Exercise 1.  Find the electrostatic potential    between the two coaxial cylinders    and  ,  

that has the boundary values,  (shown in Figure 11.39)    

                      

Solution 1.

See text and/or instructor's solution manual.

Answer.   .  

Solution.   Applying Example 11.3 in Section 11.1 we know that the form of the solution is  

                    .  

Substitute      and get    

                      

Therefore,   

                    .   

We are done.   

Aside.  We can let Mathematica double check our work.

Aside.   If polar coordinates      are used, then the polar form of the solution is     

                    .   

We are really done.   

Aside.  For illustration purposes we can graph the function   .   

                     A contour graph of the function   

                     where      for   .  

We are really really done.   

                     A contour graph of the function   

                     where      for   .  

                    A graph of the function   ,    

                      

                    A graph of the function   ,    

                       

                    A graph of the function   ,  

                       

This solution is complements of the authors.

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