Question

A coil of 'n' turns and area 'A' is suddenly removed from a magnetic field, a charge 'q' flows through the coil. If resistance of the coil is 'R' then the magnetic flux density is (in \( \text{Wb/m}^2 \))

• A. \( \frac{q^2 R}{2 n A} \)
• B. \( \frac{q R}{n A} \)
• C. \( \frac{q R^2}{n A} \)
• D. \( \frac{q R}{2 n A} \)

Hint:

Induced charge is independent of the time taken to change the flux.

Answer 1

The Correct Option is B

Step 1: Faraday's Law and Charge
Induced charge $q = \frac{\Delta \Phi}{R} = \frac{n \Delta \phi}{R}$
Step 2: Flux Change
$\Delta \phi = B \times A$ (since it is removed, flux goes from $BA$ to $0$).
Step 3: Solving for B
$q = \frac{n(BA)}{R} \Rightarrow B = \frac{q R}{n A}$
Step 4: Conclusion
Magnetic flux density is $qR/nA$.
Final Answer:(B)