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Magnetic field of the cylindrical coil

solenoid magnetic FEA finite element analysis, magnetic flux density at the coil axis

In the lab the magnetic flux density is measured by a webermeter.

Problem type
Axisymmetric problem of DC magnetics.

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
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.

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

Solution
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 from the coil center:

magnetic flux density vs. distance to the coil center

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