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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 nonmagnetic materials. Due to symmetry only rightupper 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.
 Timeharmonic 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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