In the lab the magnetic flux density is measured by a webermeter.
Axisymmetric problem of DC magnetics.
Current density in the coil j=0.1 A/mm².
Relative magnetic permeability of air and copper μ=1.
Relative magnetic permeability of steel of the core μ=500.
Make a plot of magnetic flux density distribution along the axis of the coil with and without steel core.
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 from the coil center: