EXAM 1                     March 8, 1988                    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                   -7
   1/(4 pi epsilon )  = 9.0 x 10   N m  / C     mu /(4 pi) = 10   T m / A
                  0                               0 

                                         -31                                      
    The mass of the electron is 9.11 x 10    kg.             
                                                                               
                                                                               
    1. (a).  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 heading of this exam.                                                      


    (b).  Explain a good technique for determining without                   

memorization how to determine the constant in Gauss's Law.  You                

may assume that you know Coulomb's Law.  [8 points each part]                  


    [The remaining problems count 28 points each.]                             


    2.  In the Bohr model of the hydrogen atom, an electron                    

circles a proton at a radius of  a  .  How fast must the electron       
                                  0
be moving if no forces other than the Coulomb attraction are large             

enough to matter?                                                              

3. (From homework)  A thin cylindrical shell of radius R  is          
                                                        1                      
surrounded by a second concentric concentric cylindrical shell of              

radius R . The inner shell has a total charge +Q and the outer          
        2
shell -Q.  (a)  Assuming the length L of the shells is much                  

greater than R   or R , determine the electric field as a function
              1      2                                            
of r ,  the perpendicular distance from the common axis of the                  

cylinders (the usual cylindrical-coordinate r) everywhere (i. e.             

inside both cylinders, between the two, and outside both).                    

    4.  A rod of length  L  is placed a distance  b  to the right of the

origin.  The charge density (Coul/m) on the rod is 

                        2     2  3/2
         lambda = -c ( x  +  a  )

What is the electric field at the point  x=0,y=a ?  Note that  a 
occurs in two different places in this problem.