EXAM 1                     March 13, 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 Gauss's Law,     

including the placement of the constant in the law.  You may assume     

that you know Coulomb's Law.      
                                                                      
          2.  [From homework]  Two charges, -Q  and - |alpha| Q  are a distance L     
                                              0                0
apart. These two charges are free to move but do not because there is     

a third charge nearby.  What must be the charge and placement of the     

third charge for the first two to be in equilibrium?       

          3.  Calculate the electric field everywhere inside a long     
                                                                      
cylinder of charge whose charge density is given by  rho = b/r.  The     
                                                                      
radius of the cylinder is R .      

          4.  There are two large metallic sheets having charge densities     
                                                                      
of  +sigma and -sigma  a distance  d  apart.      
                                                                      
          (a)  Find the electric field between the plates.      

          (b)  What is the force exerted per unit area by the electric     

field near the center of the positively-charged plate?      

          (c)  What object is exerting this force?      

          (d)  What is the force exerted per unit area by the electric     

field near the center of an isolated, positively charged metallic     

plate?        

          (e)  If the answer to (d) is nonzero, what object is exerting the     

force?  If the answer to (d) is zero, explain why the force vanishes     

here and does not vanish in question (b).      

          [If you have not completed this question shortly before the     

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