The magnetic field of an annular MHD thruster made of independent superconductingmodules has been studied with analytical and numerical methods. This configurationallows to obtain large magnetized volumes and high induction levels with rapidlydecreasing stray fields. When some inductors are out of order, the thruster reMaynsstill operational, but the stray fields increase in the vicinity of the failure. Forgiven structural materials and superconductors, it is possible to determine the sizeof the conductor in order to reduce the electromagnetic forces and the peak fieldsupported by the conductors. For an active field of 10 T in a 6 m ray annular activechannel of a thruster with 24 modules, the peak field is exactly 15.6 T in theNb3Sn conductors and the structure has to sustain 108 N/m forces. The necessityto place some magnetic or superconducting shield is discussed, particularly when the thruster is in a degraded regime.