omewok # P7-3 ecngul loop of widh w nd heigh h is siued ne ve long wie cing cuen i s in Fig 7- ssume i o e ecngul pulse s shown in Fig 7- Find he induced cuen i in he ecngul loop whose self-inducnce is Find he eneg dissiped in he esisnce if T >> / ns: In he ecngul loop wih he ssigned diecion fo i: whee di di, d d i h d w h d w i h w d d ln i i d i d d =, i = IU is pplied nd ecomes di i I 3 d / Soluion of 3: i Ie, T 4 T / = T, i Ie, when negive sep funcion IU is pplied If T >> /, hen i fo > T is he evese of i fo < < T; ie, / T i Ie, T i I
neg dissiped in : / W I e d I P7-4 conducing equilel ingul loop is plced ne ve long sigh wie, shown in Fig 6-48, wih d = / cuen i = I flows in he sigh wie eemine he volge egiseed high-impednce ms volmee inseed in he loop eemine he volmee eding when he ingul loop is oed 6 o ou pependicul is hough is cene ns: I, ds, S ds d, d 3 Figue 6-48 wih d = /, d 3 o 3 pependicul is o 6 d 4 3 d o 3 3 P7-6 suggesed scheme fo educing edd-cuen powe loss in nsfome coes wih cicul coss secion is o divide he coes ino lge nume of smll insuled filmen ps s illused in Fig 7-, he secion shown in p is eplced h in p ssuming h = nd h filmen es fill 5% of he oiginl coss-secionl e, find
he vege edd-cuen powe loss in he secion of coe of heigh h in Fig 7-, he ol vege edd-cuen powe loss in he filmen secions in Fig 7- ns: Flu enclosed in he ing in Fig 7-: The induced emf in he ing efeing o he ssigned diecion fo cuen: d d i d d esisnce of diffeenil cicul ing: 3 hd d h d Comining nd 3: i d d d 4 dp i h 3 d d d 5 h 4 d h 4 P dp cos 6 8 d 8 P v h 4 7 6
Fo insuled filmen ps, ech wih e S 5 5 Powe loss in filmens in Fig 7- fom 6: h P 8 4 5 5 cos P 5 P v P v P7- hollow clindicl mgne wih inne dius nd oue dius oes ou is is n ngul fequenc The mgne hs unifom il mgneiion M = M Sliding ush concs e povided he inne nd oue sufces s shown in Fig 7-4 ssuming h = 5 nd = 7 S/m fo he mgne, find nd in he mgne, open-cicui volge, c sho-cicui cuen Fig 7-4 ns: m, m 5 4 M M 5M ; 4 4 m
5 4 u d d M c : h i u u Induced volge: ln i h i d Sho cicui:,, i sc whee h ln P7- Pove h he oen condiion fo poenils s epessed in q 7-6 is consisen wih he equion of coninui ns: qs 7 63 nd 7 65 cn e modified s: nd If oen Guge,, is sisfied, hen he ove equion ecomes he equion of coninui Thus, he oen condiion is consisen wih he equion of coninui P 7-5 Wie he se of fou Mwell s equions, qs 7-53,, c nd d, s eigh scl equions in Ce coodines, in clindicl coodines, c in spheicl coodines ns: in Ce coodines
, in clindicl coodines, c in spheicl coodines,
P7-8 In qs 3-88 nd 3-8 i ws shown h fo field clculions polied dielecic m e eplced n equivlen poliion sufce chge densi ps nd n equivlen poliion volume chge densi p Find he ound condiions inefce of wo diffeen medi fo ns: he noml componen of P, he noml componens of, q 3-8: P P P P p n ps f n fs P P P p n ps in which suscip f mens fee chge Comining nd : n fs ps P7- Fo he ssumed f = in Fig 7-5, skech f /u vesus, f /u vesus o > T ns: Fig 7-5
P7-6 Given h cos5 6 /m in i, find nd Soluion: cos5 6 /m 6 d/s Use phsos e s efeence: j cos5 e j cos5 j 5 5 e j j 5 cos5 e j j 3 quing nd 3: 5 4 Thus, 3 46 d/m j, ; me 46 cos5 6 46 Fom : 5655 cos6 46 /m P7-3 Clculions concening he elecomgneic effec of cuens in good conduco usull neglec he displcemen cuen even micowve fequencies 7 ssuming nd 57 S/m fo coppe, compe he mgniude of he displcemen cuen densi wih h of he conducion cuen densi G Wie he govening diffeenil equion fo mgneic field inensi in souce-fee good conduco Soluion: isplcemen cuen 36 8 75 7 Conducion cuen 57 In souce-fee conduco:, j : 3 u, q 3 ecomes 4 Comining nd 4: j