EXAM 2                    April 17, 1991              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.                             


             (a)  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? 

             (b).  What are the two relations used in solving
those DC circuits that cannot be solved solely by using series
and parallel combinations of resistors?  Justify these two relations. 

        2.  (From homework)   An electron enters a uniform magnetic
       ->                          ->
field  B   at an angle  theta  to  B .
      
Determine the radius and pitch (distance between loops) of

the electrons's helical path, assuming its velocity  v  is known. 
 
   3.  Determine the current through each of the resistors in the
figure below,  where the resistance of each
is the same .  Show all the equations that
would be necessary to solve the problem if the resistors were
not all the same, and then use symmetries to simplify and
solve the problem.  

    --------R4-------------R2---------
    |               |                |
    V               R5               V    The high side of the potentials
    |               |                |    is on the geometrically lower 
    -------R3-------------R1---------     side in both cases.


  4.  A parallel-plate capacitor of size  a  by  b  with the plates a
distance  d  apart is filled with two dielectrics, each filling half 
of the capacitor.  Show that the capacitance is given by

       epsilon  a b     kappa  + kappa
              0              1        2
   C = --------------   ---------------
             d                 2

where the kappa's are the relative permeabilities of the two dielectrics.