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Cylindrical coaxial coils interaction force
Task
Find the force between the coils carring current with and without the shield between them.
Experiment
Forces are measured by use of digital balance on which one of coils is installed (see the right picture below). Tests are performed with currents varying, and different conductors and ferromagnetics are placed between coils.
Problem type
Plane-parallel problem of DC magnetics, AC magnetics.
Geometry
Due to symmetry of the formulation only upper half of the problem (above ab line) is defined, and at the axis of symmetry (line ab) the boundary conditions are set.
Given data
Current density in the coil j = 0.1 A/mm2.
Relative magnetic permeability of the steel disc μ= 1000.
Electrical conductivity of steel disc σ= 10 MS/m.
Electrical conductivity of aluminum disc σ=37 MS/m.
Coils are wound by insulated wire, so cross-section conductivity in coils σ= 0 S/m.
Boundary conditions
Along the horizontal symmetry axis (line ab) Bn =0.
Equation B=rot A in cylindrical coordinate system leads to A=const at the axis ab. The field fades at the infinity, so due to the condition of continuity of the potential A=0 at the line ab.
Results:
Field distribution around coils:
- Time-harmonic magnetic field, f=50 Hz.
Shield type
Interaction force, mN
Problem
No shield
0.533
lab2.pbm
Steel
0.098
lab2_Fe.pbm
Aluminum
0.282
lab2_Al.pbm
- DC magnetic field
Shield type
Interaction force, mN
Problem
No shield
0.533
lab2c.pbm
Steel
0.138
lab2c_Fe.pbm