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Main >> Applications >> Sample problems >> Cylindrical coil magnetic field

Exercise N 5. Magnetic field of the cylindrical coil

Task
Make a plot of magnetic flux density distribution along 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
Magnetic field of the cylindrical coil Make a plot of magnetic flux density distribution along the axis of the coil with and without steel core. Core Winding a b O 300 mm Ø 20 mm Ø 50 mm Ø 45 mm Ø 100 mm

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
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.

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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