Solution 13 (b).

See text and/or instructor's solution manual.

We can let Mathematica do our work.

                                                            [Graphics:../Images/HarmonicFunctionModHome_gr_857.gif]

                    The equipotentials  [Graphics:../Images/HarmonicFunctionModHome_gr_858.gif]  are shown in blue for  [Graphics:../Images/HarmonicFunctionModHome_gr_859.gif].

 

                                                            [Graphics:../Images/HarmonicFunctionModHome_gr_860.gif]

  

                    The streamlines  [Graphics:../Images/HarmonicFunctionModHome_gr_861.gif]  are shown in blue for  [Graphics:../Images/HarmonicFunctionModHome_gr_862.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell