Question

A long solenoid of radius $2\text{cm}$ has $100\text{turns/cm}$ and is surrounded by a $100$ turns coil connected with galvanometer of radius $4\text{cm}$ having a total resistance of $20\Omega$. If current in the solenoid changes from $5\text{A}$ to $-5\text{A}$, find the charge that has flown through galvanometer during this time.

• A. $500\mu \text{C}$
• B. $600\mu \text{C}$
• C. $800\mu \text{C}$
• D. $700\mu \text{C}$

Answer 1

The correct option is C $800\mu \text{C}$


Magnetic field inside the solenoid is given by

$B={\mu }_{0}ni$

Magnetic flux through the coil,

$\varphi =NBA$

So, change in magnetic flux,

$\Delta \varphi =NA(B_f-B_i)=NA({\mu }_{0}n{i}_f-{\mu }_{0}n{i}_i)$

$\Rightarrow \Delta \varphi ={\mu }_{0}nNA(i_f-i_i)$

Magnitude of charge flown through the coil,

$q=\left|\frac{\Delta \varphi }{R}\right|=\left|\frac{{\mu }_{0}nNA(i_f-i_i)}{R}\right|$

$\Rightarrow q=\left|\frac{4\pi \times {10}^{-7}\times \frac{100}{{10}^{-2}}\times 100\times \pi (0.02{)}^2\times (-5-5)}{20}\right|$

$\Rightarrow q\approx 8\times {10}^{-4}\text{C}$

$\Rightarrow q\approx 800\mu \text{C}$