Magnetic field around a Braunbek coil[1] consisting of four round current loops with identical current, which are aligned around a common symmetry axis. This arrangement removes variations in the magnetic field, up to its 7th-order derivative with respect to the center, making it the smoothest possible field achievable with four circular coils of identical current.The inner loops have an axial position z1=±0.27803R1{\displaystyle z_{1}=\pm 0.27803\,R_{1}} and radius R1{\displaystyle R_{1}}. The outer loops have an axial position z2=±0.84566R1{\displaystyle z_{2}=\pm 0.84566\,R_{1}} and radius R2=0.76390R1{\displaystyle R_{2}=0.76390\,R_{1}}. The current through all loops is I{\displaystyle I}. The central magnetic field is B0=1.28861μ0I/R1{\displaystyle B_{0}=1.28861\mu _{0}I/R_{1}}.
The dots symbolize where the current flows out of the image plane, whereas the crosses are where the current flows into the plane.
Own work
Geek3