Example 11.20.   Find the electrical potential    produced by two charged half-planes that are perpendicular to the z plane and pass through the rays    where the planes are kept at the fixed potentials  

              

Figure 11.37  The electric field produced by two charged half-planes

                    that are perpendicular to the complex plane.

Explore Solution 11.20.

Enter the formula for the electrical potential.

Check out the formula at some boundary values.

Use Mathematica to make a contour plot of the electrical potential.

The following commands will graph the contours as parametric curves.

Hence the electrical potential    is harmonic in plane slit along the rays    and has the desired boundary values.  

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