Question

A long solenoid of diameter $0.1\, m$ 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 :

• A. $16 \, \mu C$
• B. $32\, \mu C$
• C. $16 \, \pi \, \mu C$
• D. $32 \, \pi \, \mu C$

Answer 1

Answer: (B)

$32\, \mu C$

Answer 2

Sol. $\varepsilon=-N \frac{d \phi}{d t}$
$\left|\frac{\varepsilon}{R}\right|=\frac{N}{R} \frac{d \phi}{d t}$
$d q=\frac{N}{R} d \phi$
$\Delta Q=\frac{N(\Delta \phi)}{R}$
$\Delta Q=\frac{\Delta \phi_{\text {total }}}{R}$
$=\frac{(N B A)}{R}$
$=\frac{\mu_{0} n i \pi r^{2}}{R}$
Putting values
$=\frac{4 \pi \times 10^{-7} \times 100 \times 4 \times \pi \times(0.01)^{2}}{10 \pi^{2}}$
$\Delta Q=32\, \mu C$