Write the equation for the magnetic field of a current-carrying circular loop at: $(i)$ a point on the axis,and $(ii)$ a point on the plane of the loop at a distance $x$ from the center of the loop.

(N/A) For a circular loop of radius $R$ carrying current $I$:
$(i)$ The magnetic field at a point on the axis at a distance $z$ from the center is given by: $B = \frac{\mu_0 I R^2}{2(R^2 + z^2)^{3/2}}$.
$(ii)$ The magnetic field at a point in the plane of the loop at a distance $x$ from the center is generally calculated using elliptic integrals,as there is no simple closed-form algebraic expression for an arbitrary point $x$ inside or outside the loop. However,for $x \ll R$,it can be approximated using a Taylor expansion,but it is not a standard elementary formula like the axial case.