CHAPTER 5: ELECTROMAGNETIC INDUCTION PSPM II 2005/2006 NO. 5 5. An AC generator consists a coil of 30 turns with cross sectional area 0.05 m 2 and resistance 100 Ω. The coil rotates in a magnetic field 0.50 T at a frequency of 20.0 Hz. Calculate (a) The maximum induced emf. [Ans: ε max = 94. 25 V] (b) The maximum induced current. [Ans: I = 0. 94 A] PSPM II 2005/2006 NO. 12(A) 12. (a) A 400-turn solenoid has a cross-sectional area 1.81 10 3 m 2 and length 20 cm carrying a current of 3.4 A. (i) Calculate the inductance of the solenoid. [Ans: L = 1. 82 10 3 H] Calculate the energy stored in the solenoid. [Ans: U = 1. 05 10 2 J] (iii) Calculate the induced emf in the solenoid if the current drops uniformly to zero in 55 ms. [Ans: ε = 0. 11 V] (iv) Explain why a spark jumps across the contact of a switch when the switch is disconnected. PSPM II 2006/2007 NO. 4 4. A metal rod moves perpendicularly through a 1.5 T uniform magnetic field at a speed of 2 cm s 1. If the length of the rod is 40 cm and its resistance is 3 Ω, calculate (a) the induced emf. [Ans: ε = 0. 012 V] (b) the induced current. [Ans: I = 0. 004 A] PSPM II 2006/2007 NO. 12(B) 12. (b) (i) State Lenz s law. FIGURE 10 PCH 1
The solenoid in FIGURE 10 is moved at constant velocity towards a fixed bar magnet. Using Lenz s law, determine the direction of the induced current through the resistor. Explain your answer. PSPM II 2007/2008 NO. 4 4. A coil has an inductance 45 mh and resistance 0.3 Ω. An emf of 12 V is applied to the coil until equilibrium current is achieved. (a) Calculate the energy stored in the coil. [Ans: U = 36 J] (b) State the change in the stored energy if the number of turns in the coil is increased. [Ans: U increases.] PSPM II 2007/2008 NO. 12(B) 12. (b) A 300-turn solenoid of length 25 cm has a cross-sectional area of 15 cm 2. A current of 8 A flows through the solenoid. Calculate (i) the magnetic field at the axis of the solenoid. [Ans: B = 1. 21 10 2 T] the total flux linkage passing through the solenoid. [Ans: Φ = 5. 43 10 3 Wb] (iii) The self-inductance of the solenoid. [Ans: L = 6. 79 10 4 H] (iv) the energy stored in the solenoid. [Ans: U = 2. 17 10 2 J] PSPM II 2008/2009 NO. 12(A) 12. (a) A coil of inductance L carrying a steady current I has an energy U. (i) Show that U = 1 2 LI2. Where is the energy being stored? PSPM II 2009/2010 NO. 4 4. A 600 turn solenoid is 0.01 m long. When the current is increased from 0 to 3 A in 0.4 s, the induced emf is 0.015 V. Calculate the solenoid (a) inductance. [Ans: L = 0. 002 H] (b) cross-sectional area. [Ans: A = 4. 42 10 5 m 2 ] PSPM II 2010/2011 NO. 4 4. (a) State Lenz s law. PCH 2
(b) FIGURE 2 FIGURE 2 shows two coils wrapped around a soft iron core. When the current I in coil A is decreasing, determine the direction of the induced current in coil B. Explain your answer. PSPM II 2010/2011 NO. 12(C) 12. (c) A 3.0 cm diameter wire coil with 25 turns and resistance 0.015 Ω is placed coaxially inside a solenoid. The solenoid with diameter 6 cm, length 26 cm and 1000 turns carries a transient current 14 A s 1. (i) Calculate the maximum flux passing through the coil. [Ans: Φ coilmax = 4. 80 10 5 Weber] Calculate the current induced in the coil. [Ans: I induced = 0. 08 A] (iii) What is the effect on the induced current if the coil is slightly stretched? Explain your answer. [7 marks] PSPM II 2011/2012 NO. 4 4. (a) (i) Define magnetic flux. State Faraday s law of magnetic induction. [2 marks] (b) The plane of a coil of radius 0.20 m is parallel to the yz-plane in a uniform magnetic field. The magnetic field is 0.40 T and in the positive x-direction. (i) Calculate the magnetic flux through the coil. [Ans: Φ B = 0. 050 Wb] The coil is then rotated clockwise about the y-axis, such that the normal of the coil is now 30 with respect to the x-axis. Calculate the average induced emf in the coil if the time taken for the rotation is 0.50 s. [Ans: ε = 0. 012 V] (c) A current of 5.0 A flows in a 400 turn solenoid that has a length of 30.0 cm and crosssectional area of 2.00 10 4 m 2. Calculate (i) the inductance of the solenoid. [Ans: L = 1. 34 10 4 H] the energy stored in the solenoid. [Ans: U = 1. 68 10 3 J] (iii) the induced emf in the solenoid. [Ans: ε = 0 V] (iv) the induced emf in the solenoid if the current in the solenoid decreases uniformly to zero in 0.20 s. [Ans: ε = 3. 35 10 3 V] PCH 3
PSPM II 2012/2013 NO. 4 4. (a) A circular coil of N turns and radius r is rotated at constant frequency f in a uniform magnetic field B. The magnetic flux linkage of the coil is given by = Nπr 2 B cos(2πft) (i) Deduce the expression for emf induced in the coil. [Ans: ε = Nπr 2 B(2πf) sin(2πft)] If N = 100 turns, r = 5 cm, B = 1.0 T and f = 50 Hz, calculate the maximum emf generated. [Ans: ε max = 246. 74 V] (iii) A rotating coil generates a maximum emf of 500 V. Calculate the number of turns if the radius is 5 cm and rotates at the same frequency. [Ans: N = 203 turns] [7 marks] (b) A solenoid of length l = 10 cm, radius r = 2 cm has 1000 turns. (i) The current of the solenoid is lowered from 5 A to 0 A within 0.3 s. Calculate the magnitude of emf induced in the solenoid. [Ans: ε = 0. 262 V] A second coil with 50 turns is wound coaxially with the solenoid. Calculate the mutual inductance between the two. [Ans: M = 7. 90 10 4 H] ε (iii) What is the induced voltage ratio of the coil to the solenoid? [Ans: coil = 0. 05] ε solenoid PSPM II 2013/2014 NO. 4 4. (a) FIGURE 5 FIGURE 5 shows a bar moving on rails to the right with a velocity v in a uniform magnetic field directed out of the page. A resistor R connects the rails. (i) What is the direction of induced current in resistor R? Explain your answer. State TWO ways to increase the induced current with R fixed. (b) A rectangular coil of 60 turns, dimensions 0.1 m 0.1 m and total resistance 10 Ω, rotates with angular speed 30 rad s 1 about the y-axis in a 1.5 T magnetic field directed along the xaxis. Calculate the (i) maximum induced emf in the coil. [Ans: ε = 27 V] maximum rate of change of magnetic flux through the coil. [Ans: ( dφ B ) = dt max 0. 45 Wb s 1 ] [6 marks] (c) Two coaxial solenoids, P and Q have 400 and 700 turns respectively. A current of 3.5 A in coil P produces an average flux of 300 μwb through each turn of P and average flux of 90 μwb through each turn of Q. Calculate the PCH 4
(i) inductance of solenoid P. [Ans: L P = 3. 43 10 2 H] mutual inductance. [Ans: M 12 = 1. 8 10 2 H] PSPM II 2014/2015 NO. 4 4. (a) (i) Define magnetic flux. A 0.2 T magnetic field is directed parallel to the plane of a circular loop of radius 0.2 m. Calculate the magnetic flux through the loop. [Ans: φ = 0 Wb] [3 marks] (b) (i) A coil of 100 turns and area 0.5 cm 2 is placed in a changing magnetic field. The rate of change of magnetic field is 1.08 T s 1. Calculate the induced emf in the coil. [Ans: ε = 5. 4 10 3 V] A coil of N turns with an area 6.8 10 2 m 2 is rotating at frequency 90 Hz in a uniform magnetic field 0.28 T. If the maximum induced emf in the coil is 128.5 V, calculate the value of N. [Ans: N = 12] (c) A solenoid of radius 5 cm has 200 turns and length of 15 cm. Calculate the (i) inductance. [Ans: L = 2. 6 mh] rate at which current must change for it to produce an induced emf of 50 mv. [Ans: di dt = 19. 2 A s 1 ] (d) Two coaxial coils are wound around the same cylindrical core. The primary coil has 350 turns and the secondary coil has 200 turns. When the current in the primary coil is 6.5 A, the average flux through each turn of the secondary coil is 0.018 Wb. Calculate the (i) mutual inductance of the pair of coils. [Ans: M = 0. 55 H] average flux through each turn of the primary coil when the current in the secondary coil is 1.5 A. [Ans: φ 1 = 2. 36 10 3 Wb] [3 marks] PCH 5