Exercise 6.   The complex potential    determines an electrostatic field that is referred to as a dipole.

6 (a).   Show that   ,   hence a dipole is the limiting case of a source and sink.

Solution 6 (a).

This follows from the definition of the derivative, i. e. if      then      and  

        
    and    
        .

Hence         

It follows that  

         .  

Therefore, a dipole is the limiting case of a source and sink.

This solution is complements of the authors.

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