The magnetic field at the CENTRE of a circular current loop of radius $R$ carrying current $I$ is

1. syllabus derives the field at the centre by integrating the Biot-Savart law around the loop. 2. For each element $d\vec{l}$, $d\vec{l} \perp \hat{r}$ (geometry of a circle: tangent perpendicular to radius), so $\sin\theta = 1$ everywhere. 3. $dB = \dfrac{\mu_0\,I\,dl}{4\pi R^2}$ (all elements contribute parallel to the loop axis, perpendicular to plane). 4. Integrate around the loop, total length $2\pi R$: $B = \dfrac{\mu_0\,I}{4\pi R^2}\cdot 2\pi R = \dfrac{\mu_0\,I}{2R}$. 5. Direction: perpendicular to the plane of the loop, given by the right-hand rule. 6. Option A is twice the correct value. Option C omits a factor of $2\pi$. Option D has wrong dimensions. _Source: syllabus Physics Part 1, Ch 4, §4.4 (Magnetic Field on the Axis of a Circular Current Loop, Eq. 4.13), p. 11._