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12th Class Physics Electro Magnetic Induction Question Bank MCQ - Electromagnetic Induction

  • question_answer
    A long solenoid with 10 turns per cm has a small loop of area \[\text{3 }c{{m}^{2}}\] placed inside, normal to the axis of the solenoid. If the current carried by the solenoid changes steadily from 2 A to 4 A in 0.2s, what is the induced voltage in the loop, while the current in changing?

    A) \[4.2\times {{10}^{-8}}V\]                 

    B) \[2.8\times {{10}^{-8}}V\]

    C) \[7.3\times {{10}^{-6}}V\]                   

    D) \[3.8\times {{10}^{-6}}V\]

    Correct Answer: D

    Solution :

    (d) \[3.8\times {{10}^{-6}}V\] Here, \[\frac{N}{l}=10\] turns per cm = 1000 turns per metre \[A=3\,c{{m}^{2}}=3\times {{10}^{-4}}{{m}^{2}}\] or \[\frac{dl}{dt}=\frac{4-2}{0.2}=10\,A\,{{s}^{-1}}\] Also \[\varepsilon =\frac{d\phi }{dt}=\frac{d}{dt}(BA)=A\frac{d}{dt}\left( {{\mu }_{0}}\frac{N}{l}I \right)=A{{\mu }_{0}}\left( \frac{N}{l} \right)\frac{dI}{dt}\] \[=3\times {{10}^{-4}}\times 4\pi \times {{10}^{-7}}\times 1000\times 10=3.8\times {{10}^{-6}}V\]


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