Assertion (A): The strength of the magnetic field produced at the centre of a current carrying circular coil increases on increasing the number of turns in it.

Reason (R): The current in each circular turn has the same direction and the magnetic field due to each turn then just adds up.

According to the NCERT textbook:

1. Assertion (A) is true: The magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it. If we have a circular coil with $n$ turns, the magnetic field produced at the center is $n$ times as large as that produced by a single turn.
2. Reason (R) is true: This multiplication of field strength occurs because the current in each of the $n$ closely wound circular turns flows in the same direction. As a result, the magnetic field contribution from each individual turn points in the same direction at the center and simply adds up algebraically:

$$B_{total} = B_1 + B_2 + \dots + B_n = n \cdot B_{single}$$

1. Since the reason correctly explains why the magnetic field increases with the number of turns, (R) is the correct explanation of (A).

Why other options are incorrect:

• Option (b) is incorrect because (R) is indeed the direct physical explanation for (A).
• Options (c) and (d) are incorrect because both statements are scientifically accurate and fully aligned with the principles of electromagnetism described in the NCERT text.