ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS JULY 23 - JULY 29 Young and Freedman - 12th Ed - CHAPTER 27 76. Please add the following part: (d) For each of the above magnetic fields, what will be the maximum kinetic energy of the loop if it is released from rest from the position shown in Figure 27.66 (you may consider the loop to be pivoted about the y-axis and you may ignore all friction)? Young and Freedman - 12th Ed - CHAPTER 28 69. To get credit for this problem, you must show carefully how to use the Biot-Savart Law to arrive at the answer. Young and Freedman - 12th Ed - CHAPTER 29 28. Please add the following parts: (c) What is the magnitude of the induced electric field at a point just outside the center of the solenoid (lengthwise) and 4.00 cm from the axis of the solenoid? (d) Using Figure 29.54 (p. 1027), and applying that figure to the situation of this problem, what would be the direction of the induced electric field in part (a) of this problem? 33. Please add the following part: (b) What is the mutual inductance of this two-coil geometry? (Note that, in part (a), the question is asking only for the average induced EMF in the second winding due to the change of current in the first winding; in other words, you are to ignore the back EMF in the second winding due to its self inductance.) 63. The rod in this problem is intended to be the moving part in a simple DC generator. Here is a figure of such a generator; the connecting wires are not shown. This problem is most straightforwardly done by integrating vcrossBdotdl over the length of the moving rod (note that v in this integral will not be constant). Here is a pdf version of the figure. 77. Note that the metal rails in the figure for this problem are drawn in gray; the thin black lines represent a non-metal frame. For part (b), remember that the terminal speed is the maximum speed, i.e. the speed at which the acceleration becomes zero. Young and Freedman - 12th Ed - CHAPTER 30 48. The main purpose of this problem is to calculate the inductance of a length of coaxial cable (i.e. part (d)). The problem assumes (but does not state) that the cable is being used to carry high frequency alternating currents (like a cable carrying a TV signal); in such a case the currents would be largely confined to the outer surface of the inner wire and the inner surface of the outer tube (i.e. the magnetic field is confined to the nonconducting space between the two metal pieces). So the flux calculated in part (c) is in fact the total flux. Part (b) is asking you to turn the 2D flux integral into a 1D integral (the integral over dl being done implicitly); you may just ignore part (b). And in part (c), the words "over the volume" are silly; flux is always an integral over an area, so the integral is over a rectangular area perpendicular to the magnetic field between the two pieces of metal. 73. There is a misprint in this problem. The power series expansion for ln(1+z) = z - z^2/2 + higher order terms. Y&F mistakenly have a plus sign between the first and second terms of the expansion. Halliday and Resnick - 2nd Ed - CHAPTER 30 9. A stationary circular wall clock has a face with a radius of 15 cm. Six turns of wire are wound around its perimeter; the wire carries a current of 2.0 A in the clockwise direction. The clock is located where there is a constant, uniform external magnetic field of magnitude 70 mT (but the clock still keeps perfect time). At exactly 1:00 p.m., the hour hand of the clock points in the direction of the external magnetic field. (a) After how many minutes will the minute hand point in the direction of the torque on the winding due to the magnetic field? (b) Find the torque magnitude. 22. An electric field of 1.50 kV/m and a magnetic field of 0.400 T act on a moving electron to produce no net force. (a) Calculate the minimum speed v of the electron. (b) Draw the vectors E, B, and v (E, B, and v are vector symbols). 29. An alpha particle (q = +2e, m = 4.00 u) travels in a circular path of radius 4.50 cm in a uniform magnetic field with B = 1.20 T. Calculate (a) its speed, (b) its period of revolution, (c) its kinetic energy in electron- volts, and (d) the potential difference through which it would have to be accelerated to achieve this energy. 31. An electron has an initial velocity of (12.0 km/s)j + (15.0 km/s)k and a constant acceleration of (2.00 Tm/s^2)i in a region in which uniform electric and magnetic fields are present. If B = (400 microT)i, find the electric field E (E and B are vectors). (P prefixes) HRW Problem Supplement #1 - CHAPTER 30 73. A long, hollow cylindrical conductor (inner radius = 2.0 mm, outer radius = 4.0 mm) carries a current of 24 A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of 24 A in the opposite direction. What are the magnitudes of the magnetic fields (a) 1.0 mm, (b) 3.0 mm, and (c) 5.0 mm from the central axis of the wire and cylinder? WOLFSON - CHAPTER 30 42. A conducting slab extends infinitely in the x and y directions and has thickness h in the z direction. It carries a uniform current density vecJ = J(veci) (vec indicates that the first J and the i are vectors, -- the veci is the unit vector in the x direction). Find the magnetic field strength (a) inside and (b) outside the slab, as functions of the distance z from the center plane of the slab. 48. A long solenoid with n turns per unit lengths carries a current I. The current returns to its driving battery along a wire of radius R that passes through the solenoid, along its axis. Find expressions for (a) the magnetic field strength at the surface of the wire, and (b) the angle the field at the wire surface makes with the solenoid axis. 57. The figure below shows a wire of length L carrying current fed by other wires that are not shown (the current direction is to the right). Point A lies on the perpendicular bisector, a distance y from the wire. Show how to use the Biot-Savart Law to demonstrate that the magnetic field at A due to the straight wire alone has magnitude (mu_0(I)L)/((2pi)y(sqrt(L^2+4y^2))). What is the field direction? _ . B . A y - ------------------------------ I --> |<-- L -->| 58. Point B in the figure above lies a distance y perpendicular to the end of the wire. Show how to use the Biot-Savart Law to demonstrate that the magnetic field at B due to the straight wire alone has magnitude (mu_0(I)L)/((4pi)y(sqrt(L^2+y^2))). What is the field direction? 68. A solid conducting wire of radius R runs parallel to the z axis and carries a current density given by vecJ = J_0(1-(r/R))veck, where J_0 is a constant and r the radial distance from the wire axis (vec indicates that the first J and the k are vectors, -- the veck is the unit vector in the z direction). Find expressions for (a) the total current in the wire, (b) the magnetic field strength for r > R, and (c) the magnetic field strength for r < R. FISHBANE PROBLEMS - CHAPTER 30 32. Consider a toroidal solenoid with a square cross section, each side of which has length 3 cm. The inner wall of the torus forms a cylinder of radius 12 cm (figure 28.25(a) on page 976 could roughly be a toroid of this description -- for a cutaway view see figure 30.8 on page 1037). The torus is wound evenly with 200 turns of 0.3 mm- DIAMETER copper wire. The wire is connected to a 3.0 V battery with negligible internal resistance. (a) Calculate the largest and smallest magnetic field across the cross section of the toroid. (b) Calculate the absolute value of the magnetic flux through one turn of the toroidal solenoid. (c) Do you need to cool the solenoid? (Calculate the heat created per second when current is flowing.) Halliday and Resnick - 2nd Ed - CHAPTER 31 5. A square loop of wire of edge a carries a current i. Show that the value of B at the center of the square is given by B =(2sqrt2)(mu_0)(i)/(pi)a Hint: You may use the result of Wolfson 30: 57. 25. A circular loop of radius 12 cm carries a current of 15 A. A flat coil of radius 0.82 cm, having 50 turns and a current of 1.3 A, is concentric with the loop. (a) What magnetic field strength B does the loop produce at its center? (b) What torque acts on the coil? Assume that the planes of the loop and coil are perpendicular and that the magnetic field due to the loop is essentially uniform throughout the volume occupied by the coil. Halliday and Resnick - 2nd Ed - CHAPTER 32 7. An elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s. What EMF is induced in the loop at that instant? WOLFSON - CHAPTER 32 9. A rectangular loop of length L and width w is located a distance a from a long, straight wire. What is the mutual inductance of this arrangement? The picture for this problem is Y&F Figure 29.27 on page 1021, with b-a in that figure equal to w in this problem statement.