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Exercise N 4. Electromagnetic 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.

Spherical shield

Cylindrical shield

models of spherical and cylindrical shields

Given data
Relative magnetic permeability of air and copper μ=1.
Relative magnetic permeability of steel μ=1000.
Magnetic field is uniform, 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:

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

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