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Chapter 31. Electromagnetic Induction

Induced Electromotive Force
31-1. A coil of wire 8 cm in diameter has 50 turns and is placed in a B field of 1.8 T. If the B field in reduced to 0.6 T in 0.002 s, what is the induced emf?
[pic] ΔB = 1.8 T – 0.6 T = 1.20 T
[pic]; E = -151 V

31-2. A square coil of wire having 100 turns of area 0.044 m2 is placed with its plane perpendicularto a constant B field of 4 mT. The coil is flipped to a position parallel with the field in a time of 0.3 s. What is the induced emf?
[pic]; E = -58.7 mV

31-3 A coil of 300 turns moving perpendicular to the flux in a uniform magnetic field experiences a flux linkage of 0.23 mWb in 0.002 s. What is the induced emf?
[pic]; E = –34.5 V.

31-4. The magnetic flux linking a loop ofwire changes from 5 mWb to 2 mWb in 0.1 s. What is the average induced emf?
[pic]; E = –30.0 mV

31-5. A coil of 120 turns is 90 mm in diameter and has its plane perpendicular to a 60-mT magnetic field produced by a nearby electromagnet. The current in the electromagnet is cut off, and as the filed collapses, an emf of 6 V is induced in the coil. How long does it take for the fieldto disappear? [ A = (R2 = ((0.045 m)2 = 6.36 x 10-3 m2 ]
[pic]
Δt = 7.63 ms.

31-6. A coil of 56 turns has an area of 0.3 m2. Its plane is perpendicular to a 7-mT magnetic field. If this field collapses to zero in 6 ms, what is the induced emf?
[pic]; E = -19.6 V

31-7. A wire 0.15 m long moves at a constant velocity of 4 m/s in a direction that is 360 with respect to a 0.4-Tmagnetic field. The axis of the wire is perpendicular to the magnetic flux lines. What is the induced emf?
[pic]; E = 141 mV

31-8. A 0.2-m wire moves at an angle of 280 with an 8-mT magnetic field. The wire length is perpendicular to the flux. What velocity v is required to induce an emf of 60 mV?
[pic]
[pic]
v = 79.9 m/s

Generators
31-9. The magnetic field in the air gap betweenthe magnetic poles and the armature of an electric generator has a flux density of 0.7 T. The length of the wires on the armature is 0.5 m. How fast must these wires move to generate a maximum emf of 1.00 V in each armature wire?
[pic]; v = 2.86 m/s

31-10. A single loop of wire has a diameter of 60 mm and makes 200 rpm in a constant 4-mT magnetic field. What is the maximum emfgenerated?
[pic] f = 200 rpm = 3.33 rev/s
[pic]; E = 237 (V

31-11. The armature of a simple generator has 300 loops of diameter 20 cm in a constant 6-mT magnetic field. What must be the frequency of rotation in revolutions per second in order to induce a maximum emf of 7.00 V? [ A = (R2 = ((0.10 m)2 = 0.314 m2 ]
[pic] f = 19.7 rev/s

31-12. An armature in an ac generator consists of500 turns, each of area 60 cm2. The armature is rotated at a frequency of 3600 rpm in a uniform 2-mT magnetic field. What is the frequency of the alternating emf? What is the maximum emf generated?
[pic] f = 60.0 Hz
[pic]; Emax = 2.26 V
31-13. In Problem 37-12, what is the instantaneous emf at the time when the plane of the coil makes an angle of 600 with the magnetic flux? [ Note( = 900 – 600 = 300 ]
[pic] Einst = 1.13 V

31-14. The armature of a simple ac generator has 100 turns of wire, each having a radius of 5.00 cm. The armature turns in a constant 0.06-T magnetic field. What must be the rotational frequency in rpm to generate a maximum voltage of 2.00 V?
[pic]
[pic] f = 6.75 rev/s
[pic] f = 405 rpm
31-15. A circular coil has 70 turns, each 50mm in diameter. Assume that the coil rotates about an axis that is perpendicular to a magnetic filed of 0.8 T. How many revolutions per second must the coil make to generate a maximum emf of 110 V?
[pic]
[pic] f = 159 rev/s

*31-16. The armature of an ac generator has 800 turns, each of area 0.25 m2. The coil rotates at a constant 600 rpm in a 3-mT field. What is the maximum induced emf?...
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