Question

two statements are given — one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
Assertion (A): The intensity of the magnetic field produced at the centre of a current-carrying circular coil increases on increasing the number of turns in the coil.
Reason (R): The current that flows in each turn of the coil has the same magnitude and same direction, and the magnetic field, due to each turn, just adds up.

• 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 and Reason (R) is false.
• D. Assertion (A) is false and Reason (R) is true.

Answer 1

The Correct Option is A

Step 1: Understanding the Assertion (A):
The assertion states that the magnetic field at the center of a current-carrying circular coil is directly proportional to the number of turns (N) in the coil. This is given by the formula:
\[ B = \frac{\mu_0 NI}{2r} \] where:
- \( B \) is the magnetic field at the center of the coil,
- \( \mu_0 \) is the permeability of free space,
- \( I \) is the current flowing through the coil,
- \( r \) is the radius of the coil, and
- \( N \) is the number of turns in the coil.
According to this formula, as \( N \) increases, the magnetic field \( B \) increases as well, because the magnetic field is directly proportional to the number of turns.

Step 2: Understanding the Reason (R):
The reason provides an explanation for why the magnetic field is proportional to the number of turns. It states that since the current in each turn is the same and the magnetic field due to each turn is in the same direction, the total magnetic field is the sum of the individual magnetic fields generated by each turn. As a result, the more turns there are, the greater the cumulative magnetic field at the center of the coil.

Step 3: Connecting Assertion (A) and Reason (R):
- The assertion tells us that the magnetic field at the center of the coil is proportional to the number of turns. This is mathematically expressed in the given formula.
- The reason explains how this happens: since the current in each turn is the same and the magnetic fields from each turn add together, the total magnetic field increases with the number of turns. This directly supports the assertion.

Step 4: Conclusion:
Both the assertion and the reason are true, and the reason correctly explains the assertion. The increase in the number of turns results in an increased magnetic field at the center of the coil, as described by the formula \( B = \frac{\mu_0 NI}{2r} \).