JULY 23 - JULY 29
         Young and Freedman - 12th Ed - CHAPTER 27
         76.  Please add the following part:
              (d) For each of the above magnetic fields, what 
              will be the maximum kinetic energy of the loop if 
              it is released from rest from the position shown
              in Figure 27.66 (you may consider the loop to be
              pivoted about the y-axis and you may ignore all

         Young and Freedman - 12th Ed - CHAPTER 28
         69.  To get credit for this problem, you must show
              carefully how to use the Biot-Savart Law to arrive
              at the answer.

         Young and Freedman - 12th Ed - CHAPTER 29
         28.  Please add the following parts:
              (c) What is the magnitude of the induced electric
              field at a point just outside the center of the
              solenoid (lengthwise) and 4.00 cm from the axis of
              the solenoid?  (d) Using Figure 29.54 (p. 1027),
              and applying that figure to the situation of this
              problem, what would be the direction of the induced
              electric field in part (a) of this problem?

         33.  Please add the following part:
              (b) What is the mutual inductance of this two-coil
              geometry?  (Note that, in part (a), the question
              is asking only for the average induced EMF in the
              second winding due to the change of current in the
              first winding; in other words, you are to ignore
              the back EMF in the second winding due to its
              self inductance.)

         63.  The rod in this problem is intended to be the moving
              part in a simple DC generator.  Here is a figure
              of such a generator; the connecting wires are not
              shown.  This problem is most straightforwardly done
              by integrating vcrossBdotdl over the length of the
              moving rod (note that v in this integral will not
              be constant).  Here is a pdf version of the figure.
         77.  Note that the metal rails in the figure for this
              problem are drawn in gray; the thin black lines
              represent a non-metal frame.  For part (b), remember 
              that the terminal speed is the maximum speed, i.e. 
              the speed at which the acceleration becomes zero.

         Young and Freedman - 12th Ed - CHAPTER 30
         48.  The main purpose of this problem is to calculate
              the inductance of a length of coaxial cable (i.e.
              part (d)).  The problem assumes (but does not
              state) that the cable is being used to carry high
              frequency alternating currents (like a cable carrying
              a TV signal); in such a case the currents would be
              largely confined to the outer surface of the inner
              wire and the inner surface of the outer tube (i.e.
              the magnetic field is confined to the nonconducting
              space between the two metal pieces).  So the flux
              calculated in part (c) is in fact the total flux.
              Part (b) is asking you to turn the 2D flux integral
              into a 1D integral (the integral over dl being
              done implicitly); you may just ignore part (b).
              And in part (c), the words "over the volume" are
              silly; flux is always an integral over an area, so
              the integral is over a rectangular area perpendicular
              to the magnetic field between the two pieces of metal.

          73. There is a misprint in this problem.  The power series
              expansion for ln(1+z) = z - z^2/2 + higher order terms.
              Y&F mistakenly have a plus sign between the first
              and second terms of the expansion.
         Halliday and Resnick - 2nd Ed - CHAPTER 30
          9.  A stationary circular wall clock has a face with a 
              radius of 15 cm.  Six turns of wire are wound around
              its perimeter; the wire carries a current of 2.0 A in
              the clockwise direction.  The clock is located where
              there is a constant, uniform external magnetic field 
              of magnitude 70 mT (but the clock still keeps perfect
              time).  At exactly 1:00 p.m., the hour hand of the
              clock points in the direction of the external magnetic
              field.  (a) After how many minutes will the minute hand
              point in the direction of the torque on the winding due
              to the magnetic field?  (b) Find the torque magnitude.

         22.  An electric field of 1.50 kV/m and a magnetic field of
              0.400 T act on a moving electron to produce no net force.
              (a) Calculate the minimum speed v of the electron.  
              (b) Draw the vectors E, B, and v (E, B, and v are vector 

         29.  An alpha particle (q = +2e, m = 4.00 u) travels in a
              circular path of radius 4.50 cm in a uniform magnetic
              field with B = 1.20 T.  Calculate (a) its speed, (b) its
              period of revolution, (c) its kinetic energy in electron-
              volts, and (d) the potential difference through which it
              would have to be accelerated to achieve this energy.

         31.  An electron has an initial velocity of 
              (12.0 km/s)j + (15.0 km/s)k and a constant acceleration
              of (2.00 Tm/s^2)i in a region in which uniform electric
              and magnetic fields are present.  If B = (400 microT)i,
              find the electric field E (E and B are vectors).

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 30
         73.  A long, hollow cylindrical conductor (inner radius
              = 2.0 mm, outer radius = 4.0 mm) carries a current
              of 24 A distributed uniformly across its cross
              section.  A long thin wire that is coaxial with
              the cylinder carries a current of 24 A in the
              opposite direction.  What are the magnitudes of
              the magnetic fields (a) 1.0 mm, (b) 3.0 mm, and
              (c) 5.0 mm from the central axis of the wire and

         WOLFSON - CHAPTER 30
         42.  A conducting slab extends infinitely in the x and y
              directions and has thickness h in the z direction.
              It carries a uniform current density vecJ = J(veci)
              (vec indicates that the first J and the i are vectors,
              -- the veci is the unit vector in the x direction).
              Find the magnetic field strength (a) inside and 
              (b) outside the slab, as functions of the distance z
              from the center plane of the slab.

         48.  A long solenoid with n turns per unit lengths carries
              a current I.  The current returns to its driving 
              battery along a wire of radius R that passes through
              the solenoid, along its axis.  Find expressions for
              (a) the magnetic field strength at the surface of 
              the wire, and (b) the angle the field at the wire
              surface makes with the solenoid axis.

         57.  The figure below shows a wire of length L carrying
              current fed by other wires that are not shown (the
              current direction is to the right).  Point A lies 
              on the perpendicular bisector, a distance y from the 
              wire.  Show how to use the Biot-Savart Law to 
              demonstrate that the magnetic field at A due to the 
              straight wire alone has magnitude


              What is the field direction?

                      _  . B            . A


                      -  ------------------------------  I -->

                         |<--           L          -->|

         58.  Point B in the figure above lies a distance y
              perpendicular to the end of the wire.  Show how to
              use the Biot-Savart Law to demonstrate that the
              magnetic field at B due to the straight wire alone
              has magnitude


              What is the field direction?

         68.  A solid conducting wire of radius R runs parallel
              to the z axis and carries a current density given by
              vecJ = J_0(1-(r/R))veck, where J_0 is a constant and
              r the radial distance from the wire axis (vec 
              indicates that the first J and the k are vectors,
              -- the veck is the unit vector in the z direction).
              Find expressions for (a) the total current in the
              wire, (b) the magnetic field strength for r > R,
              and (c) the magnetic field strength for r < R.

         32.  Consider a toroidal solenoid with a square cross
              section, each side of which has length 3 cm.
              The inner wall of the torus forms a cylinder of
              radius 12 cm (figure 28.25(a) on page 976 could
              roughly be a toroid of this description -- for a
              cutaway view see figure 30.8 on page 1037).  The 
              torus is wound evenly with 200 turns of 0.3 mm-
              DIAMETER copper wire.  The wire is connected to a 
              3.0 V battery with negligible internal resistance.  
              (a) Calculate the largest and smallest magnetic 
              field across the cross section of the toroid.  
              (b) Calculate the absolute value of the magnetic 
              flux through one turn of the toroidal solenoid.  
              (c) Do you need to cool the solenoid?  (Calculate 
              the heat created per second when current is flowing.)

         Halliday and Resnick - 2nd Ed - CHAPTER 31
          5.  A square loop of wire of edge a carries a current i.
              Show that the value of B at the center of the square
              is given by

                           B =(2sqrt2)(mu_0)(i)/(pi)a

              Hint: You may use the result of Wolfson 30: 57.

         25.  A circular loop of radius 12 cm carries a current of
              15 A.  A flat coil of radius 0.82 cm, having 50 turns
              and a current of 1.3 A, is concentric with the loop.  
              (a) What magnetic field strength B does the loop 
              produce at its center?  (b) What torque acts on the
              coil?  Assume that the planes of the loop and coil
              are perpendicular and that the magnetic field due to
              the loop is essentially uniform throughout the 
              volume occupied by the coil.

         Halliday and Resnick - 2nd Ed - CHAPTER 32
          7.  An elastic conducting material is stretched into a
              circular loop of 12.0 cm radius.  It is placed with
              its plane perpendicular to a uniform 0.800 T
              magnetic field.  When released, the radius of the 
              loop starts to shrink at an instantaneous rate of 
              75.0 cm/s.  What EMF is induced in the loop at 
              that instant?

         WOLFSON - CHAPTER 32
          9.  A rectangular loop of length L and width w is
              located a distance a from a long, straight wire.
              What is the mutual inductance of this arrangement?
              The picture for this problem is Y&F Figure 29.27 on 
              page 1021, with b-a in that figure equal to w in 
              this problem statement.