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

Assertion (A) is true. The magnetic field at the center of a current-carrying circular coil is directly proportional to the number of turns (N) in the coil, as given by the formula:

\( B = \frac{\mu_0 NI}{2r} \), where \( \mu_0 \) is the permeability of free space, \( I \) is the current, and \( r \) is the radius of the coil. Increasing \( N \) increases the magnetic field intensity.

Reason (R) correctly explains this. 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 simply the sum of the individual magnetic fields from each turn. Therefore, Reason (R) provides the correct explanation for Assertion (A).