Question

Assertion (A) : 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: \[ e=-N\frac{d\Phi}{dt}. \] Induced emf depends on the rate of change of magnetic flux, not on the amount of flux itself.

Answer 1

The Correct Option is D

Concept: According to Faraday's law of electromagnetic induction, the induced emf in a coil depends upon the rate of change of magnetic flux linked with the coil and not on the magnetic flux itself. Mathematically, \[ e=-N\frac{d\Phi}{dt}, \] where
• \(e\) = induced emf,
• \(N\) = number of turns,
• \(\Phi\) = magnetic flux linked with each turn. The negative sign represents Lenz's law.

Step 1: Examine the Assertion. The assertion states that induced emf will be more when the magnetic flux linked with the coil is more. This statement is not necessarily true. A large magnetic flux may be constant with time. For example, if \[ \Phi=100\,\text{Wb} \] and remains constant, then \[ \frac{d\Phi}{dt}=0. \] Hence, \[ e=0. \] Thus, induced emf depends on the rate of change of flux and not on the magnitude of flux alone. Therefore, the Assertion is false.

Step 2: Examine the Reason. The reason states that induced emf is directly proportional to magnetic flux. This is incorrect. Faraday's law gives \[ e\propto \frac{d\Phi}{dt}, \] not \[ e\propto \Phi. \] Hence the Reason is also false.

Step 3: Draw the final conclusion. \[ \boxed{\text{Assertion is false}} \] and \[ \boxed{\text{Reason is false}}. \] Therefore, \[ \boxed{\text{(D)}} \] is the correct answer.