Question

The magnetic flux through a coil is $4 \times 10^{-4} \text{ Wb}$ at time $t = 0$. It reduces to $30%$ of its original value in time $t$ second. If e.m.f. induced in the coil is $0.56 \text{ mV}$ then the value of $t$ is

• A. 0.5 s
• B. 0.4 s
• C. 0.8 s
• D. 0.7 s

Hint:

Faraday's Law: Emf is the rate of change of magnetic flux.

Answer 1

The Correct Option is A

Step 1: Concept
Induced e.m.f. $e = |\Delta \Phi / \Delta t|$.

Step 2: Meaning
$\Phi_1 = 4 \times 10^{-4} \text{ Wb}$. $\Phi_2 = 30% \text{ of } \Phi_1 = 1.2 \times 10^{-4} \text{ Wb}$. $\Delta \Phi = (4 - 1.2) \times 10^{-4} = 2.8 \times 10^{-4} \text{ Wb}$.

Step 3: Analysis
$0.56 \times 10^{-3} = (2.8 \times 10^{-4}) / t \implies t = (2.8 \times 10^{-4}) / (5.6 \times 10^{-4})$.

Step 4: Conclusion
$t = 0.5 \text{ s}$. Final Answer: (A)