EXAM 2                 April 12, 1989                      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 ) = 9.1 x 10  N m  / C                                    
                    0                                                          
                                                                               
                      -7                                                       
     mu  / (4 pi) = 10   T m/ A                                                
       0                                                                       
                                                                               
                                           -31                                 
     The mass of the electron is 9.11 x 10     kg.                             
                                                                               


   1.  (a).  Explain the relationships among Force, Electric Field,
Potential Energy, and Electrical Potential.  How can you use these
relationships to remember the formula giving the Electrical Potential
when the Electric Field is known?
 

   (b).  What are the relationships among the formulae for
effective capacitance for series and parallel combinations of
capacitors and the effective resistance for series and parallel
combinations of resistors?
 

   2.  (Simplified from homework).  Determine the current through
each of the resistors in the figure below.  Write down the junction
and both possible loop equations explicitly.  [Hint: with a little
thought, you can do the algebra for this problem rather easily.]


      _______ R  ________________  R  _____
     |         2        |           2      |
   __|__                |                __|__
 _________ V            r             __________  V
     |                  |                  |
     |                  |                  |
     r            ______|_______           r
     |                _____       2V       |
     |                  |                  |
     |_______ R  _______|_________ R ______|
               1                    1
                                                            
[Don't miss the r 's in the vertical branches]

   3.  A spherical capacitor is to be constructed by using a metal
sphere of radius  b  as one plate and a concentric spherical metal
shell of inner radius  a  as the other plate.
 

   (a).  Use Gauss's law to determine the electric field between
the plates.
 

   (b).  How is the result for this field changed if a dielectric
of dielectric constant  epsilon   completely fills the volume between the
plates?
 

   (c).  Find the capacitance of the device when the dielectric is
present (or in the absence of dielectric if you cannot complete
part (b) ).
 

   4.  A coil of wire is wound on an evacuated, hollow glass tube
with inner diameter  d  meters.  The coil produces a uniform
magnetic field of  B  parallel to the axis of the tube.  Protons
with speed  v  are shot into the tube at a point on its axis.
What is the maximum angle to the axis that a particle can be
moving as it enters the tube if it is not to hit the wall as it
spirals down the tube?