Download presentation

Presentation is loading. Please wait.

Published byQuentin Mills Modified over 2 years ago

1
3.5 Two dimensional problems Cylindrical symmetry Conformal mapping

2
Laplace operator in polar coordinates

3
Example: Two half pipes

4
Conformal Mapping Is there a simple solution?

5
For two-dimensional problems complex analytical function are a powerful tool of much elegance. x iy Maps (x,y) plane onto (u,v) plane. For analytical functions the derivative exists. Examples:

6
Analytical functions obey the Cauchy-Riemann equations which imply that g and h obey the Laplace equation, If g(x,y) fulfills the boundary condition it is the potential. If h(x,y) fulfills the boundary condition it is the potential.

7
g and h are conjugate. If g=V then g=const gives the equipotentials and h=const gives the field lines, or vice versa. If F(z) is analytical it defines a conformal mapping. A conformal transformation maps a rectangular grid onto a curved grid, where the coordinate lines remain perpendicular. Cartesian onto polar coordinates: Example Polar onto Cartesian coordinates: Full plane z w

8
A corner of conductors

9
Edge of a conducting plane equipotentials field lines

10
Parallel Plate Capacitor

Similar presentations

OK

1 LAPLACE’S EQUATION, POISSON’S EQUATION AND UNIQUENESS THEOREM CHAPTER 6 6.1 LAPLACE’S AND POISSON’S EQUATIONS 6.2 UNIQUENESS THEOREM 6.3 SOLUTION OF.

1 LAPLACE’S EQUATION, POISSON’S EQUATION AND UNIQUENESS THEOREM CHAPTER 6 6.1 LAPLACE’S AND POISSON’S EQUATIONS 6.2 UNIQUENESS THEOREM 6.3 SOLUTION OF.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Convert doc file to ppt online ticket Ppt on natural resources for class 8 Ppt on main idea Ppt on robert frost poems Ppt on electronic media Ppt on pi in maths lesson Ppt on mid day meal Ppt on water scarcity and conservation Ppt on share market basics Ppt on periscope