ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS
                               
                              JULY 6 - JULY 10
        
         Young and Freedman - 12th Ed - CHAPTER 22
         30.  Do not use Gauss' Law for any part of this problem.
              We have already found the result for the E field due
              to a infinitely thin sheet of charge in two different
              ways; you may simply use that result here.  First
              consider each of the four infinitely thin sheets of
              charge separately.  Then at each of the locations
              A, B, and C, add the vector contributions to the
              field from each of the four infinitely thin sheets.
              Show your work carefully. GBA

         54.  Omit part (a) of this problem.  To find the E field
              strength within the slab, 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.  You must give your
              symmetry argument clearly for this problem. 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 - 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 orientations of the
              electric dipole moment p (p is a vector) and the
              electric field E (E is a vector) when the torque
              is a maximum.  (c) Suppose that the electric field
              of part (b) points in the +y direction.  If the
              dipole swings from an initial orientation pointing in
              a direction 20 degrees below the -x axis to a final
              orientation pointing in a direction 20 degrees above
              the -x axis, what is the change in the dipole's
              electric potential energy?

         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 - 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.  
              The value of L is 0.30 m.
              (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
              (also conducting) 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 - 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?
         
         22.  Three identical charges +q and a fourth charge -q form
              a square of side a.  (a) Find the magnitude of the
              electric force on a charge Q placed at the center of
              the square.  (b) Describe the direction of this 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.

         34.  A positive charge +2q lies on the x axis at x = -a,
              and a charge -q lies at x = +a.  (a) Find an expression
              for the electric field as a function of x for points to
              the right of the charge -q.  (b) Taking q = 1.0 microC
              and a = 1.0 m, plot the field as a function of position
              for x = 5.0 m to x = 25 m.

         50.  A seimcircular loop of radius a carries positive charge
              Q distributed uniformly over its length (the loop begins
              at the point (0,a) and extends counterclockwise to the
              point (0,-a)).  Find the electric field at the center of
              the loop.  Show all the steps in your work.

         54.  A thin rod of length L carries charge Q distributed
              uniformly over its length (the rod begins at the point
              (-L/2,0) and extends rightward to the point (+L/2,0)).
              (a) What is the line charge density on the rod?
              (b) What must be the electric field direction on the
              rod's perpendicular bisector (i.e. the y axis).
              (c) Find an expression for the electric field at a
              point P at the location (0,+y).  (d) Show that your
              result for (c) reduces to the field of a point charge
              Q for y >> L.

         56.  How strong an electric field is needed to accelerate
              electrons in an old-style TV tube from rest to one-tenth
              the speed of light in a distance of 5.0 cm?

         58.  An oscilloscope display requires that a beam of
              electrons moving at 8.2 Mm/s be deflected through
              an angle of 22 degrees by a uniform electric field
              that occupies a region 5.0 cm long.  What should be
              the field strength?

         (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.

         (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?

         66.  A metallic spherical shell of inner radius a1 and outer
              radius a2 has charge Qa.  Concentric with it is another
              metallic spherical shell of inner radius b1 (where b1 > a2)
              and outer radius b2; shell b has charge Qb.  Both Qa and Qb
              are positive.  Find the electric field strength at points a
              distance r from the common center, where (a) r < a1,
              (b) a2 < r < b1, and (c) r > b2.  (d) Determine how the
              charges are distributed on the inner and outer surfaces of
              the shells (give the surface charge densities).  (e) Graph
              the electric field strength as a function of r over the
              range r=0 to r=2*b2.

         WOLFSON - CHAPTER 24
         24.  A thin spherical shell of radius 15 cm carries 4.8 microC,
              distributed uniformly over its surface.  At the center of
              the shell is a point charge.  (a) If the electric field at
              the surface of the sphere is 750 kN/C and points outward,
              what is the charge of the point charge?  (b) What is the
              field just inside the shell?

         56.  A point charge -q is at the center of a insulating thin
              spherical shell carrying charge -(3/2)q.  That shell, in
              turn, is concentric with a larger shell (also insulating
              and also thin) carrying charge +2q.  (a) Draw a cross section
              of this structure, and sketch the electric field lines
              using the convention that 8 lines correspond to a charge
              of magnitude q.  (b) If the shells were metallic instead
              of insulating, how would the field lines that you have
              drawn be different, and what would be the total charge on
              each of the inner and outer surfaces of each of the two
              shells?

         FISHBANE - 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?

         A Prefixes
         A1:  An isolated copper sphere of radius 16 cm is found to have
              an electric field at its surface which is radially inward
              (i.e. pointing towards the center of the sphere) and which
              has a strength 1150 N/C.  (a) How many excess electrons are
              on this copper sphere?  (b) A square made up of nine copper
              atoms (3 atoms by 3 atoms) takes up an area of about one
              square nanometer.  Approximately how many copper atoms are
              on the surface of this copper sphere? (c) On the surface
              of the copper sphere, there are about how many copper atoms
              per excess electron?

         A2:  Assume that water flowing through a pipe with a circular
              cross section flows most rapidly at the center of the pipe
              and least rapidly near the pipe walls (this might be 
              reasonable because of friction between the water and the
              pipe walls).  Assume that the water speed at the walls is
              half as great as the speed at the center, and assume that
              the decrease is linear (i.e. the graph of water speed 
              versus radius is a straight line).  If the radius of the
              pipe is 10 cm and if the volume flux of water is 5.0 liters
              per second, find the speed of the water at the center of
              the pipe.  (One liter is 1000 cubic centimeters or 0.001
              cubic meters).  HINT: Draw the graph of water speed versus
              distance from the centerline of the pipe; you must do 
              the integral for volume flux symbolically.
             
         A3:  Consider a thin disk, of negligible thickness, of radius R
              which is oriented perpendicular to the x axis such that the
              x axis runs through the center of the disk. The disk is
              centered at x=0, and has positive charge density sigma.
              (a) Show that the electric field on the positive x axis is
              given by
 
                 E_x = (sigma/(2epsilon0))*(1-1/sqrt(1+(R/x)^2))

              (b) Show how to apply the binomial expansion to your result
                  for (a) in order to demonstrate that the commonly-used
                  expression, E=sigma/(2epsilon0), is valid to within
                  1.0% for all values of x which are 1.0% of R or less.

         A4:  A thin wooden stick of length 12 cm has a tiny metal sphere
              glued to each end.  A charge of +3 microC is placed on one
              sphere and a charge of -2 microC is placed on the other.
              The center of mass is located 7 cm from the positively-
              charged sphere.  The system is mounted on a fixed
              horizontal E-W axle passing through the center of mass
              about which the system is free to rotate with no friction.
              When the system is then placed in a horizontal uniform
              southward electric field of 800 N/C, the resulting
              equilibrium position of the system is horizontal with
              the positive charge due S of the negative charge.
              (a) When the system is in its equilibrium position,
              what is the horizontal force on the system by the axle?
              (b) What amount of torque (about the axle) is required
              to hold the system at an angular displacement of 25
              degrees away from the equilibrium position?
              (c) What minimum amount of work must be done to move
              the system from its equilibrium position to an angular
              displacement of 25 degrees?  (HINT: write the needed 
              torque as a function of displacement, then integrate
              from zero to 25 degrees to find the needed work.)
              (d) What work would be done by the electric field
              during the displacement described in part (c)?

         A5:  Two conductors, A and B, are each in the shape of a
              tetrahedron, but of different sizes. They are charged
              in the following manner:

              1. Tetrahedron A is charged from an electrostatic
                 generator to charge q.
              2. Tetrahedron A is briefly touched to tetrahedron B.
              3. Steps 1 and 2 are repeated until the charge on
                 tetrahedron B reaches a maximum value; i.e.
                 the process is repeated until further repetitions
                 will no longer result in the transfer of additional
                 charge from tetrahedron A to tetrahedron B.

              If the charge on tetrahedron B was q/5 after the first
              time it touched tetrahedron A, what is the final charge
              on tetrahdedron B?  HINT:  the way to make progress is
              to think carefully about the first and second transfers,
              and then about the final attempted transfer (in which
              no charge is actually transferred).  Be sure to express
              your logic clearly and thoroughly when writing up this
              question.