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: Analyzing Assertion (A):
The assertion posits that the magnetic field strength at the core of a circular coil carrying current is directly proportional to its number of turns (N). This relationship is mathematically represented by:
\[B = \frac{\mu_0 NI}{2r}\]In this equation:
- \( B \) denotes the magnetic field at the coil's center,
- \( \mu_0 \) represents the permeability of free space,
- \( I \) is the current flowing through the coil,
- \( r \) is the coil's radius,
- \( N \) signifies the number of turns in the coil.
Based on this formula, an increase in \( N \) leads to a corresponding increase in the magnetic field \( B \), confirming their direct proportionality.

Step 2: Analyzing Reason (R):
The reason elucidates the basis for the magnetic field's proportionality to the number of turns. It explains that as the current in each turn is consistent and the magnetic fields generated by individual turns are aligned in the same direction, the total magnetic field is the summation of these individual fields. Consequently, a greater number of turns amplifies the cumulative magnetic field at the coil's center.

Step 3: Evaluating the Link between Assertion (A) and Reason (R):
- The assertion establishes the direct proportionality between the magnetic field at the coil's center and the number of turns, as quantified by the given formula.
- The reason substantiates this by explaining that the additive nature of magnetic fields from each turn, given uniform current and field direction, results in an increased total field with more turns. This explanation directly corroborates the assertion.

Step 4: Conclusion:
Both the assertion and the reason are factually correct, and the reason accurately elucidates the assertion. The increase in the number of turns demonstrably results in a stronger magnetic field at the center of the coil, as indicated by the formula \( B = \frac{\mu_0 NI}{2r} \).