EXAM 2                    April 15, 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 ) = 9.1 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.  (10 points) 
   
   (a) Give a good argument for remembering the following:  

     (1).  The electric potential caused by a point charge.  

     (2).  The capacitance of a parallel plate capacitor.  

     (3).  The resistance of a wire of given resistivity and size.  

  (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.  Derive with reasonable care the expression for the 

capacitance of a parallel-plate capacitor, whose plates are a constant 

distance  d  from each other, and each of which has the same shape and 

a total area of  A . Assume  d << the length and width of the plates.  

The management suggests getting the same result as that in problem 1a. 

Some extra credit will be given for accurately including the 

effects of a dielectric between the plates.   

 3.  (Simplified from homework)  Determine the current through 

each of the resistors in the figure below, where  R  = R   and  
                                                   4    2
     
R  = R .  Show all the equations that would be necessary to solve the 
 3    1                                                        

problem if the resistors were not related, and then use symmetries to 

simplify and solve the problem.   

      _______ R  ________________  R  _____
     |         4        |           2      |
   __|__                |                __|__
 _________ V            R             __________  V
     |                   5                 |
     |                  |                  |
     |_______ R  _______|_________ R ______|
               3                    1
                                                            


      4.  A flat disk of radius  b   carries a constant surface 

                                 2
charge density of  sigma [in C/m  ] and rotates around an axis AA' perpendicular

to the disk and passing through its center.  It rotates at an angular

speed of  omega  [in 1/sec]. Show that each ring of width  dr  carries a 

current  dI = sigma * omega * r * dr  [It may help to think of the surface 

charge density as  sigma = rho*h , where  rho  is a volume charge density and  

h  is the thickness of the charge layer].  Given this expression for 
                                             ->     
the current,  and a constant magnetic field  B  perpendicular to the axis of 

rotation, show that the torque on the disk is  

       1                             4
tau =  - * sigma * omega * pi * B * b
       4