Make a plot of magnetic flux density distribution along the axis of the coil with and without steel core.
Magnetic flux density is measured in laboratory by webermeter.
Linear axisymmetrical problem of magnetostatics.
Due to problem symmetry only upper-right quarter is defined, and at the axes of symmetry boundary conditions are set.
At the vertical axis of symmetry (line Ob) Ht=0. At the horizontal axis of symmetry Oa Bn=0. From B=rotA in the cylindrical coordinate system we have at the axis Oa A=const. Field fades at the infinity, so at the line Oa A=0 due to continuity of A.
Dependence of the magnetic flux density upon the distance to the coil center: