Consider a circular current carrying conducting coil.

What is the ratio of the magnetic fields at the centre of a circular coil carrying current to that at a point whose distance is half of the radius of the coil ?

5 \(\sqrt {5}\) : 8

magnetic field at the centre of a circular coil carrying current I, Bc = μ_oI/2R

magnetic field at a point whose distance is half of the radius of the coil (R/2) ,

Bz = μ_oI/(R² + (R/2)²)^3/2

Ratio = Bc/Bz = (5/4)^3/2