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March 19, 2009 PHY 2054 Discussion Spring ‘09 Conceptual Review: Chapter 21 A . Magnetic Flux 1. Write down the unit for magnetic flux using V. 2. A cube is in a uniform magnetic field. What is the total flux through the cube? B. Faraday’s Law & Lenz’s Law 1. How do you actually use the minus sign in Faraday’s law? 2. The current in the long straight wire is increasing in the figure 1. What is the direction of the current induced in the loop? C. Motional Emf 1. A steal beam along east-west direction is falling toward Earth’s surface near the equator. Which end of the beam is positive? 2. An N-turn coil with length l and width w has resistance R. What is the magnetic force on the loop when it moves into a uniform magnetic field B? D. Generators & Motors 1. An AC generator with a cross sectional area of 1 m2 rotates at a frequency of 50 Hz in a 1-T magnetic field perpendicular to the axis of rotation. Compare the maximum induced emf with the average induced emf as the angle between the normal and the field changes from 0 to π/2. E. Self-Inductance & RL Circuits 1. Explain why the time constant is inversely proportional to R? 2. Current in an RL circuit increases to 90 % of its final value in 5 ms. What is the time constant? F. Energy Stored in an Inductor 1. A 500-turn solenoid with a radius of 10 cm and length of 50 cm. What is the energy stored in the solenoid when the current in it is 1A? March 19, 2009 PHY 2054 Discussion – Spring ‘09 Practice Exam Problems (Chapter 21) 1. A coil in a magnetic field encloses a flux of 0.256 T·m2 when the angle between the normal to the coil and the direction of the magnetic field is 70.0°. What flux would go through the coil if the angle were changed to 40.0°? (Magnetic Flux) a. 0.332 T·m2 b. 0.198 T·m2 c. 0.114 T·m2 d. 0.573 T·m2 2. A 10-turn square coil of area 0.036 m2 and a 20-turn circular coil are both placed perpendicular to the same changing magnetic field. The voltage induced in each of the coils is the same. of the circular coil? (Faraday’s Law) a. 0.072 m2 b. 0.60 m2 c. 0.018 m2 What is the area d. 0.036 m2 3. An airplane with a wingspan of 60.0 m flies parallel to the Earth’s surface at a point where the downward component of the Earth's magnetic field is 0.400 l04 T. If the induced potential between wingtips is 0.900 V, what is the plane’s speed? (Motional Emf) a. 250 m/s b. 338 m/s c. 375 m/s d. 417 m/s 4. A 500-turn circular coil with an area of 0.050 0 m2 is mounted on a rotating frame that turns at a rate of 20.0 rad/s in the presence of a 0.050 0-T uniform magnetic field that is perpendicular to the axis of rotation. What is the instantaneous emf in the coil at the moment that the normal to its plane is at a 30.0 angle to the field? (Generators) a. zero b. 12.5 V c. 21.6 V d. 25.0 V 5. A motor has an internal resistance of 12 . When running, the motor has a back emf of 30 V and draws a current of 4.0 A. What is the supply voltage in this case? (Motors) a. 30 V b. 48 V c. 78 V d. 120 V 6. What is the self-inductance in a coil that experiences a 3.0-V induced emf when the current is changing at a rate of 110 A/s? (Self-Inductance) a. 83 mH b. 45 mH c. 37 mH d. 27 mH 7. A series circuit contains a 12-V battery, a 2.0- resistor, and a 3.0-mH inductor. If the switch to the battery is closed at t = 0, find the time required for the current in the circuit to reach 63% of its final value. (RC circuit) a. 1.5 ms b. 3.0 ms c. 4.0 ms d. 5.0 ms 8. A 12-V battery is connected in series with a switch, 6.0- resistor and coil. What energy is stored in the coil when the current is 2.0 A? The time constant is 4.0 104 s. (Energy Stored in Inductors) 3 10 J 3 b. 9.6 10 J Answers: 1-d 2-c 3 c. 14 10 J 3-c 4-b 5-c 3 c. 29 10 J 6-d 7-a 8-a a. 4.8