \) and \( \vec{B}=-(5 \hat{k}) \mathrm{T} \) for \( 1.8 \mathrm{~m} \leq x \leq 2.4 \mathrm{~m} \).

A screen is placed parallel to \( y-z \) plane at \( x=3 \mathrm{~m} \). Neglect gravity forces.

Time after which the particle will collide the screen is (in seconds)
(1) \( \frac{1}{5}\left(3+\frac{\pi}{6}+\frac{1}{\sqrt{3}}\right) \)
(2) \( \frac{1}{5}\left(6+\frac{\pi}{3}+\sqrt{3}\right) \)
(3) \( \frac{1}{3}\left(5+\frac{\pi}{6}+\frac{1}{\sqrt{3}}\right) \)
(4) \( \frac{1}{3}\left(6+\frac{\pi}{18}+\sqrt{3}\right) \)
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