- •Advanced chapters of theoretical electroengineering.
- •Inductance of the two-wire transmission line per unit length
- •External fluxes
- •Total inductance
- •Forces. The first line.
- •Forces. The second line.
- •Solution of the Laplace’s equation by separation of variables.
- •Properties of the Laplace’s equation.
- •Choice of a coordinate system
- •Variable separation in cylindrical coordinates
- •Angular function
- •Radial function
- •General solution of the Laplace’s equation in a cylindrical coordinate system
- •Application of the variable separation method for the magnetic field modeling
- •Reduced scalar magnetic potential
- •Combination of scalar magnetic potential and the reduced magnetic potential
- •Combination of scalar magnetic potential and reduced magnetic potential
- •Combination of scalar magnetic potential and reduced magnetic potential
- •Magnetic field of the line current near a magnetized cylinder
- •The scalar potential induced by the current line
- •The current potential in the cylindrical coordinate system
- •The current potential in the complex plane
- •Expansion of the current potential in the cylindrical coordinate system
- •Potentials in the problem domain
- •Magnetic field intensity in the problem domain
- •Magnetic field intensity induced by the wire with the current
- •Definition of coefficients
- •Solution of the problem
- •Magnetic field directions
- •Inductance of the two-wire transmission line per unit length
- •The flux induced by the magnetized cylinder
Advanced chapters of theoretical electroengineering.
Lecture 5
SPbTU, IE, Prof. A.G. Kalimov 2022 |
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Inductance of the two-wire transmission line per unit length
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External fluxes
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Total inductance
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Forces. The first line.
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6
Solution of the Laplace’s equation by separation of variables.
Решение уравнения Лапласа методом разделения переменных
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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.
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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:
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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
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Presentation of the potential |
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Laplace’s equation:
or:
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10