Solution 15.

See text and/or instructor's solution manual.

Solution.  The equipotentials      can be written as  .  

Then we get  ,  and  then  .

Taking anti-logs this we have   ,  which are

concentric circles centered at the origin with radii  .  

        The streamlines    can be written as  .   Using the polar form  ,  we see that

this is the equation for rays emanating from the origin making an angle of    radians for  .  

We can let Mathematica do our work.

                    The equipotentials    are shown in blue for  .

                    The streamlines    for    are shown in blue for  .  

This solution is complements of the authors.

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