Field induced by the line sources
The normal component of |
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the field intensity induced |
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by the charged line in the |
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cylinder center |
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EnC |
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2 0 |
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The normal component of the field intensity induced by the charged line in the inverse point:
EnB |
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1 |
cos |
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21
Geometrical relations
The normal component of |
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the field intensity induced |
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a |
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by the surface charges |
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C |
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may be expressed as |
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A |
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B |
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2 |
1 |
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2 |
1 |
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1 |
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E |
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cos( ) |
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n |
2 0 |
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2 |
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a |
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2 0 |
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2 |
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1 |
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1 r |
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The first term corresponds to field induced by the charged line in the inverse point. The second term corresponds to field induced by the charged line in the central point.
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2 |
1 |
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1 |
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2 0 |
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2 0 |
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22
The field sources for the external domain
0 |
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0 |
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A 
B C
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0 |
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The field sources for the internal domain
0 |
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0 |
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A 
C
2 0 0
24
Application of the Images Method for calculating magnetic fields in the presence of cylindrical objects
25
Image method for the flat boundary between magnetic media.
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H (1) |
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H |
(2) |
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Boundary conditions: |
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2 |
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i |
y |
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H (1) |
H (2) |
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1 |
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x |
For the chosen coordinate system: |
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H |
(1) |
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(2) |
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2 |
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y |
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y |
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H x(1) |
H x(2) |
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26
Equivalent magnetic charge density.
Assuming the same magnetic permeability in the whole space: |
1 |
i y
1 |
h |
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x |
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1 |
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Charge density H y(1) |
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H y2 |
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1 |
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(x) 2 |
1 2B(ext) |
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(1) |
(ext) |
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Hn |
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2 1 |
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(2) |
(ext) |
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Hn |
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2 1 |
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27
The field in the presence of a cylindrical magnetic object
0 |
r |
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i |
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A C
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The field sources for the magnetic field intensity in the external domain
0 
r 0
A 
B C 
i 
i 0
0
i 00
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The field sources for the magnetic field intensity in the internal domain
0 
r 0
A 
C
i 2 0
0
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