ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS JULY 6 - JULY 12 WOLFSON - CHAPTER 23 4. Assume the ball is made mostly of carbon, for which the number of protons is equal to the number of neutrons. 32. (b) Sketch the net electric field lines qualitatively. E1. This is the exercise accompanying Example 23-6 on page 582. (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 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? 55. The figure for this problem is Wolfson Fig. 24-9(a). An electric field given by E = 4i - 3(y^2 + 2)j pierces the Gaussian cube shown in the figure. (E is in N/C and y is in m.) The i direction is to the right, the j direction is toward the top of the page, and the z direction is out of the page (i.e. perpendicular to face A). The distance s is 2.0 m, with y = 0 at the bottom of the cube. What is the electric flux through (a) the top face (face B), (b) the bottom face, (c) the left face, and (d) the back face. (e) What is the net electric flux through the cube? (f) What net charge is enclosed by the Gaussian cube? 66. A thin, metallic, spherical shell of radius a has a charge Qa. Concentric with it is another thin, metallic, spherical shell of radius b (where b > a) and charge Qb. Find the electric field at points a distance r from the common center, where (a) r < a, (b) a < r < b, and (c) r > b. (d) Determine how the charges are distributed on the inner and outer surfaces of the shells (give the surface charge densities). 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 E2. This is the exercise accompanying Example 26-1 on page 660.