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Main >> Applications >> Sample problems >> 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 |

**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* 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