A numerical solution for the self-consistent differential equations describing the laminar-flow equilibrium in magnetically focused relativistic electron beams is given and proved to be available by comparison with analytical results of solid electron beam in the case of pθ=0 （magnetically shielded sources）. With the numerical method, the space-charge limited current and the externally applied magnetic field of both solid and annular electron beam in three cases of pθ=0,pθ=const and pθ∝r2 （magnetically immerged sources） are presented and compared. It is shown that the conditions at the source with respect to the canonical angular momentum pθ have little effect on the space-charge limited current and the externally applied magnetic field, but more intense annular electron beam generated by the source with pθ=const. can be transported in the same drift tube under lower guided magnetic field than solid ones.