Question

Assertion (A): It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.
Reason (R): The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.

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

Hint:

Lenz's Law states that the direction of the induced current opposes the change in the magnetic flux, which is the reason why it's difficult to move a magnet into a coil.

Answer 1

The Correct Option is A

In the problem presented, we assess the validity of an assertion and its corresponding reasoning. To solve this, we'll analyze both Assertion (A) and Reason (R) individually and collectively: 

• Assertion (A): It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.
• Reason (R): The direction of induced current in a coil with its circuit closed, due to the motion of a magnet, is such that it opposes the cause.

Let's break down the concepts involved:

1. When a magnet moves into a coil, an electromotive force (EMF) is induced due to the changing magnetic flux through the coil's turns, as per Faraday's Law of Electromagnetic Induction.
2. The induced EMF generates a current in the closed circuit of the coil, called the induced current.
3. According to Lenz's Law, the direction of the induced current is such that the magnetic field it creates opposes the change in magnetic flux that produced it. This is often summarized as the phrase "opposes the cause." Lenz's Law mathematically emphasizes that for the coil with turns \(N\), the induced EMF (\(\mathcal{E}\)) can be expressed as \(\mathcal{E} = -N \frac{d\Phi}{dt}\), where \(\Phi\) is the magnetic flux.
4. Because of this opposition by the induced current, greater effort is required to move the external magnet into the coil, thus making it “difficult to move a magnet into a coil of a large number of turns” when the circuit is closed. This aligns with the assertion given.

Based on the analysis:

• Both the Assertion (A) and Reason (R) are indeed true.
• Reason (R) correctly explains why Assertion (A) holds true; the opposition provided by the induced current (due to Lenz's Law) results in the difficulty described in Assertion (A).

Hence, the correct option is:
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)