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NEET Sample Paper NEET Sample Test Paper-17

  • question_answer
    A conducting loop of resistance R and radius r has its centre at the origin of the coordinate system in a magnetic field of induction B. When it is rotated about F-axis through \[90{}^\circ \], the net charge flown in the loop is directly proportional to:

    A) \[{{B}^{-1}}\]                                 

    B)  R                                

    C) \[{{r}^{2}}\]                        

    D)  r 

    Correct Answer: C

    Solution :

    \[\varepsilon =\frac{d\Phi }{dt}\Rightarrow \frac{{{\Phi }_{2}}}{{{\Phi }_{1}}}\int_{{{\Phi }_{1}}}^{{{\Phi }_{2}}}{d\Phi =\Delta \Phi =\int_{{}}^{{}}{\varepsilon dt}}\] The total charge flown in the loop \[q=\int_{{}}^{{}}{Idt}\] or \[q=\int_{{}}^{{}}{\frac{\varepsilon }{R}dt}=\frac{\Delta \Phi }{R}=\frac{B\pi {{r}^{2}}}{R}\] i.e., \[q\propto B,\,q\propto {{r}^{2}},\]and \[q\propto \frac{1}{R}\] Hence, the correction option is [c].


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