HSSC-II (12th Class) Physics Unit-14: Electromagnetic Inductions: Numerical Problems List (New Book/KPK Text Board, Peshawar) With Verified Answers

1: A wheel with 12 metal spokes each 0.6 m long is rotated with a speed of 180 r.p.m in a plane normal to earth's magnetic field at a place. If the magnitude of the field is 0.6 G, what is the magnitude of induced e.m.f. between the axle and rim of the wheel? (Answer: 2.035 ｘ 10⁻⁴ V) 

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2: A circuit has 1000 turns enclosing a magnetic circuit 20 cm² in section with 4 A current, the flux density is 1 Wb m⁻² and with 9A current, it is 1.4 Wb m⁻². Find the mean value of the inductance between these current limits and the induced e.m.f. if the current falls from 9A to 4A in 0.05s. (Answer: 0.16H, 16V)

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3: A coil of resistance 1000 is placed in a magnetic field of 1 m Wb. The coil has 100 turns and a galvanometer of 400Ω resistance is connected in series with it: find the average e.m.f. and the current if the coil is moved in 1/10th s from the given field to a field of 0.2 m Wb. (Answer: 1.6 mA ). 

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4: A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s⁻¹, at right angles to the horizontal component of the earth's magnetic field, 0.30 ｘ10⁻⁴ Wb m⁻² 

(a) what is the instantaneous value of the e.m.f. induced in the wire? 

(b)What is the direction of the e.m.f.? 

(c)Which end of the wire is at the higher electrical potential? 

(Answer: 1.5 ｘ10⁻³ V)

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5: Current in a circuit falls from 5.0 A to 0.1 A in 0.1 s. If an average e.m.f. of 200 V induced, give an estimate of the self-inductance of the circuit. (Answer: 4 H) 

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6: A long solenoid with 15 turns per cm has a small loop of area 2.0 cm? placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced e.m.f. in the loop while the current is changing? (Answer: 7.54 ｘ10⁻⁶ V). 

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7: A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the e.m.f. developed across the cut if the velocity of the loop is 1 cm s⁻¹ in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case? (Answer: 2.4 ｘ10⁻⁴ V, 2 s, & 0.6 ｘ 10⁻⁴ V, 8 s)  

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8: A 90-mm length of wire moves with an upward velocity of 35 m s⁻¹ between the poles of a magnet. The magnetic field is 80 mT directed to the right. If the resistance in the wire is 5.00 mΩ, what are the magnitude and direction of the induced current? (Answer: 50.4 A) 

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9: A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil? (Answer: 30 Wb)

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