Device for generating an orientable and locally uniform magnetic field, including N≧3 identical assemblies of cylindrical coils, each assemblies having a first and a second coil, the coils being coaxial with an axis oriented along a direction z and arranged symmetrically on either side of the plane, with a gap in the axial direction, the assemblies arranged such that their outlines in a plane xy perpendicular to the z-axis are regularly spaced along a circle of center O and of radius a0>0, so to leave a central free space. A supply system supplies the coils with a current set to obtain, at the center of the device, a magnetic field having the desired orientation. The device may include two pairs of cylindrical coils having a common axis oriented in said z-direction and passing through the center of the circle, these coils being arranged symmetrically on either side of said xy-plane.