Finding magnetic field outside a current loop with Biot-Savart

[a9211l]

Applying the Biot-Savart eq'n for inside a current loop is pretty simple to find the magnetic field inside a current loop.

But how would one find the magnetic field outside of one?

 

[Meir Achuz]

On the axis, it is fairly simple.
Off axis, you need a Legendre polynomial expansion of the magnetic scalar potential.

 

[robphy]

Elliptic Integrals:
e.g.,
http://www.netdenizen.com/emagnettest/offaxis/?offaxisloop