EXAM 3                   March 7, 1990              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.  (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.  
  
  
  
(The remaining problems count 30 points each.)  
  
  
  
     2.  (From homework)  A very long solid nonconducting cylinder 
  
  
of radius  R  and length  L  (with  R  << L ) possesses a uniform 
            0                        0
  
volume charge density  rho.  Determine the electric field for 
  
  
all points inside the cylinder (r < R ).    
                                     0
  
  
     3.  A thin charged rod of length  L  lies along the positive 
  
  
x axis with one end at the origin.  Its charge per unit length is  
  
  
lambda  = A x , where  A  is a constant.  Find the electric field at a
      
  
point on the x axis, with  x = b + L  .  [Integration hint: you 
  
  
may find it useful to make a change of variables to make the 
  
  
denominator in the integrand as simple as possible.]  
  
  
  
  
  
     4.  A small sphere of mass  m  and charge  q  hangs as a 
  
  
pendulum of length  L  in a region where the electric field is 
  
  
directed downward and has magnitude  E .  Show that the period of 
  
                        
the pendulum is  omega = sqrt(L/[ g + qE/m ]) .  [Note that the expression 
  
  
for  omega  under gravity alone is contained in this expression.]