NEET Physics Electro Magnetic Induction NEET PYQ-Electro Magnetic Induction

  • question_answer
    A long solenoid of diameter \[0.1\text{ }m\] has \[2\times {{10}^{4}}\] turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is \[10\,{{\pi }^{2}}\Omega ,\] the total charge flowing through the coil during this time is                                     [NEET-2017]

    A)  \[16\pi \,\mu C\]

    B)                   \[32\,\,\pi \,\mu C\]

    C)  \[16\mu C\]      

    D)       \[32\,\mu C\]

    Correct Answer: D

    Solution :

    [d]        \[\varepsilon =-N\frac{d\phi }{dt}\]
                \[\left| \frac{\varepsilon }{R} \right|=\frac{N}{R}\frac{d\phi }{dt}\] 
                \[dq=\frac{N}{R}d\phi \]
                \[\Delta Q=\frac{N(\Delta \phi )}{R}\]
                \[\Delta Q=\frac{\Delta {{\phi }_{total}}}{R}\]
                \[=\frac{{{\mu }_{0}}ni\pi {{r}^{2}}}{R}\]
    Putting values
                \[=\frac{4\pi \times {{10}^{-7}}\times 100\times 4\times \pi \times {{(0.01)}^{2}}}{10{{\pi }^{2}}}\]
    \[\Delta Q=32\,\mu C\]

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