Two-Dimensional Electrostatics

 

Example 11.21. Find the electrical potential [Graphics:e4.txtgr1.gif] in the disk
D: |z| < 1 that satisfies the boundary values:
[Graphics:e4.txtgr2.gif]

Solution: Use the mapping:

[Graphics:e4.txtgr4.gif][Graphics:e4.txtgr3.gif]

The electrical potential is:

[Graphics:e4.txtgr4.gif][Graphics:e4.txtgr5.gif]

The inverse transformation is useful in carrying out the computations.

[Graphics:e4.txtgr4.gif][Graphics:e4.txtgr6.gif]

A graph for the solution is:

The electric potential in a disk.

 

 

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(c) John Mathews, 1998, 2006