KVPY Sample Paper KVPY Stream-SX Model Paper-25

  • question_answer
    Wire bent as ABOCD as shown, carries current I entering at A and leaving at D. Three uniform magnetic fields each \[{{B}_{0}}\] exist in the region as shown. The force on the wire is:

    A) \[\sqrt{3}\,I\,R\,{{B}_{0}}\]

    B) \[\sqrt{5}\,I\,R\,{{B}_{0}}\]

    C) \[\sqrt{8}\,I\,R\,{{B}_{0}}\]

    D) \[\sqrt{6}\,I\,R\,{{B}_{0}}\]

    Correct Answer: D

    Solution :

    \[\vec{F}=\vec{F}=I\vec{\ell }\times \vec{B}\]
    \[\vec{\ell }=\overrightarrow{AD}=R\,(\hat{i}-\hat{j})\]
    \[\therefore \]      \[\vec{F}=IR{{B}_{0}}\,(\hat{i}-\hat{j})\times (\hat{i}+\hat{j}-\hat{k})=IR{{B}_{0}}\,\,\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    1 & -1 & 0  \\    1 & 1 & -1  \\ \end{matrix} \right|\]
    \[\vec{\ell }=R\,(\hat{i}-\hat{j})\]
    \[\vec{B}\,\,\vec{\ell }=0\]          \[\Rightarrow \]   \[\text{Angle}=90{}^\circ \]       \[\Rightarrow \]    \[F=BI\ell \]

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