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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    A non conducting ring of radius r has charge per unit length \[\lambda .\] The magnetic field is perpendicular to the plane of the ring. The radius of the ring charges at the constant rate, K. Torque experienced by the ring is :

    A)  \[\lambda BK{{r}^{2}}\]                     

    B)  \[2\pi \lambda BK{{r}^{2}}\]

    C)  \[2\pi \lambda BKr\]                  

    D)  \[\pi \lambda BK{{r}^{2}}\]

    Correct Answer: B

    Solution :

    \[e=\frac{d\phi }{dt}=\frac{d}{dt}\,(B\pi {{r}^{2}})=2\pi Br\,\frac{dr}{dt}\] \[=2\pi BKr.\,\,\left( \sin ce\,\frac{dr}{dt}=K \right)\] \[E.2\pi r=2\pi BKr\]\[E=BK\] \[\tau =\lambda \,BKr\,\,\int_{{}}^{{}}{ds\,=\lambda \,BKr.\,2\pi r=2\pi \lambda \,BK{{r}^{2}}}\]


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