EXAM 3                 December 2, 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 )  =  9.0 x 10  N m / C 
                        0
                                             -31
        The mass of the electron is 9.11 x 10    kg.
 

1.  (10 points)
  Quote Gauss's, Ampere's, and Faraday's laws, and explain  
how you can use the similarities among them to help remember the  
forms.  Which law plays for the calculation of magnetic fields a role  
equivalent to that played by Gauss's Law for the calculation of  
electric fields.  (You needn't know which name goes with which law).  

     2.  [From homework]   A rectangular loop of wire of width  d  and

length  l  has a resistance  R  and lies in a plane which also contains

a very long straight wire parallel to the length (l) of the loop and a

distance  s  away.  If the current in the wire decreases from 

I  to  zero in a time  t , what is the current induced in the rectangular
 2      

loop?  Assume no initial current in the loop.  Prove that the magnetic  

field due to the wire is given by  mu   I    (t) / (2 pi x), x being 
                                     0   wire

the magnitude of the distance of the observation point from the wire.   
    
     3.  What is the force exerted on the wire in the problem above if  

the rectangular loop carries a current  I   and the wire carries a  
                                         1
constant current  I  ?  [You can solve this problem using only magnetic  
                   2
fields known from problem 2].  

     4.  (a)  What is the effective impedance
                                                   -------V cos(omega t)----
of the circuit to the right?  Give  Z  in the     |        0                |
                                                  R                         |
form of real and imaginary parts.                  1                        |
                                                  |                         |
         (b)  What is the absolute magnitude      |    ____L____            |
                                                  |___/         \___________|
of the impedance?                                     \____C____/         

         (c)  What would be the resonant 

frequency of this circuit (i. e. for what 

value of  omega  is  I  lowest)?

         (d)  How is the circuit oversimplified?