Using the Biot–Savart law, the magnetic field at the centre of a circular loop of radius R carrying current I is:

1. On the axis at distance $x$: $B = \dfrac{\mu_0 I R^2}{2(x^2+R^2)^{3/2}}$. 2. At the centre, $x = 0$. 3. Then $(x^2+R^2)^{3/2} = R^3$, giving $B = \dfrac{\mu_0 I R^2}{2R^3}$. 4. Simplify: $B = \dfrac{\mu_0 I}{2R}$ (the $2\pi$ form is for a straight wire, not a loop centre). _Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", p.146_