ADDITIONS TO WOLFSON PROBLEMS AND PROBLEMS FROM OTHER TEXTS JULY 21 - JULY 27 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). 33. A single-turn current loop, carrying a current of 4.00 A, is in the shape of a right triangle with sides 50.0, 120, and 130 cm. The loop is in a uniform magnetic field of magnitude 75.0 mT whose direction is parallel to the current in the 130 cm side of the loop. (a) Find the magnitude of the magnetic force on each of the three sides of the loop. (b) Show that the total magnetic force on the loop is zero. (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? 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. WOLFSON - CHAPTER 30 8. (c) In a configuration called a "Helmholtz coil", the two coils in Fig. 30-47 each have N turns, carry a current I in the same direction and are separated by a distance equal to their radius R. Find the magnitude of the net magnetic field on the axis midway between the two coils. E4. This is the exercise accompanying Example 30-3 on page 780. 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. 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.) (P prefixes) HRW Problem Supplement #1 - CHAPTER 31 90. The figure for this problem is Fig. 31-30, except that the magnitude of B is decreasing, rather than increasing. A uniform magnetic field is confined to a cylindrical volume of radius 10 cm. The magnitude of B is decreasing at a constant rate of 10 mT/s. What are the instantaneous accelerations (direction and magnitude) experienced by an electron placed (a) 5 cm below the center of the cylinder; (b) at the center of the cylinder; and (c) 5 cm above the center of the cylinder. 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? 27. At a certain place, Earth's magnetic field has magnitude B = 0.590 gauss and is inclined downward at an angle of 70.0 degrees to the horizontal. A flat horizontal circular coil of wire with a radius of 10.0 cm has 1000 turns and a total resistance of 85.0 Ohms. It is connected to a meter with 140 Ohm resistance. The coil is flipped through a half- revolution about a diameter, so that it is again horizontal. How much charge flows through the meter during the flip? (HINT: Wolfson 31: 63 is similar.) WOLFSON - CHAPTER 32 E5. This is the exercise accompanying Example 32-1 on page 834.