ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS JULY 11 - JULY 18 Young and Freedman - 11th Ed - CHAPTER 23 45. To get any credit for this problem, you MUST prove any result that you take from problem 23.44. 72. In part (a) of this question, Y&F ask "What will a voltmeter read ....". This is not a serious question as asked. The shell is insulating and all voltmeters measure current (as you will learn in section 26.3). No current will flow in this case, so the voltmeter will always read zero. So please change the wording of this phrase to "What is the absolute value of the potential difference between the following points?" In part (b), there should be four parts rather than three; compare (i) a and b, (ii) b and c, (iii) c and infinity, and (iv) a and c. Part (c) should read, "Which, if any, of the answers to (b) would change if the charge were -150 microC?" Young and Freedman - 11th Ed - CHAPTER 24 9. In showing your work for this problem, you should first work out, from the definition of capacitance, the capacitance per unit length for infinitely long coaxial cylinders. Then apply that result to these coaxial cylinders of finite length. Young and Freedman - 11th Ed - CHAPTER 25 46. In part (b), Y&F want the NET power output of the battery, i.e. the power output of the EMF minus the power dissipated in the internal resistance of the battery. In part (c), you are to assume that the 8 volt battery is rechargeable; i.e., running current "backward" through the battery will result in the conversion of electric potential energy into chemical energy of the battery. Also in part (d), Y&F are again asking for the net rate of energy conversion, i.e. the rate of production of thermal energy in the internal resistance of the battery plus the rate of energy storage in the battery's chemicals. (Running current "backward" through a non-rechargeable battery would result in a dramatic increase in the internal resistance of the battery; i.e., all of the energy would then be converted into thermal energy.) WOLFSON - CHAPTER 25 50. A charge +4q is located at the origin and a charge -q is on the x axis at x = a. (a) Write an expression for the potential on the x axis for x > a. (b) Find a point in this region where V = 0. (c) Use the result of (a) to find the electric field on the x axis for x > a, and (d) find a point where E = 0. 58. Two small metal spheres are located 2.0 m apart. One has radius 0.50 cm and carries 0.20 microC. The other has radius 1.0 cm and carries 0.080 microC. (a) What is the potential difference between the spheres? (b) If they were connected by a thin wire, how much charge would move along it, and in what direction? (P prefixes) HRW Problem Supplement #1 - CHAPTER 25 58. Consider a flat, nonconducting ring of outer radius R and inner radius r = 0.200R; the ring has a uniform charge per unit area of sigma. With V = 0 at infinity, find an expression for the electric potential at point P on the central axis of the ring, at a distance z = 2.00R from the center of the ring. Halliday and Resnick - 2nd Ed - CHAPTER 26 19. A positive charge per unit length lambda is distributed uniformly along a straight-line segment of length L. (a) Determine the potential (chosen to be zero at infinity) at a point P a distance y from one end of the charged segment and in line with it. (b) Use the result of (a) to compute the component of the electric field at P in the y-direction (along the line). (c) Determine the component of the electric field at P in a direction perpendicular to the straight line. - . P | | y | | - + Figure for H 26:19 | + | + | + the line of plus marks L + stands for the line of | + positive charge | + | + - + 20. On a thin rod of length L lying along the x-axis with one end at the origin (x=0), there is distributed a positive charge per unit length given by lambda = cx, where c is a constant. (a) Taking the electrostatic potential at infinity to be zero, find V at the point P on the y-axis. (b) Determine the vertical component E_y of the electric field at P from the result of part (a). (c) Why cannot E_x, the horizontal component of the electric field at P, be found using the result of part (a)? y axis | | Figure for H 26:20 P is on the | y axis, a . P distance y | from the | the line of plus marks origin | stands for the line of | positive charge | --------+++++++++++++++++++------ x axis (0,0)|<------ L ------> | | WOLFSON - CHAPTER 26 10. Two square conducting plates measure 5.0 cm on a side. The plates are parallel, spaced 1.2 mm apart, and initially uncharged. (a) How much work is required to transfer 7.2 microC from one plate to the other? (b) How much work is required to transfer a second 7.2 microC? 15. Two conducting spheres of radius a are separated by a distance L >> a; since the distance is large, neither sphere affects the other's electric field significantly, and the fields remain spherically symmetric. (a) If the spheres carry equal but opposite charges +-q, show that the potential difference between them is 2kq/a. (b) Write an expression for the work dW involved in moving an infinitesimal charge dq from the negative to the positive sphere. (c) Integrate your expression to find the work involved in transferring a charge Q from one sphere to the other, assuming both are initially uncharged. (P prefixes) HRW Problem Supplement #1 - CHAPTER 26 53. A certain parallel-plate capacitor is filled with a dielectric for which Kappa = 5.5. The area of each plate is 0.034 m^2, and the plates are separated by 2.0 mm. The capacitor will fail (short out and burn up) if the electric field between the plates exceeds 200 kN/C. What is the maximum energy that can be stored in the capacitor? 66. Two parallel-plate capacitors A and B are connected in parallel across a 600 V battery. Each plate has area 80.0 cm^2 and the plate separations are 3.0 mm. Capacitor A is filled with air; capacitor B is filled with a dielectric of dielectric constant Kappa = 2.60. Find the magnitude of the electric field within (a) the dielectric of capacitor B and (b) the air of capacitor A. What are the free charge densities sigma on the higher-potential plate of (c) capacitor A and (d) capacitor B? (e) What is the induced charge density sigma' on the surface of the dielectric which is nearest to the higher-potential plate of capacitor B. WOLFSON - CHAPTER 27 4. The electron beam that "paints" the image on a computer screen contains 5 million electrons per cm of its length. If the electrons move toward the screen at 60 million m/s, how much current does the beam carry? What is the direction of this current? 62. A power plant produces 1000 MW to supply a city 40 km away. Current flows from the power plant on a single wire of resistance 0.050 Ohms/km, through the city, and returns via the ground, assumed to have negligible resistance. At the power plant the voltage between the wire and the ground is 115 kV. (a) What is the current in the wire? (b) What fraction of the power is lost in transmission? (c) What should be the power line voltage if the transmission loss is not to exceed 2.0 %. Halliday and Resnick - 2nd Ed - CHAPTER 27 7. Two metal objects, a saw and a wrench, are lying side-by-side on an non-conducting table; the two metal objects are not in contact with one another; they have net charges of +70 pC and -70 pC, and this results in a 20 V potential difference between them. (a) What is the capacitance of the system? (b) If the charges are changed to +200 pC and -200 pC, what does the capacitance become? (c) What does the potential difference become? 13. The figure for this problem is Fig. 24-28 (p. 939), except that the width of the slab is now b instead of a. A slab of copper of thickness b is thrust into a parallel-plate capacitor of plate area A; it is exactly halfway between the plates. (a) What is the capacitance after the slab is introduced? (b) If a charge q is maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted? (c) How much work is done on the slab as it is inserted? Is the slab sucked in or must it be pushed in? 18. Two parallel plates of area 100 cm^2 are given charges of equal magnitudes 0.89 microC but opposite signs. The electric field within the dielectric material filling the space between the plates is 1.4 MV/m. (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface. 43. You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 10000 V. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 15 cm tall with an inner radius of 3.6 cm and an outer radius of 3.8 cm. What are the (a) capacitance and (b) breakdown potential of this capacitor? 45. The figure for this problem is Fig. 24-28 (p. 939), except that the slab is a dielectric with kappa = 2.61 instead of a conductor, and a 85.5 V battery is connected to the capacitor plates while the dielectric is being inserted. The area A = 115 cm^2, d = 1.24 cm, and the width of the slab is (0.629)d. Calculate (a) the capacitance, (b) the charge on the capacitor plates, (c) the electric field in the gap, and (d) the electric field in the slab, after the slab is in place. WOLFSON - CHAPTER 28 12. A defective starting motor in a car draws 300 A from the car's 12 V battery, dropping the battery terminal voltage to only 6 V. A good starter motor should draw only 100 A. What will the battery terminal voltage be with a good starter?