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CH15_Problems

# CH15_Problems - Problems 751 S ummary 1 T he r ight-hand r...

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Summary 1. The right-hand rule can be used to determine th e dir e ction of th e magn e tic fi e ld produc ed by a curr e nt. This is illustrat ed in Figure 15.2 on page 719. 2. Force is exerted on a charge moving through a magnetic field according to the equation f = qu x B Similarly , force s appear on a current-carr y ing wir e imm er se d in a magnetic fi eld. The forc e on an incremental length of wire is given by df = idl X B 3. According to Farada y' s law of induction, volt- age is induc ed in a coil wh en it s magnetic flux linkag es change with time. Similarly , voltag es ar e induced in conductors that cut through magnetic flux lines. We can determine the polarity of the induced voltage by us ing Lenz's law. 4. Magnetic flux den s ity B and the magnetic field intensity Hare related by B = p,H where p, is the magnetic permeability of the material. For air or vacuum , p, = JLO = 4rr x 10- 7 . 5. According to Ampere 's law , the line integral of H around a closed path is equal to the algebraic s um of th e curr e nts flowing through the ar ea bound ed Problems Section 15.1: Magnetic Fields P15.1. What is the fundamental cause of magnetic fields? P15.2. Stat e th e right-hand rule as it appli es to a. a curr e nt-carrying conductor ; b. a current- carrying coil. P15.3. State Ampere's law, includin g the reference direction s for the currents. Problems 751 by the path. We can use thi s law to find the field around a long straight wire or in s ide a toroidal coil. 6. Practical magnetic device s can be approximately analyzed by us ing circuit concepts. Magneto- motive forces are analogous to voltage sources , reluctance is analogous to resi s tance, and flux is analogous to current. 7. The inductance and mutual inductance of coils can be comput ed from knowl e dge of the phy si- cal parameter s of the coils and the core on which they are wound. 8. The B-H relationship for iron take s the form of a hy s tere sis loop , which displays saturation in the neighborhood of 1 to 2 T. The area of the loop rep- resents energ y converted to heat per cycle. Eddy curr e nts ar e another caus e of cor e loss. Energy can be s tored in magnetic fi e ld s. In a magn e tic circuit consisting of an iron core with an air gap , most of the energy is stored in the gap. 9. In an ideal transformer , the volta ge acros s each coil is proportional to it s number of turns , the net mmf is z ero, and the power efficiency is 100 percent. 10. Equival e nt circuits for real tran s form ers ar e s hown in Figures 15.28 and 15.29 on pages 747 and 748 , respectively. 11. Efficiency and regulation are important as pects of tran s former operation. P15.4. State Faraday's law of magnetic induction and Len z's law. *P15.5. The magnetic field of the earth is approxi- mat ely 3 x 10- 5 T. At what distanc e from a long s traight wire carrying a s teady current of 10 A is the field equal to 10 percent of the earth 's field? Suggest at least two way s to help reduce the effect of electrical circuit s on the navigation compass in a boat or airplane.

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CH15_Problems - Problems 751 S ummary 1 T he r ight-hand r...

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