Question

In a magnetic field of 0.05 T, area of a coil changes from \( 10 \, \text{cm}^2 \) to \( 100 \, \text{cm}^2 \) without changing the resistance which is 2 \( \Omega \). The amount of charge that flows during this period is:

• A. \( 25 \times 10^{-6} \, \text{C} \)
• B. \( 2 \times 10^{-6} \, \text{C} \)
• C. \( 10^{-6} \, \text{C} \)
• D. \( 8 \times 10^{-6} \, \text{C} \)

Hint:

The amount of charge is directly proportional to the induced emf and time, and inversely proportional to the resistance.

Answer 1

The Correct Option is A

Step 1: Use the formula for induced emf.
The induced emf in the coil is given by Faraday's law of induction: \[ \mathcal{E} = - \frac{d\Phi}{dt} \] where \( \Phi = B A \) is the magnetic flux.
Step 2: Calculate the charge.
The amount of charge is given by: \[ Q = \frac{\mathcal{E} \Delta t}{R} \] Substituting the values and solving for \( Q \), we get \( Q = 25 \times 10^{-6} \, \text{C} \).
Final Answer: \[ \boxed{25 \times 10^{-6} \, \text{C}} \]