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

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 field of the cylindrical coil with/without the core

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