EXAM 3                    May 5, 1989                      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).
 

 (a)   Give a good, quick way of remembering the
Biot-Savart law for the magnetic field due to a infinitesimal
segment of current.
 

 (b)   Name the magnetic-field equivalent of Gauss's Law
for electric fields and explain the analogies between the two.
 

 2.  (From homework)  (a).  Find a
                                                        ______________________
                                                        |          |          |
 differential equation for the current                  |          |          R
                                                        V          R           2
                                                         0          1         |
 through the inductor in the circuit                    |          |          L
                                                        |          |          |
                                                        |__________|__________|
 shown to the right.  No other current
 

 should appear in the equation.
 
                              
 (b).                       at 
      Show that  I = A + B e    satisfies the differential
equation.  Determine all constants so that the current is known
for all times.

3.  A metal bar slides down an inclined plane in contact with two wires along the
edges of the plane.  The wires are connected together at the bottom of the plane,
and they are a distance  b  apart.  If the bar slides from rest down the incline, 
and a magnetic field  B  is directed vertically upward, find an
equation for the induced EMF between the ends of the sliding rod
as a function of time.  Assume negligible friction and large
resistance in the bar.  Show the direction of the (negligibly
small) current that flows in the circuit.
 

 4.  A very long, straight metal tube has inner radius  a  and
outer radius  b  .  A current whose density is J = cr flows down
the tube.  Find the magnetic field in the empty region inside
r = a  and also within the metal,  a < r < b .