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Chapter 30: Induction and Inductance

Fundamentals Of Physics
Pages: 866 - 902

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110 Questions for Chapter 30: Induction and Inductance

  1. Figure 30-78 shows a wire that has been bent into a circular arc of radius r = 24cm, centred at O. A straight wire OP can be rotated about O and makes sliding contact with the arc at P. Another straight wire OQ completes the conducting loop. The three wires have cross-sectional area 1.20mm2 and resistivity p=1.70×10-8Ω.m, and the apparatus lies in a uniform magnetic field of magnitude B = 0.150Tdirected out of the figure. Wire OP begins from rest at angle θ=0 and has constant angular acceleration of 12rad/sec. As functions of u (in rad), find (a) the loop’s resistance and (b) the magnetic flux through the loop. (c) For what θis the induced current maximum and (d)what is the maximum?

    Found on Page 902
  2. A toroid has a 5.00 cmsquare cross section, an inside radius of 0.15m, 500turns of wire, and a current of 0.800A. What is the magnetic flux through the cross section?

    Found on Page 902
  3. Figure 30-39 shows a closed loop of wire that consists of a pair of equal semicircles, of radius3.7 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic fieldB→of magnitude 76 mTis directed perpendicular to the fold diameter and makes equal angles (of45°) with the planes of the semicircles. The magnetic field is reduced to zero at a uniform rate during a time interval of4.5 ms. During this interval, what are the (a) magnitude and (b) direction (clockwise or counterclockwise when viewed along the direction of B→) of the emf induced in the loop?

    Found on Page 896
  4. Figure 30-30 gives the variation with time of the potential difference VRacross a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance Rand emf εbut differ in the inductance L . Rank the circuits according to the value of L, greatest first.

    Found on Page 894
  5. A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field, as indicated in Figure. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) Show that the emf induced in the coil is given (as a function of time t) byε=2ττfNabsin(2ττft)=ε0sin(2ττft). This is the principle of the commercial alternating-current generator. (b) What value of Nabgives an emf withε0150Vwhen the loop is rotated at 60.0revs in a uniform magnetic field of 0.500 T?

    Found on Page 896
  6. Figure 30-31 shows three situations in which a wire loop lies partially in a magnetic field.The magnitude of the field is either increasing or decreasing, as indicated. In each situation, a battery is part of the loop. In which situations are the induced emf and the battery emf in the same direction along the loop?

    Found on Page 895
  7. In Figure, a wire loop of lengths L = 40.0 cmand W = 25.0 cmlies in a magnetic field B→.(a)What is the magnitude εif B→=(4.00×10-2Tm)yk^?(b)What is the direction (clockwise or counterclockwise—or “none” if 0) of the emf induced in the loop if B→=(4.00×10-2Tm)yk^?(c)What is theεif B→=(6.00×10-2Ts)tk^(d)what is the direction if B→=(6.00×10-2Ts)tk^(e)What is theεif B→=(8.00×10-2Tm.s)ytk^(f)What is the direction if B→=(6.00×10-2Ts)tk^(g)What is theεif B→=(3.00×10-2Tm.s)xtk^(h)What is the direction if B→=(3.00×10-2Tm.s)xtk^(i)What is the if B→=(5.00×10-2Tm.s)ytk^(j)What is the direction if B→=(5.00×10-2Tm.s)ytk^

    Found on Page 896
  8. Figures 30-32 give four situations in which we pull rectangular wire loops out of identical magnetic fields page) at the same constant speed. The loops have edge lengths of either L or 2L, as drawn. Rank the situations according to (a) the magnitude of the force required of us and (b) the rate at which energy is transferred from us to the thermal energy of the loop greatest first.

    Found on Page 895
  9. One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 1.20×10-3m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is13.0Ω. If an externally applied uniform longitudinal magnetic field in the core changes from 1.60 Tin one direction to1.60 T in the opposite direction, how much charge flows through a point in the circuit during the change?

    Found on Page 896
  10. In Figure (a), a uniform magnetic field increases in magnitude with time t as given by Figure (b), where the vertical axis scale is set by Bs=9.0mTand the horizontal scale is set by ts=3.0sA circular conducting loop of area 8.0×10-4m2lies in the field, in the plane of the page. The amount of charge q passing point A on the loop is given in Figure (c) as a function of t, with the vertical axis scale set by qs=3.0s and the horizontal axis scale again set by localid="1661854094654" ts=3.0s. What is the loop’s resistance?

    Found on Page 896

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