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JEE Main & Advanced Physics Electro Magnetic Induction Question Bank Self Evaluation Test - Electromagnetic Induction

  • question_answer
    A straight conducting metal wire is bent in the given shape and the loop is closed. Dimensions are as shown in the figure. Now the assembly is heated at a constant rate \[~dT/dt\text{ }=\text{ }l{}^\circ C/s\]. The assembly is kept in a uniform magnetic field B=1 T, perpendicular into the paper. Find the current in the loop at the moment, when the heating starts. Resistance of the loop is \[10\Omega \] at any temperature. Coefficient of linear expansion \[\alpha ={{10}^{-6}}/{}^{o}C\].    

    A) \[1.5\times {{10}^{-6}}\,A\] anticlockwise  

    B) \[1.5\times {{10}^{-6}}\,A\]clockwise  

    C) \[0.75\times {{10}^{-6}}\,A\] anticlockwise

    D) \[0.75\times {{10}^{-6}}\,A\]clockwise

    Correct Answer: A

    Solution :

    [a] Rate of change of area of the loop \[\frac{dA}{dt}=A\],   \[\beta \frac{dT}{dt}=A.(2\alpha )\frac{dT}{dt}=\frac{3}{4}\times 2\times {{10}^{-6}}\times 1\] \[=11.5\times {{10}^{-6}}{{m}^{2}}/s\] \[emf=-\frac{d\phi }{dt}=-\frac{\beta .dA}{dt}=-1.5\times {{10}^{-6}}V\] current in the loop\[=1.5\times {{10}^{-6}}A\] The direction will be anticlockwise as the induced current will try to negate the increase in fluix due to increase in area.


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