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?