Question

A current carrying circular coil of radius r and current I is flowing the magnetic field at the centre of coil is

Answer 1

The magnetic field at a distance axially $x$ from the center of a current carrying loop of radius $r$ is

$B(x)=\frac{\mu_0I}{2} \frac{r^2}{(x^2+r^2)^{3/2}}$.

The magnetic field at the center of the coil is

$B(0)=\frac{\mu_0I}{2} \frac{r^2}{(0^2+r^2)^{3/2}}\\ B(0)=\frac{\mu_0I}{2} \frac{r^2}{r^3}\\ B(0)=\frac{\mu_0I}{2r}$