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: Understanding the Question:
Removing a coil from a magnetic field causes a change in flux, which induces an emf and a current, leading to charge flow.
Step 2: Key Formula or Approach:
Induced charge \( q = \frac{\Delta \Phi}{R} \), where \( \Delta \Phi \) is the total change in magnetic flux.
Step 3: Detailed Explanation:
Initial flux through the coil: \( \Phi_1 = n B A \).
Final flux after removal: \( \Phi_2 = 0 \).
Change in flux: \( \Delta \Phi = n B A \).
The total charge that flows is:
\[ q = \frac{\Delta \Phi}{R} = \frac{n B A}{R} \] Rearranging for magnetic flux density \( B \):
\[ B = \frac{q R}{n A} \] Step 4: Final Answer:
The magnetic flux density is \( \frac{q R}{n A} \).