Tutorial 9 – Electromagnetic Induction 29–1 and 29–2 Faraday’s Law of Induction 1. (I) The magnetic flux through a coil of wire containing two loops changes at a constant rate from 2 58 Wb to 1 38 Wb in 0.42 s. What is the emf induced in the coil? 2. (I) The north pole of the magnet in Fig. 29–36 is being inserted into the coil. In which direction is the induced current flowing through the resistor R? 3. (I) The rectangular loop shown in Fig. 29–37 is pushed into the magnetic field which points inward. In what direction is the induced current? 5. (II) A circular wire loop of radius r 12 cm is immersed in a uniform magnetic field B 0.500 T with its plane normal to the direction of the field. If the field magnitude then decreases at a constant rate of 2 0.010 T/s, at what rate should r increase so that the induced emf within the loop is zero? 12. (II) Part of a single rectangular loop of wire with dimensions shown in Fig. 29–40 is situated inside a region of uniform magnetic field of 0.650 T. The total resistance of the loop is 0.280 V . Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.40 m/s. Neglect gravity. 29–3 Motional EMF 27. (I) The moving rod in Fig. 29–12b is 13.2 cm long and generates an emf of 120 mV while moving in a 0.90-T magnetic field. What is its speed? 28. (I) The moving rod in Fig. 29–12b is 12.0 cm long and is pulled at a speed of 15.0 cm/s. If the magnetic field is 0.800 T, calculate the emf developed. 29. (II) In Fig. 29–12a, the rod moves to the right with a speed of 1.3 m/s and has a resistance of 2.5 V . The rail separation is , 25.0 cm. The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is 25.0 V at a given instant. Calculate (a) the induced emf, (b) the current in the U-shaped conductor, and (c) the external force needed to keep the rod’s velocity constant at that instant. 29–6 Transformers [Assume 100% efficiency, unless stated otherwise.] 46. (I) A transformer has 620 turns in the primary coil and 85 in the secondary coil. What kind of transformer is this, and by what factor does it change the voltage? By what factor does it change the current? 48. (II) A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 7.5 A to the train. (a) What voltage is present across the tracks? (b) Is the transformer step-up or step-down? 49. (II) The output voltage of a 75-W transformer is 12 V, and the input current is 22 A. (a) Is this a step-up or a step-down transformer? (b) By what factor is the voltage multiplied? CHAPTER 30 Inductance 30–1 Mutual Inductance 1. (II) A 2.44-m-long coil containing 225 loops is wound on an iron core (average m 1850m0 ) along with a second coil of 115 loops. The loops of each coil have a radius of 2.00 cm. If the current in the first coil drops uniformly from 12.0 A to zero in 98.0 ms, determine: (a) the mutual inductance M; (b) the emf induced in the second coil. 3. (II) A small thin coil with N 2 loops, each of area A2 , is placed inside a long solenoid, near its center. The solenoid has N1 loops in its length , and has area A1 . Determine the mutual inductance as a function of u, the angle between the plane of the small coil and the axis of the solenoid. 30–2 Self-Inductance 5. (I) If the current in a 280-mH coil changes steadily from 25.0 A to 10.0 A in 360 ms, what is the magnitude of the induced emf? 7. (I) What is the inductance of a coil if the coil produces an emf of 2.50 V when the current in it changes from 2 28.0 mA to 1 25.0 mA in 12.0 ms? 9. (II) A coil has 3.25-V resistance and 440-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.60 A/s, what is the potential difference across the coil at this moment? 30–3 Magnetic Energy Storage 15. (I) The magnetic field inside an air-filled solenoid 38.0 cm long and 2.10 cm in diameter is 0.600 T. Approximately how much energy is stored in this field? 17. (II) What is the energy density at the center of a circular loop of wire carrying a 23.0-A current if the radius of the loop is 28.0 cm? 18. (II) Calculate the magnetic and electric energy densities at the surface of a 3.0-mm-diameter copper wire carrying a 15-A current.