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**Unformatted text preview: **Fundamentals of Physics Halliday & Resnic 98 2 0401 0409 . CH30Inductance 1, 5, 7, 11, 13, 15, 21, 29, 31, 34, 37, 39, 45, 47, 51, 57, 63, 65, 73, 75 Problem 30-1 In Fig. 30-37, the magnetic flux through the loop increases according to the relation 2 6 7 B t t Φ = + , where B Φ is in milliwebers and t is in seconds. (a) What is the magnitude of the emf induced in the loop when 2 t s = ? (b) Is the direction of the current through R to the right or left? 30-37 <>(a) The magnitude of the emf is ε = = + = + = + = d dt d dt t t t B Φ 6 0 7 0 12 7 0 12 2 0 7 0 31 2 . . . . . c h bg mV. (b) Appealing to Lenzs law (especially Fig. 30-5(a)) we see that the current flow in the loop is clockwise. Thus, the current is to left through R . Problem 30-5 In Fig. 30-39, a 120-turn coil of radius 1.8 cm and resistance 5.3 is coaxial with a solenoid of 220 turns/cm and diameter 3.2 cm. The solenoid current drops from 1.5 A to zero in time interval 25 t ms = . What current is induced in the coil during t ? 30-39 <>The total induced emf is given by 1 13 Fundamentals of Physics Halliday & Resnic 98 2 ( 29 2 2 ( ) ( ) 1.5 A (120)(4 T m A)(22000/m) 0.016m 0.025 s 0.16V. B d dB d di di N NA NA ni N nA N n r dt dt dt dt dt ε μ μ μ π Φ = - = - = - = - = - ÷ = - × × ÷ =-7 π 10 π Ohms law then yields | |/ 0.016 V /5.3 0.030 A i R ε = = = . Problem 30-7 In Fig. 30-40, a wire forms a closed circular loop, with radius 2 R m = and resistance 4 . The circle is centered on a long straight wire; at time t = , the current in the long straight wire is 5.0 A rightward. Thereafter, the current changes according to 2 2 5 (2 / ) i A A s t =- . (The straight wire is insulated; so there is no electrical contact between it and the wire of the loop.) What is the magnitude of the current induced in the loop at times t ? 30-40 <>The field (due to the current in the straight wire) is out-of-the-page in the upper half of the circle and is into the page in the lower half of the circle, producing zero net flux, at any time. There is no induced current in the circle. Problem 30-11 A square wire loop with 2.00 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in Fig. 30-44.The loop contains an ideal battery with emf 20 V ε = . If the magnitude of the field varies with time according to 0.042 0.87 B t =- , with B in teslas and t in seconds, what are (a) the net emf in the circuit and (b) the direction of the (net) current around the loop?...

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