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12th Class Physics Magnetism Question Bank Case Based (MCQs) - Moving Charges and Magnetism

  • question_answer
    The magnetic field in a certain region of space is given by \[\overrightarrow{B}=8.35\times {{10}^{-2}}\widehat{i}\,\,T\]. A proton shot into the field with velocity \[\overrightarrow{v}=(2\times {{10}^{5}}\widehat{i}+4\times {{10}^{2}}\widehat{j})m/s\]. The proton follows a 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 proton \[=1.67\times {{10}^{-27}}kg\]):

    A) 0.053 m                       

    B) 0.136 m

    C) 0.157 m                       

    D) 0.236 m

    Correct Answer: C

    Solution :

    (c) 0.157 m Here,         \[\overrightarrow{B}=8.35\times {{10}^{-2}}\widehat{i}\,T\] \[\overrightarrow{v}=2\times {{10}^{5}}\widehat{i}+4\times {{10}^{5}}\widehat{j}\,m/s,\,m=1.67\times {{10}^{-27}}kg\] Pitch of the helix (i.e., the linear distance moved along the magnetic field in one rotation) is given by Pitch of the helix \[=\frac{2\pi mvx}{qB}\] \[=\frac{2\times 3.14\times 1.67\times {{10}^{-27}}\times 2\times {{10}^{5}}}{1.6\times {{10}^{-19}}\times 8.35\times {{10}^{-2}}}=0.157\,m\]


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