This paper uses the basic knowledge of electromagnetic field theory to study the magnetic field distribution of a uniformly charged spherical shell rotating at a constant speed in the whole space. First, due to the symmetry of the current distribution, the corresponding magnetic field is axially symmetric; the two components of the magnetic induction intensity at a certain point are directly written according to the BiotSavart law, and numerical simulation is performed to calculate the magnetic field inside and outside the spherical shell. The results show that the inside of the spherical shell is a uniform magnetic field. Secondly, the magnetic field is discussed respectively using the magnetic scalar potential and the magnetic multipole method. By comparing the magnetic field outside the spherical shell, it is found that the current distribution in this problem has certain particularities. Finally, the magnetic field excited by a spherical shell formed by a single thin wire with a steady current passing through it is discussed.