• # 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)       $32\,\mu C$

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