JULY 15 - JULY 21
         Young and Freedman - 12th Ed - CHAPTER 23
         50.  To get any credit for this problem, you MUST prove
              any result that you take from problem 23.49.

         74.  In part (a) of this question, Y&F ask "What will a 
              voltmeter read ....".  This is not a serious question 
              as asked.  The shell is insulating and all voltmeters 
              measure current (as you will learn in section 26.3).  
              No current will flow in this case, so the voltmeter 
              will always read zero.  So please change the wording 
              of this phrase to "What is the absolute value of the
              potential difference between the following points?"
              In part (b), there should be four parts rather than
              three; compare (i) a and b, (ii) b and c, (iii) c
              and infinity, and (iv) a and c.  Part (c) should read,
              "Which, if any, of the answers to (b) would change if
              the charge were -150 microC?"

         Young and Freedman - 12th Ed - CHAPTER 24
          9.  In showing your work for this problem, you should first
              work out, from the definition of capacitance, the
              capacitance per unit length for infinitely long coaxial
              cylinders.  Then apply that result to these coaxial
              cylinders of finite length.

         YOUNG - 11e - CHAPTER 24
         62.  A 4.00 microF capacitor and a 6.00 microF capacitor are
              connected in series across a 660-V supply line.  
              (a) Find the charge on each capacitor and the voltage
              across each.  (b) The charged capacitors are disconnected
              from the line and from each other and then reconnected
              to each other, with terminals of like sign together. 
              Find the final charge on each and the voltage across each.
         Young and Freedman - 12th Ed - CHAPTER 25
         48.  In part (b), Y&F want the NET power output of the 
              battery, i.e. the power output of the EMF minus the 
              power dissipated in the internal resistance of the 
              battery. In part (c), you are to assume that the 8 volt 
              battery is rechargeable; i.e., running current "backward" 
              through the battery will result in the conversion of 
              electric potential energy into chemical energy of the 
              battery. Also in part (d), Y&F are again asking for the 
              net rate of energy conversion, i.e. the rate of 
              production of thermal energy in the internal resistance 
              of the battery plus the rate of energy storage in the 
              battery's chemicals. (Running current "backward" through 
              a non-rechargeable battery would result in a dramatic 
              increase in the internal resistance of the battery; i.e., 
              all of the energy would then be converted into thermal 

         60.  In my copy of Y&F 12e, there is a misprint in this problem.  
              The total length of the composite wire is 2.0 m (not 2.0 mm).

         64.  It is very important to do this problem by the general
              method for finding resistance: (1) apply a selected
              voltage V to the two relevant locations on the conducting 
              material;  (2) find E in the material in terms of V and
              in terms of location within the material, then J in the 
              material (in terms of location and V), and then I through 
              the material between the two relevant locations; and
              (3) use the DEF of resistance for an Ohmic material,
              namely R=V/I -- your selected V will drop out, leaving
              only geometry and resistivity.

         YOUNG - 11e - CHAPTER 25
         58.  The available kinetic energy per unit volume, due to the
              drift speed of the conduction electrons in a current-
              carrying conductor, can be defined as 
              K/volume=n((1/2)m(v_d)^2).  Evaluate K/volume for the
              copper wire and current of Example 25.1 (page 850).
              (b) Calculate the total change in electric potential
              energy for the conduction electrons in 1.0 cm^3 of
              copper if they fall through a potential drop of 1.0 V.
              How does your answer compare to the available kinetic
              energy in 1.0 cm^3 due the the drift speed?

         WOLFSON - CHAPTER 25
         50.  A charge +4q is located at the origin and a charge -q
              is on the x axis at x = a.  (a) Write an expression
              for the potential on the x axis for x > a.  (b) Find
              a point in this region where V = 0.  (c)  Use the result
              of (a) to find the electric field on the x axis for
              x > a, and (d) find a point where E = 0.

         58.  Two small metal spheres are located 2.0 m apart.  One
              has radius 0.50 cm and carries 0.20 microC.  The other
              has radius 1.0 cm and carries 0.080 microC.  (a) What 
              is the potential difference between the spheres?  
              (b) If they were connected by a thin wire, how much 
              charge would move along it, and in what direction?

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 25

         58.  Consider a flat, nonconducting ring of outer
              radius R and inner radius r = 0.200R;  the ring
              has a uniform charge per unit area of sigma.
              With V = 0 at infinity, find an expression for
              the electric potential at point P on the central
              axis of the ring, at a distance z = 2.00R from
              the center of the ring.

         Halliday and Resnick - 2nd Ed - CHAPTER 26
         19.  A positive charge per unit length lambda is distributed
              uniformly along a straight-line segment of length L.
              (a) Determine the potential (chosen to be zero at
              infinity) at a point P a distance y from one end of
              the charged segment and in line with it.  (b) Use the
              result of (a) to compute the component of the electric
              field at P in the y-direction (along the line).  (c)
              Determine the component of the electric field at P in
              a direction perpendicular to the straight line.

                   -   . P
                   -   +          Figure for  H  26:19
                   |   +
                   |   +
                   |   +      the line of plus marks 
                   L   +      stands for the line of
                   |   +      positive charge
                   |   +
                   |   +
                   -   +

         20.  On a thin rod of length L lying along the x-axis with one 
              end at the origin (x=0), there is distributed a positive
              charge per unit length given by lambda = cx, where c is a 
              constant.  (a) Taking the electrostatic potential at 
              infinity to be zero, find V at the point P on the y-axis.  
              (b) Determine the vertical component E_y of the electric 
              field at P from the result of part (a).  (c) Why cannot 
              E_x, the horizontal component of the electric field at P, 
              be found using the result of part (a)?

                 y axis
                   |         Figure for H 26:20
     P is on the   |
     y axis, a     . P
     distance y    |
     from the      |         the line of plus marks
     origin        |         stands for the line of
                   |         positive charge
           --------+++++++++++++++++++------ x axis
              (0,0)|<------  L ------>

         WOLFSON - CHAPTER 26
         10.  Two square conducting plates measure 5.0 cm on a
              side.  The plates are parallel, spaced 1.2 mm
              apart, and initially uncharged.  (a) How much work
              is required to transfer 7.2 microC from one plate
              to the other?  (b) How much work is required to
              transfer a second 7.2 microC?

         15.  Two conducting spheres of radius a are separated
              by a distance L >> a; since the distance is large,
              neither sphere affects the other's electric field
              significantly, and the fields remain spherically
              symmetric.  (a) If the spheres carry equal but
              opposite charges +-q, show that the potential
              difference between them is 2kq/a.  (b) Write an
              expression for the work dW involved in moving an
              infinitesimal charge dq from the negative to the
              positive sphere.  (c) Integrate your expression
              to find the work involved in transferring a
              charge Q from one sphere to the other, assuming
              both are initially uncharged.

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 26
         53.  A certain parallel-plate capacitor is filled with
              a dielectric for which Kappa = 5.5.  The area of
              each plate is 0.034 m^2, and the plates are
              separated by 2.0 mm.  The capacitor will fail
              (short out and burn up) if the electric field 
              between the plates exceeds 200 kN/C.  What is the
              maximum energy that can be stored in the capacitor?

         66.  Two parallel-plate capacitors A and B are connected
              in parallel across a 600 V battery.  Each plate has
              area 80.0 cm^2 and the plate separations are 3.0 mm.
              Capacitor A is filled with air; capacitor B is
              filled with a dielectric of dielectric constant
              Kappa = 2.60.  Find the magnitude of the electric
              field within (a) the dielectric of capacitor B and
              (b) the air of capacitor A.  What are the free
              charge densities sigma on the higher-potential
              plate of (c) capacitor A and (d) capacitor B?
              (e) What is the induced charge density sigma' on
              the surface of the dielectric which is nearest to
              the higher-potential plate of capacitor B.
         WOLFSON - CHAPTER 27
          4.  The electron beam that "paints" the image on a
              computer screen contains 5 million electrons per
              cm of its length.  If the electrons move toward
              the screen at 60 million m/s, how much current
              does the beam carry?  What is the direction of
              this current?

         62.  A power plant produces 1000 MW to supply a city
              40 km away.  Current flows from the power plant
              on a single wire of resistance 0.050 Ohms/km,
              through the city, and returns via the ground,
              assumed to have negligible resistance.  At the
              power plant the voltage between the wire and the
              ground is 115 kV.  (a) What is the current in
              the wire?  (b) What fraction of the power is
              lost in transmission?  (c) What should be the 
              power line voltage if the transmission loss is
              not to exceed 2.0 %.

         Halliday and Resnick - 2nd Ed - CHAPTER 27
          7.  Two metal objects, a saw and a wrench, are lying
              side-by-side on an non-conducting table; the two
              metal objects are not in contact with one another;
              they have net charges of +70 pC and -70 pC, and
              this results in a 20 V potential difference 
              between them.  (a) What is the capacitance of the
              system?  (b) If the charges are changed to +200 pC
              and -200 pC, what does the capacitance become?
              (c) What does the potential difference become?

         13.  The figure for this problem is Fig. 24-36 (p. 843),
              except that the width of the slab is now b instead
              of a.  A slab of copper of thickness b is thrust 
              into a parallel-plate capacitor of plate area A; it 
              is exactly halfway between the plates.  (a) What is 
              the capacitance after the slab is introduced?  
              (b) If a charge q is maintained on the plates, what 
              is the ratio of the stored energy before to that 
              after the slab is inserted?  (c) How much work is 
              done on the slab as it is inserted?  Is the slab 
              sucked in or must it be pushed in?

         18.  Two parallel plates of area 100 cm^2 are given charges
              of equal magnitudes 0.89 microC but opposite signs.
              The electric field within the dielectric material 
              filling the space between the plates is 1.4 MV/m.
              (a) Calculate the dielectric constant of the material.
              (b) Determine the magnitude of the charge induced on
              each dielectric surface.

         43.  You are asked to construct a capacitor having a
              capacitance near 1 nF and a breakdown potential in
              excess of 10000 V.  You think of using the sides of
              a tall Pyrex drinking glass as a dielectric, lining
              the inside and outside curved surfaces with aluminum
              foil to act as the plates.  The glass is 15 cm tall
              with an inner radius of 3.6 cm and an outer radius
              of 3.8 cm.  What are the (a) capacitance and (b)
              breakdown potential of this capacitor?

         45.  The figure for this problem is Fig. 24-36 (p. 843),
              except that the slab is a dielectric with kappa = 2.61
              instead of a conductor, and a 85.5 V battery is
              connected to the capacitor plates while the dielectric
              is being inserted.  The area A = 115 cm^2, d = 1.24 cm,
              and the width of the slab is (0.629)d.  Calculate
              (a) the capacitance, (b) the charge on the capacitor
              plates, (c) the electric field in the gap, and (d) the
              electric field in the slab, after the slab is in place.

         WOLFSON - CHAPTER 28
         12.  A defective starting motor in a car draws 300 A from
              the car's 12 V battery, dropping the battery terminal
              voltage to only 6 V.  A good starter motor should draw
              only 100 A.  What will the battery terminal voltage
              be with a good starter?