The magnitude of the magnetic field due to a current-carrying circular coil varies with the number of turns n as

Correct option is A

Solution:

The magnitude of the magnetic field (B) at the center of a current-carrying circular coil depends on the number of turns (n), the current (I) flowing through the coil, and the radius (r) of the coil.

Magnetic field at the center of a current-carrying circular coil:

​$$B = \frac{\mu_0 n I}{2r}$$ 

Where:

B =Magnetic field at the center

n =Number of turns in the coil

​I =Current through the coil

r =Radius of the coil​​

​$$\mu_0 : \text{Permeability of free space}$$ $$(4\pi \times 10^{-7})$$T/A

From the formula, B is directly proportional to n. If the number of turns n increases, the magnetic field B increases linearly.

​$$B \propto n$$ 

Thus the correct answer is (A)