How does the strength of the magnetic field at the centre of a circular coil of a wire depend on:
$(a)$ radius of the coil
$(b)$ number of turns in the coil.

(N/A) The strength of the magnetic field $(B)$ at the centre of a circular coil is inversely proportional to the radius $(r)$ of the coil. Mathematically, $B \propto 1/r$. Therefore, as the radius of the coil increases, the magnetic field strength at the centre decreases.
$(b)$ The strength of the magnetic field $(B)$ at the centre of a circular coil is directly proportional to the number of turns $(n)$ in the coil. Mathematically, $B \propto n$. Therefore, as the number of turns in the coil increases, the magnetic field strength at the centre increases.