Advanced chapters of theoretical electroengineering.
Lecture 5
SPbTU, IE, Prof. A.G. Kalimov 2022 |
1 |
Inductance of the two-wire transmission line per unit length
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Thin wire approach:
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External fluxes
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Ris the radius of wire
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3
Total inductance
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4
Forces. The first line.
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5
Forces. The second line.
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6
Solution of the Laplace’s equation by separation of variables.
Решение уравнения Лапласа методом разделения переменных
7
Properties of the Laplace’s equation.
Electrostatic field.
U 0 |
E U |
This equation for the potential is valid in the absence of the distributed electric charges .
Magnetostatic field.
U 0 |
H U |
U here is magnetic scalar potential. The equation is valid if there are no currents in the problem domain
Laplace’s equation has a unique solution when the boundary conditions are defined at the border of the problem domain:
U F1 |
1st type boundary conditions. |
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2nd type boundary conditions. |
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Choice of a coordinate system
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Reasonable choice is a cylindrical system with the center in O.
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Variable separation in cylindrical coordinates
Cylindrical coordinate system; variables: |
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Laplace’s equation in cylindrical system |
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Presentation of the potential |
U R(r) S( ) |
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Laplace’s equation:
or:
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