PROBLEMS FROM HRW SUPPLEMENT #1 and FISHBANE JULY 7 - JULY 11 Problems from HRW Problem Supplement #1 (6th edition) CHAPTER 23 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? CHAPTER 24 55. The figure for this problem is Fig. 24-5. 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.) What is the electric flux through (a) the top face, (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). 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? Problems from Fishbane, Gasiorowicz, and Thornton (2nd edition) CHAPTER 22 57. An electron moves in a circular planetary orbit about a proton. (a) If the only force acting is the attractive Coulomb force, what is the speed of the electron in terms of the charge e and the radius of the circular orbit? (b) What is the angular momentum L of the electron in its orbit? (c) Express the speed in terms of e and L. (d) Express the radius of the orbit in terms of e and L (and the mass of the electron). (e) Express in terms of e and L (and mass) the time it takes for the electron to go around the circle once. (f) Evaluate all these quantities, given that L = 1.05 X 10^{-34} kg m^2/s. This corresponds to a simplified version of the hydrogen atom. 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?