AIIMS 2006 Physics Faraday's Law Assertion Reason Question

To analyze the given question, we need to break down the assertion and the reason in the context of electromagnetic induction, specifically referring to Faraday's Law of Electromagnetic Induction.

Assertion Explanation

Assertion: An emf $E$ is induced in a closed loop where magnetic flux is varied. The induced $E$ is not a conservative field.

According to Faraday's Law, the induced electromotive force (emf) $E$ in a closed loop is directly related to the rate of change of magnetic flux $\Phi_B$ through the loop:

$$E = -\frac{d\Phi_B}{dt}$$

Here, $\Phi_B$ is the magnetic flux, given by:

$$\Phi_B = \int \mathbf{B} \cdot d\mathbf{A}$$

where $\mathbf{B}$ is the magnetic field and $d\mathbf{A}$ is the infinitesimal area vector.

The negative sign in Faraday's Law indicates that the induced emf creates a current that opposes the change in magnetic flux (Lenz's Law). This induced emf is not a conservative field because the work done around a closed path is not zero when magnetic flux changes over time. In conservative fields, the line integral of the field around any closed loop would yield zero.

Reason Explanation

Reason: The line integral $\int \mathbf{E} \cdot d\mathbf{l}$ around the closed loop is non-zero.

The line integral of the electric field $\mathbf{E}$ around a closed path is given by:

$$\oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt}$$

When there is a changing magnetic flux, $\frac{d\Phi_B}{dt}$ is non-zero, which means that:

$$\oint \mathbf{E} \cdot d\mathbf{l} eq 0$$

This confirms that the induced electric field is indeed non-conservative, as the work done in moving a charge around the closed loop is not zero.

Conclusion

Both the assertion and the reason are true, and the reason correctly explains why the assertion holds. Therefore, the correct option is:

A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

Clarification of Other Options

B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

• This option is incorrect because the reason provided is indeed the correct explanation of why the induced emf is non-conservative.

C) Assertion is true but Reason is false.

• This option is incorrect as both the assertion and reason are true.

D) Both Assertion and Reason are false.

• This option is incorrect as both statements are true.

Summary

In summary, Faraday's Law illustrates that a changing magnetic flux induces an emf in a closed loop, creating a non-conservative electric field. The non-zero line integral around a closed path confirms this, reinforcing the relationship between changing magnetic fields and induced electric fields. This understanding is crucial for mastering concepts in electromagnetism for NEET/JEE exams.