The correct option is n times that of a single turn.
Explanation
The magnetic field generated by a current-carrying circular coil is determined by the Biot-Savart Law. The magnitude of this field at the center of the coil is influenced by the current strength, the radius of the coil, and the number of windings (turns).Detailed Analysis:
- Single Turn Field: The magnetic field ($B$) at the center of a single circular turn of radius $r$ carrying current $I$ is given by the expression $B = \frac{\mu_{0}I}{2r}$.
- Multiple Turns: When a coil consists of $n$ turns, the current flows around the loop $n$ times in the same direction.
- Superposition Principle: The magnetic field produced by each individual turn adds vectorially to the fields produced by the other turns. Since the current direction is identical in all turns, the fields add up constructively.
- Conclusion: The total magnetic field is the sum of the fields from each turn. Therefore, the field produced by a coil with $n$ turns is $n$ times the field produced by a single turn of the same radius ($B_{total} = n \times B$).
Key Takeaway:
The magnetic field strength at the center of a circular coil is directly proportional to the number of turns ($n$), assuming the radius of the coil and the current flowing through it remain constant.