ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS
                               
                              JULY 2 - JULY 10
        
         Young and Freedman - 12th Ed - CHAPTER 24
         54.  You may omit part (a) of this problem.  To find the
              E field strength within the slab, I recommend that 
              you use a Gaussian pillbox which is centered on the 
              center of the slab, and which has its parallel faces 
              equidistant from the central plane of the slab.  With
              such a Gaussian pillbox, the symmetry argument in 
              part (a) is not required; instead a simpler symmetry
              argument about the E field direction within the slab
              will suffice.  GBA

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 22
         26.  Calculate the number of coulombs of positive charge
              in 250 cm^3 of (neutral) water (about a glassful).

         YOUNG 11e - CHAPTER 21
         60.  The potassium chloride molecule (KCl) has a dipole
              moment of 8.9 x 10^-30 Cm.  (a) Assuming that this 
              dipole moment arises from two charges, each of
              magnitude 1.6 x 10^-19 C, separated by distance d,
              calculate d.  (b) What is the maximum magnitude of
              the torque that a uniform electric field with
              magnitude 6.0 x 10^5 N/C can exert on a KCl 
              molecule?  Sketch the relative orienations of the
              electric dipole moment p (p is a vector) and the
              electric field E (E is a vector) when the torque
              is a maxium.

         78.  (a) Suppose all the electrons in 20.0 g of carbon 
              atoms were located at the North Pole of the earth and
              all the protons at the South Pole.  What would be the 
              total force of attraction exerted on each group of
              charges by the other?  The atomic number of carbon
              is 6, and the atomic mass of carbon is 12 g/mol.
              (b) What would be the magnitude and direction of 
              the force exerted by the charges in part (a) on a
              third charge that is equal to the charge at the 
              South Pole, and located at a point of the surface 
              of the earth at the equator?  Draw a diagram showing
              the locations of the charges and the forces on the
              charge at the equator.

         YOUNG 11e - CHAPTER 22
         30.  This is essentially problem 22:32 in Y&F 12e but
              with a nonuniform electric field.  The x-component
              of the E field is given by (-5.00 N/(Cm))x.  The
              y-component of the E field is zero.  The z-component
              of the E field is given by (+3.00 N/(Cm))z.  
              (a) Find the electric flux through each of the six
              cube faces S_1 through S_6.  (b) In the uniform
              field case, the electric flux through the entire
              cube would have been zero (what goes in must come
              out); but, in this case you will find that the
              electric flux through the entire cube is not zero.
              Find the total electric charge inside the cube.

          44. A small, INSULATING, spherical shell with inner
              radius a and outer radius b is concentric with a 
              larger INSULATING spherical shell with inner 
              radius c and outer radius d (Figure 22.39 in
              Y&F 12e).  The inner shell has total charge +q
              distributed uniformly over its volume, and the
              outer shell has charge -q distributed uniformly
              over its volume.  (a) Calculate the charge 
              densities in the inner shell and the outer shell.
              (b) Calculate the electric field (magnitude and 
              direction) in terms of q and the distance r from
              the common center of the two shells for (i) r<a;
              (ii) a<r<b; (iii) b<r<c; (iv) c<r<d; (v) r>d.
              (c) Show your results in a graph of the radial 
              component of E (E is a vector) as a function of 
              the distance r.

          45. A long coaxial cable consists of an inner cylindrical
              conductor with radius a and an outer coaxial cylinder
              with inner radius b and outer radius c.  The outer
              cylinder is mounted on insulating supports and has 
              no net charge.  The inner cylinder has a uniform 
              positive charge per unit length lambda.  Calculate
              the electric field (a) at any point between the
              cylinders, a distance r from the axis;  (b) at any
              point outside the outer cylinder.  (c) Graph the
              magnitude of the electric field as a function of
              the distance r from the axis of the cable, from 
              r=0 to r=2c.  (d) Find the charge per unit length
              on the inner surface and on the outer surface of
              the outer cylinder.

          48. A very long, solid cylinder with radius R has
              positive charge uniformly distributed throughout it, 
              with charge per unit volume rho.  (a) Derive the
              expression for the electric field inside the volume 
              at a distance r from the axis of the cylinder in
              terms of the charge density rho.  (b) What is the
              electric field at a point outside the volume in
              terms of the charge per unit length labmda in the
              cylinder?  (c) Compare the answers to parts (a)
              and (b) for r=R.  (d) Graph the electric field
              magnitude as a function of r from r=0 to r=3R.

         YOUNG 11e - CHAPTER 23
         48.  Three small spheres with charge 2.00 microC are
              arranged in a line, with sphere 2 in the middle.
              Adjacent spheres are initially 8.0 cm apart.  The
              spheres have masses m1=20.0 g, m2=85.0 g, and
              m3=20.0 g, and their radii are much smaller than
              their separation.  The three spheres are released
              from rest.  (a) What is the acceleration of sphere 1
              just after it is released?  (b) What is the speed of
              each sphere when they are far apart?

         WOLFSON - CHAPTER 23
         16.  A charge 3q is at the origin, and a charge -2q is on
              the positive x axis at x = a.  Where would you place
              a third charge so it would experience no net electric
              force?
         
         32.  A 1.0 microC charge and a 2.0 microC charge are 10 cm
              apart.  (a) Find a point where the net electric field 
              is zero.  (b) Sketch the net electric field lines 
              qualitatively.


         (P prefixes) HRW Problem Supplement #1 - CHAPTER 23
         25.  A semi-infinite nonconducting rod (i.e. infinite in one
              direction only) has uniform positive linear charge density 
              lambda.  Show that the electric field at point P makes an 
              angle of 45 degrees with the rod and that this result is
              independent of the distance R.  (HINT: Separately find 
              the parallel and perpendicular (to the rod) components
              of the electric field at P, and then compare those 
              components.)

                 rod
                starts
                 here
               _   +++++++++++++++++++++++++ =====> very long
               |  |
                  |
               R  |
                  |
               |  |
               -  P  <== this point is a distance R from the end
                         of the rod

         37.  In Millikan's experiment, an oil drop of radius 
              1.64 microns and density 0.851 g/cm^3 is suspended in
              the experimental chamber when a downward-directed
              electric field of 1.92 X 10^5 N/C is applied.  Find
              the charge on the drop, in terms of e.

         55.  A charge (uniform linear density = 9.0 nC/m) lies on a 
              string that is stretched along an x axis from x = 0 to 
              x = 3.0 m.  Determine the magnitude of the electric 
              field at x = 4.0 m on the x axis.

         59.  An electric dipole swings from an initial orientation i 
              to a final orientation f in a uniform external electric 
              field E.  E points in the +y direction, in orientation i 
              the dipole points 20 degrees below the -x direction, and 
              in orientation f the dipole points 20 degrees above the 
              -x direction.  The electric dipole moment is 1.60 x 
              10^{-27} Cm; the field magnitude is 3.00 x 10^6 N/C.  
              What is the change in the dipole's potential energy?

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 24
         24.  A charge of uniform linear density 2.0 nC/m is distributed
              along a long, thin, nonconducting rod.  The rod is coaxial
              with a long, hollow, conducting cylinder (inner radius =
              5.0 cm, outer radius = 10 cm).  The net charge on the
              conductor is zero.  (a) What is the magnitude of the
              electric field 15 cm from the axis of the cylinder?  What
              is the surface charge density on (b) the inner surface and 
              (c) the outer surface of the conductor?


         FISHBANE PROBLEMS - CHAPTER 24
         38.  Two large, thin, metallic plates are placed parallel to 
              each other, separated by 15 cm.  The top plate carries a 
              uniform charge density of 24 microC/m^2, while the bottom 
              plate carries a uniform charge density of -38 microC/m^2.  
              What is the electric field (magnitude and direction) (a) 
              halfway between the plates? (b) above the two plates?  
              (c) below the two plates? (d)  What are the surface charge 
              densities on the top and bottom surfaces of both plates?

         45.  A metal sphere of radius a is surrounded by a metal shell 
              of inner radius b and outer radius R.  The flux through a 
              spherical Gaussian surface located between a and b is 
              Q/epsilon0, and the flux through a spherical Gaussian 
              surface just outside radius R is 2Q/epsilon0.  (a) What 
              are the total charges on the inner sphere and on the shell?  
              (b) Where are the charges located, and (c) what are the 
              charge densities?

         Halliday and Resnick - 2nd Edition - CHAPTER 25
          1.  Water in an irrigation ditch of width w = 3.22 m and
              depth d = 1.04 m flows with a speed of 0.207 m/s.  The
              mass flux of the flowing water through an imaginary
              surface is the product of the water's density (1000 kg/m^3)
              and its volume flux through that surface.  Find the mass
              flux through the following imaginary surfaces:  (a) a
              surface of area wd, entirely in the water, perpendicular
              to the flow;  (b) a surface with area 3wd/2, of which wd
              is in the water, perpendicular to the flow;  (c) a surface
              of area wd/2, entirely in the water, perpendicular to the 
              flow;  (d) a surface of area wd, half in the water and 
              half out, perpendicular to the flow;  (e) a surface of
              area wd, entirely in the water, with its normal 34 degrees
              from the direction of flow.

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 25
         88.  Three particles with the same charge q and same mass m are 
              initially fixed in place to form an equilateral triangle 
              with edge lengths d.  (a) If the particles are released 
              simultaneously, what are their speeds when they have 
              traveled a large distance (effectively an infinite distance)
              from each other?  (Measure the speeds in the original rest 
              frame of the particles.)

              Suppose, instead, the particles are released one at a time:  
              The first one is released, and then, when the first one is 
              at a large distance, a second one is released, and then, when 
              that second one is at a large distance, the last one is
              released.  What then are the final speeds of (b) the first 
              particle, (c) the second particle, and (d) the last particle?

         WOLFSON - CHAPTER 26
          3.  Four 50 microC charges are brought from far apart onto a
              line where they are spaced at 2.0 cm intervals.  How much
              work does it take to assemble this charge distribution?