EXAM 3                  December 5, 1986          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.  Show carefully that the field between two
                                                            |         |
 wires carrying current in opposite directions as       ^   |         | |
                                                        |   |         | V
 in the diagram to the right is                             |         |
                                                             <---d--->
     mu  I                        
       0             1             1
 B = ------- [   ---------- + -----------  ]
       2 pi       d/2 + x       d/2 - x
 

2.   The circuit  shown  on  the right is a           --- L=0.20 hen ----
                                                     |                   |
                                                     |                   |
rather primitive "low-pass" filter.  For            EMF                R=50 ohm
                                                     |                   |
                                                     |                   |
an EMF of 20 V, find the potential drop              |___________________|
 

across the 50 Ohm resistance if the
 

input frequency is omega   = 20/s and if the
                        1

input frequency is  omega  = 3000/s . In a
                         2

maximum of one sentence and one equation tell what would happen if

equal EMF's of each frequency were applied simultaneously.
 
 
 3.  Show that the inductance per unit length of the wires in

                    mu
                      0      d-a
problem 1 is  L/l = ---- ln ----- ,
                     pi       a

where a is the wire radius.

Neglect the flux within the wires.
 
 

 4.  A  metal ring of area A is placed in a constant, uniform field

B in such a way that its area vector makes an angle  theta  to the lines

of B.  The loop now rotates about a diameter so that  theta = omega*t.  If

the resistance of the coil is R, find the current through the coil

as a function of time.  The current-carrying coil experiences a

torque in the magnetic field.  How large is this torque?