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

To solve the question, we need to analyze both the assertion and the reason given and determine their individual truthfulness as well as their relationship to each other.

1. Understanding the Assertion (A): "Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more."
   • This statement refers to the relationship between induced electromotive force (emf) and magnetic flux.
   • According to Faraday’s law of electromagnetic induction, the induced emf in a coil is proportional to the rate of change of magnetic flux linked with the coil.
   • This implies that if the magnetic flux linked with a coil increases, the induced emf will also increase, provided that the rate of change of this flux is considered.
   • Hence, the assertion is true.
2. Understanding the Reason (R): "Induced emf produced is directly proportional to the magnetic flux."
   • This statement claims that the induced emf is directly proportional to the magnetic flux itself.
   • However, according to Faraday’s law, the induced emf is actually proportional to the rate of change of magnetic flux, i.e., \(E = -\frac{d\Phi}{dt}\), where \(E\) is the emf and \(\Phi\) is the magnetic flux.
   • This indicates that a constant magnetic flux would not induce any emf; it is the change that matters.
   • Thus, the reason is false because it incorrectly states the relationship between emf and magnetic flux.
3. Conclusion:
   • The assertion is true, but the reason given is false because it misrepresents the fundamental concept of electromagnetic induction.
   • Therefore, the correct answer is: Assertion (A) is true, but Reason (R) is false.

Answer 2

A useful way to test an assertion-reason pair in electromagnetism is to try to construct a situation that breaks the reason while leaving the assertion's everyday claim intact.

Testing the Reason with a counter-example: Imagine a coil sitting inside a magnetic field that is large and completely unchanging in time. According to the reason's claim, "emf is directly proportional to flux," a large constant flux should produce a large constant emf. But by Faraday's law, \( \varepsilon = -\dfrac{d\Phi}{dt} \), a flux that isn't changing produces exactly zero induced emf, no matter how large it is. This single counter-example is enough to show the reason, as stated, is false, emf tracks the rate of change of flux, not its magnitude.

Revisiting the Assertion on its own: The assertion talks about flux linked with the coil being "more," in the practical exam sense this is usually taken to mean a stronger source producing more induced effect, and within typical classroom scenarios, like a magnet moving toward a coil, more linked flux does tend to accompany a larger induced emf. So the assertion, read at face value, is accepted as true.

Conclusion: Since the constant-flux counter-example disproves the reason on its own, independent of whether the assertion is true, the reason cannot be a valid explanation for the assertion either.

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