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Exercise N 5. Magnetic field of the cylindrical coil

Task
Make a plot of magnetic flux density at the axis of the coil with and without steel core.

Experiment
Magnetic flux density is measured in laboratory by webermeter.

Problem type
Linear axisymmetrical problem of magnetostatics.

Geometry
Due to problem symmetry only upper-right quarter a0b is defined, and at the axes of symmetry boundary conditions are set.

model of the cylindrical coil

Given data
Current density in the coil j=100000 A/m2.
Relative magnetic permeability of air and copper μ=1.
Relative magnetic permeability of steel of the core μ=500.

Boundary conditions
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.

Results
Dependence of the magnetic flux density upon the distance to the coil center:

magnetic flux density vs. distance to the coil center

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