Question

In a closed circuit there is only a coil of inductance $L$ and resistance $100\Omega$. The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by 5 Weber. What amount of charge will flow in the circuit as a result?

• A. $500C$
• B. 0.05 C
• C. 20 C
• D. Value of L is to be known to find the charae flown

Answer 1

Answer: (C)

Emf $=-\frac{d\phi }{dt}(\text{ Faraday’s Law })$
$i_{\text{indused }}=\frac{Emf}{R}=-\frac{d\phi }{dt}\times \frac{1}{R}$
$\Rightarrow \frac{dq}{dt}=-\frac{1}{R}\frac{d\phi }{dt}$
$\Rightarrow dq=-\frac{d\phi }{R}$
$\Rightarrow \int dq=-\int \frac{d\phi }{R}$
$\Rightarrow q_{\text{flown }}=\frac{{\phi }_i-{\phi }_f}{R}=\frac{5\text{ weber }}{100}=0.05C$