12th Class Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Question Bank Case Based (MCQs) - Moving Charges and Magnetism

  • question_answer
    The magnetic field in a certain region of space is given by \[\overrightarrow{B}=8\,.\,35\,\times {{10}^{-2}}\hat{i}\,T\]. A proton is shot into the field with velocity \[\overrightarrow{v}=\left( 2\times {{10}^{5}}\hat{i}+4\times {{10}^{5}}\hat{j} \right)\]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

    A) \[0\centerdot 053m\]

    B) \[0\centerdot 136m\]

    C) \[0\centerdot 157m\]

    D) \[0\centerdot 236m\]

    Correct Answer: C

    Solution :

    Here, \[\overrightarrow{B}=8\,.\,35\times {{10}^{-2}}\,\,\hat{i}\,T\] \[\overrightarrow{v}=2\times {{10}^{5}}\,\hat{i}+4\times {{10}^{5}}\hat{j}\,\,m/s\] \[m=1\,.\,67\times {{10}^{-27}}\,kg\] Pitch of the helix (i.e. the linear distance moved along the magnetic field in one rotation) is given by Pitch of the helix \[=\frac{2\pi m{{v}_{||}}}{qB}\] \[=\frac{2\times 3\,.\,14\times 1.\,67\times {{10}^{-27}}\times 2\times {{10}^{5}}}{1\,.\,6\,{{10}^{-19}}\times 8\,.\,33\times {{10}^{-2}}}=0.157\,m\]


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