A circular loop of radius R carries current I. The magnetic field at a point on its axis at distance x from the centre is

1. Apply Biot-Savart to each current element on the loop; vertical components cancel by symmetry. 2. Each element contributes dB·sin α along the axis, where sin α = R/(R²+x²)^(1/2). 3. Integrating around the loop gives B = μ₀IR² / (2(R²+x²)^(3/2)). 4. At x = 0 the formula reduces to μ₀I/(2R), as expected for the centre. _Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", §4.6_