Question

Assertion : Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more. Reason (R): Induced emf produced is directly proportional to the magnetic flux.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Always remember Faraday’s law: Induced emf depends on how fast flux changes, not how large the flux is.

Answer 1

The Correct Option is C

Concept: Faraday’s law of electromagnetic induction: \[ \mathcal{E} = -\frac{d\Phi}{dt} \] Where:

\( \mathcal{E} \) = induced emf
\( \Phi \) = magnetic flux
Important idea: Induced emf depends on rate of change of flux, not just flux.
Step 1: Analyze Assertion (A). If magnetic flux linked with a coil increases (and especially changes rapidly), induced emf increases. Thus, the assertion is generally considered true in practical context.
Step 2: Analyze Reason (R). The reason states: \[ \mathcal{E} \propto \Phi \] This is incorrect. From Faraday’s law: \[ \mathcal{E} \propto \frac{d\Phi}{dt} \] So emf depends on the rate of change of flux, not flux itself.
Step 3: Conclusion.

Assertion → True
Reason → False
Hence, option (C).

Answer 2

Assertion-reason questions are best handled by judging the truth of each statement completely independently before deciding whether one explains the other.

Checking the Assertion: "Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more." Faraday's law states that induced emf equals the rate at which flux changes, \( \varepsilon = -\dfrac{d\Phi}{dt} \). In everyday and exam contexts, a coil linked with a larger changing flux, for example a stronger magnet moving at the same speed, typically does produce a correspondingly larger induced emf, so taken in that practical sense, the assertion holds.

Checking the Reason: "Induced emf produced is directly proportional to the magnetic flux." This claims \( \varepsilon \propto \Phi \) directly. But Faraday's law says emf depends on how fast the flux changes, \( \dfrac{d\Phi}{dt} \), not on the flux's own size. A coil sitting in a very large but perfectly constant flux produces zero emf, since nothing is changing, while a coil in a small flux that's changing rapidly can produce a large emf. So emf is tied to the rate of change, not the magnitude, of flux, making the reason's stated proportionality false.

Relating the two: Since the reason describes the wrong physical quantity, flux itself, instead of its rate of change, it cannot correctly explain the assertion, and it is false in its own right regardless of the assertion.

Therefore, the correct answer is Assertion (A) is true, but Reason (R) is false.