EXAM 1                     October 1, 1992                    PS 208    
      
   If you need a constant not given here or do not understand a  
problem, please ask me about it.  No notes, books, etc. may be used  
during this exam.    
                2                                -19
   g = 9.8 m/sec                     e = 1.6 x 10    C    

                                  9    2   2
    1 / (4 pi epsilon )=  9.0 x 10  N m / C          
                     0
                                        -31
   The mass of the electron is 9.11 x 10    kg.    

      

        1. [10 points]   

           Describe a good way to reconstruct Coulomb's Law without  

memorization.  You need not have a technique for finding the arbitrary  

form of the constant, and you may use anything in the exam heading.    

      

        The rest of the problems are worth 30 points each.  Include diagrams.    

           ______R __________________________R _______
          |       1             |             2       |
          |                     |                     |
    ______|                     R                     |____________
   |      |                      3                    |            |
   |      |                     |                     |            |
   |      |______R _____________|____________R _______|            |
   |              4                           5                    |
   |                                                               |
   |                                                               |
   |___________________________ V _________________________________|


        2. (From homework)   What is the current through the battery in  

the figure above if all the resistances are the same?  Set up the  

problem as if the resistances were all different and then use the  

symmetry to make the algebra simple.   


        3.  Find the electric field a distance  a  along a line  

perpendicular to the center of a rod of length  2L . The charge  

density along the rod is given by    

                    2    2  3/2
   lambda = alpha (a  + y  )    

   where  y  is the distance from the center of the rod and  lambda  is in  

Coulombs/m.  [Note that  a  really  appears twice in this problem].     

      
                                           -4
        4.  The force on a charge of 6 x 10   Coulombs placed 12 cm  
                                                                      2
outside of the *surface* of a long cylinder is measured to be 1.8 x 10 
                                                                    -6  
Newtons.  If the cylinder carries a charge per unit length of 5 x 10   

Coulombs/m, what is the radius of the cylinder?  Prove any formulae  

you use for electric fields near cylinders.          

      

   [If you are still working on any question shortly before the papers  

are due, tell me what issues and options you are considering.]