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Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 AP Physics Electricity and Magnetism #6 Magnetism #2 Name Period 1. A 1.5 m length of wire carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes and angle of 38° to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earths magnetic field of 5.5 x 10-5 T at this point. 2.3 x 10-4 N 2. A long straight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction of B at each of the points, C, D, and E in the plane of the page. C D I E 1 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 3. A jumper cable used to start a stalled vehicle carries a 65 A current. How strong is the magnetic field 6.0 cm away from it? 2.2 x 10-4 T 4. The force on a wire is a maximum of 6.50 x 10-2 N when placed between the pole faces of a magnet. The current flows horizontally to the right an the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on. (a) What type of magnetic pole is the top pole face? (b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. (c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it feel now? South pole, 4.1 A, 6.4 x 10-2 N 5. Two long thin parallel wires 13.0 cm apart carrying 25 A current in the same direction. Determine the magnetic filed at point P, 12 cm from one wire and 5.0 cm from the other (Fig. 20-55, page 579). 1.1 x 10-4 T 2 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 6. A rectangular loop of wire lies in the same plane as a straight wire, as shown in Fig. 20-57, page 579. There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop. 2.6 x 10-6 N, toward wire 7. Two long wires are oriented so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. 20-59, page 579). What is the magnitude of the magnetic field at appoint midway between them if the top on carries a current of 20.0 A and the bottom one carries 5.0 A. 4.12 x 10-5 T 8. The long, straight wire shown in Figure 1 below is in the plane of the page and carries a current I. Point P is also in the plane of the page and is a perpendicular distance d from the wire. Gravitational effects are negligible. a. With reference to the coordinate system in Figure 1, what is the direction of the magnetic field at point P due to the current in the wire? 3 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 Problem 8 continued A particle of mass m and positive charge a is initially moving parallel to the wire with a speed do when it is at point P. as shown in Figure 2 below. b. With reference to the coordinate system in Figure 2, what is the direction of the magnetic force acting on the particle at point P? c. Determine the magnitude of the magnetic force acting on the particle at point P in terms of the given quantities and fundamental constants. d. An electric field is applied that causes the net force on the particle to be zero at point P. i. With reference to the coordinate system in Figure 2, what is the direction of the electric field at point P that could accomplish this? ii. Determine the magnitude of the electric field in terms of the given quantities and fundamental constants. 4 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 9. A rigid rod of mass m and length l is suspended from two identical springs of negligible mass as shown in the diagram above. The upper ends of the springs are fixed in place and the springs stretch a distance d under the weight of the suspended rod. a. Determine the spring constant k of each spring in terms of the other given quantities and fundamental constants. As shown above, the upper end of the springs are connected by a circuit branch containing a battery of emf ε and a switch S so that a complete circuit is formed with the metal rod and springs. The circuit has a total resistance R, represented by the resistor in the diagram. The rod is in a uniform magnetic field directed perpendicular to the page. The upper ends of the springs remain fixed in place and the switch S is closed. When the system comes to equilibrium, the rod is lowered an additional distance ∆d. b. What is the direction of the magnetic field relative to the coordinate axes shown on the right in the previous diagram? 5 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 Problem 9 continued c. Determine the magnitude of the magnetic field in terms of m, Q, d, ∆d, ε, R, and fundamental constants. d. When the switch is suddenly opened, the rod oscillates. For these oscillations, determine the following quantities in terms of d, ∆d, and fundamental constants: i. The period ii. The maximum speed of the rod 6 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 10. The magnitude of the magnetic field in teslas at a distance d from a long straight wire carrying a current I is given by the relation B = 2 X 10-7 I/d. The two long straight wires shown above are perpendicular, insulated from each other, and small enough so that they may be considered to be in the same plane. The wires are not free to move. Point P, in the same plane as the wires, is 0.5 meter from the wire carrying a current of 1 ampere and is 1.0 meter from the wire carrying a current of 3 amperes. a. What is the direction of the net magnetic field at P due to the currents? b. Determine the magnitude of the net magnetic field at P due to the currents. 7 Dr. Campbell 15 HW Electricity and Magnetism #6.docx 26 January 2016 Problem 10 continued A charged particle at point P that is instantaneously moving with a velocity of 106 meters per second toward the top of the page experiences a force of 10-7 newtons to the left due to the two currents. c. State whether the charge on the particle is positive or negative. d. Determine the magnitude of the charge on the particle. e. Determine the magnitude and direction of an electric field also at point P that would make the net force on this moving charge equal to zero. 8