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Electromagnetic shielding

electromagnetic shielding FEA finite element analysis, field attenuation by magnetic shielding

Task
Find the level of magnetic field reduction inside the shield. Shields made of steel and copper of the same geometry are analyzed.

Experiment
Uniform external magnetic field is produced by the electric magnet. The shield with the measuring coil inside is placed between its poles. EMF in the coil is measured: in case of DC current in the coil - by ballistic galvanometer (in the moment of switching on), in case of AC current - by use of voltmeter.

Geometry
The shield consists of two halves. Possible positions of the slot in the shield is shown by dotted line. The slot could be enlarged up to 2 mm by sheets of non-magnetic materials. Due to symmetry only right-upper quarter aOb is analyzed, and at the axes of symmetry the boundary conditions are set.
Electromagnetic shielding The shield consists of two halves. Cylindrical shield Ø63mm 5mm 31.5mm 31.5mm Gap 0.. 2mm Spherical shield The shield consists of two halves. Spherical shield Ø63mm 5mm Gap 0.. 2mm

Given
Electrical conductivity of copper 57 MS/m.
Electrical conductivity of steel 10 MS/m.
Relative magnetic permeability of steel μ=1000.
External magnetic field flux density B = 0.139 T (peak value for AC magnetic problem).

Boundary conditions
Due to symmetry at the line Ob Ht=0. At the line Oa Bn =0. Equation B=rot A in the cylindrical coordinate system leads to A=const (0.0695) at the axis Oa. Field fades at the infinity, so due to continuity at the line Oa A=0 also. The field is uniform, and the right boundary has the same condition as the left one Ht=0.

Results:
Current density in spherical and cylindrical shielding:

spherical and cylindrical magnetic shields simulation

Shielding coefficient - relation of magnetic flux densities outside and inside the shield.

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