The magnetic field in a certain region of space is given by \( \vec{B}=8.35 \times 10^{-2} \hat{...

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The magnetic field in a certain region of space is given by \( \vec{B}=8.35 \times 10^{-2} \hat{i} T \). A proton is shot into the field with
\( \mathrm{P} \) velocity \( \vec{v}=\left(2 \times 10^{5} \hat{i}+4 \times 10^{5} \hat{j}\right) \mathrm{m} / \mathrm{s} \). The proton follows a W helical path in the field. The distance moved by proton in the \( x \)-direction during the period of one revolution in the yz-plane will be (Mass of proton \( =1.67 \times 10^{-27} \mathrm{~kg} \) ) [AMU (Med.) 2012]
(a) \( 0.053 m \)
(b) \( 0.136 m \)
(c) \( 0.157 \mathrm{~m} \)
(d) \( 0.236 m \)
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