EXAM 2                   November 6, 1987            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.  Four equal point charges  Q  are placed at the four corners of
a square of side  a .  Find  V  at the center of the square.

     2.  A battery with EMF  V  and internal resistance  r  is
connected across a single resistor of resistance  R .  For what
value of  R  will the power dissipated in the resistor be a
maximum?  What will the maximum dissipated power be?

     3.  (From homework)  Determine the
current through each battery in the           --------V---r-------
figure.  Note that the values of the         |                    |
batteries and resistances have been          R1                   R2
changed so as to reduce the total            |                    |
number of unknown quantities.                |--------V---r-------|
                                             |                    |
             (The high side of all the       R1                   R2
             batteries is to the right.)     |                    |
                                             ---------V---r-------

     4.  A capacitor is made of two concentric cylinders of length  L

and radii  R   and  R  , with a dielectric of constant  kappa  between
            1        2
the cylinders.  If the inside cylinder carries a charge  +Q  and

the outside cylinder carries a charge  -Q , determine the electric

field in the dielectric, the potential difference between the

cylinders, and the capacitance of the device.  Neglect end

effects.