Example 11.21.  Find the electrical potential    in the disk    that satisfies the boundary values

              

            Figure 11.38  The potentials    and  .  

Explore Solution 11.21.

Construct the solution with a conformal mapping.  This example is similar to Example 11.8.

Use Mathematica to make a contour plot of the temperature.  For computational purposes we use the following formula   .  

The following commands will graph the contours as parametric curves.

Hence the electrical potential    is harmonic in the disk |z| < 1 and has the desired boundary values.  

(c) 2006 John H. Mathews, Russell W. Howell