# Magnetic Field of a Current Loop using Ampère's Law

A typical exercise while introducing the Biot-Savart Law is to calculate the magnetic field caused by a circular current loop at a point P located in its central axis, as shown in the following figure:

The result is well known:

$$\mathbf{B} = \dfrac{\mu_0 I a^2}{2(a^2+z^2)^{3/2}} \mathbf{\hat{k}}$$

My goal now is to find this magnetic field using Ampère's Law, so what Amperian loop you recommend me to use in order to apply this Law?

Ampere's law is not useful in this case. It says that the line integral of the B field around a closed path is equal to $\mu_0$ times the current passing through the closed path (for steady currents).