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. $500\, C$
• 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 \varphi}{d t}(\text { Faraday's Law }) $
$ i_{\text {indused }}=\frac{E m f}{R}=-\frac{d \varphi}{d t} \times \frac{1}{R} $
$ \Rightarrow \frac{d q}{d t}=-\frac{1}{R} \frac{d \varphi}{d t} $
$\Rightarrow d q=-\frac{d \varphi}{R} $
$\Rightarrow \int d q=-\int \frac{d \varphi}{R} $
$ \Rightarrow q_{\text {flown }}=\frac{\varphi_i-\varphi_f}{R}=\frac{5 \text { weber }}{100}=0.05 C$