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
Uniformal 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 millivoltmeter.
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 |
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Given data
Relative magnetic permeability of air and copper μ=1.
Relative magnetic permeability of steel μ=1000.
Magnetic field is uniformal, 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 uniformal, and the right boundary has the same condition as the left one Ht=0.
Results
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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