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The magnetic flux density inside the CMS superconducting coil is reproducible with the TOSCA magnet model within 0.1%. The CMS magnet model represent the field measured in steel with the flux-loops at the central field of 3.68 and 4.01 T within (0.7±6.49)% in average that allows using the model to describe the magnetic flux density distribution inside the CMS steel yoke. The ring coil increases the radial magnetic flux density at the radius of 0.5 to 1.0 m and 9.5<|Z|<11.0 m from ~20 to ~100 mT. The azimuthal magnetic flux density produced with the proposed air-core toroid varies from 0.7 to 3.4 T.