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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.

**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* H_{t}=0. At the line *Oa* B_{n} =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 H_{t}=0.

**Results:**

Current density in spherical and cylindrical shielding:

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

- Time-harmonic magnetic field,
*f*=50 Hz

**Shield type****Peak value of B in point (0; 0), mT****Shielding coefficient****Problem**Steel sphere without slot 0.082 1695 lab4Fe.pbm Steel sphere with slot 36.0 3.86 lab4Fe+.pbm Steel cylinder without slot 0.013 10700 lab4cFe.pbm Steel cylinder with slot 40.3 3.45 lab4c_Fe+.pbm Copper sphere without slot 97.94 1.42 lab4Cu.pbm Copper sphere with slot 100 1.39 lab4Cu+.pbm Copper cylinder without slot 68.98 2.02 lab4cCu.pbm Copper cylinder with slot 70.73 1.97 lab4cCu+.pbm - DC magnetic field

**Shield type****Value of B in point (0; 0), mT****Shielding coefficient****Problem**Steel sphere without slot 1.52 91.45 lab4_f.pbm Steel sphere with slot 39.0 3.56 lab4_f+.pbm Steel cylinder without slot 2.08 66.83 lab4c_f.pbm Steel cylinder with slot 45.5 3.05 lab4c_f+.pbm