Write the formula for the magnetic field due to a circular current-carrying loop having $N$ turns and $R$ radius at a point on the axis of the loop at a distance $x$ from the center.

(N/A) The magnetic field $B$ at a point on the axis of a circular current-carrying loop is given by the Biot-Savart Law.
For a single loop with radius $R$,current $I$,and a point at distance $x$ from the center along the axis,the magnetic field is $B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$.
For a coil having $N$ turns,the total magnetic field is the sum of the fields produced by each turn.
Therefore,the formula is $B = \frac{\mu_0 N I R^2}{2(R^2 + x^2)^{3/2}}$,where $\mu_0$ is the permeability of free space.