KVPY Sample Paper KVPY Stream-SX Model Paper-25

  • question_answer
    A charged particle moves with a constant velocity \[(\hat{i}+\hat{j})\,\,m/s\] in a magnetic field \[\vec{B}=(2\hat{i}+3\hat{k})\,T\]and uniform electric field \[\vec{E}=(a\hat{i}+b\hat{j}+c\hat{k})\,N/C,\] then (assuming all quantities in S.I. unit):

    A) \[a=3\]

    B) \[b=-\,3\]

    C) \[c=-\,2\]

    D) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=22\]

    Correct Answer: D

    Solution :

    \[\vec{v}\times \vec{B}=-\vec{E}\] \[(\hat{i}+\hat{j})\times (2\hat{i}+3\hat{k})=-\vec{E}\] \[(-\,3\hat{i}+3\hat{j}+2\hat{k})=\vec{E}\]

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