Exercise 9.  Use the result of Exercise 8 to find the points z where the total charge    given the following conditions.  

9 (a).  Three positively charged rods carry a charge of    coulombs per unit length and pass through the points  .  

Solution 9 (a).

See text and/or instructor's solution manual.

    Each rod contributes the amount  ,  for    and  .

With rods at the points  ,  each carrying a charge of    coulombs per unit length, the total electric field intensity at z will be  

         .

Observe that    iff   ,  and the latter will be easier to solve.   

Since  k  is a constant it will suffice to solve  .  

Combine the terms and get

          

Now solve    and get  

           

Equipotential curves  .   Flux lines  .

The points where the equipotential curves , and the flux lines , are .
Remark.  The charged rods are located at the points  ,

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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