### NEET Solved Paper 2017 Question 17

##### 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

#### Options:

A) $ 16\pi ,\mu C $

B) $ 32\pi ,\mu C $

C) $ 16\mu C $

D) $ 32,\mu C $

## Show Answer

#### Answer:

Correct Answer: D

#### Solution:

$ \varepsilon =-N\frac{d\text{o }|}{dt} $ $ | \frac{\varepsilon }{R} |=\frac{N}{R}\frac{d\text{o }|}{dt} $ $ dq=\frac{N}{R}d\text{o }| $ $ \Delta Q=\frac{N(\Delta \text{o }|)}{R} $

$ \Delta Q=\frac{\Delta o{| _{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 $